Senter for bærekraftig, risikoavers og etisk KI (SURE-AI)

• Barreira, João Carlos; Sonego, Maicon & Zuazua, Enrique (2026). Boundary and interior control in a diffusive Lotka-Volterra model. Journal of Differential Equations. 466. doi: 10.1016/j.jde.2026.114257. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the controllability of a generalized diffusive Lotka-Volterra competition model for two species, incorporating boundary controls and an interior multiplicative control. Considering a smooth, bounded N-dimensional domain, we analyze ecologically pertinent scenarios characterized by constraints on both the controls and system states. Our results demonstrate how integrated control strategies can effectively overcome the limitations identified in previous studies. We prove two main results: (1) asymptotic controllability to single-species survival steady states under arbitrary system parameters, ensured by a combination of boundary and interior controls which act jointly to stabilize the system; and (2) finite-time controllability to a specific heterogeneous coexistence steady state via a two-phase strategy - first steering the system near the target with boundary control, then activating an interior multiplicative control in a localized region. The strong synergy between the two control mechanisms is crucial in both cases. We also analyze extinction dynamics and homogeneous coexistence, and support our findings with numerical simulations. The work concludes with perspectives for future research.

• Amblard, Benjamin; Bouch, Sara El; Mura, Mauro Dalla; Ferrari, Andre & Richard, Cèdric (2026). Contrastive learning for open-set anomaly detection of radio transients. I IEEE (Red.), 34th European Signal Processing Conference (EUSIPCO). IEEE (Institute of Electrical and Electronics Engineers). s. 1786–1790. Fulltekst i vitenarkiv Vis sammendrag

  Radio transient detection is a key challenge in modern radio astronomy, where rare events must be identified amid noise and radio-frequency interference. This setting naturally calls for open-set anomaly detection, in which the detector must recognize both known and unseen anomalies while maintaining a low false-positive rate. In this work, we introduce a dualhead architecture that combines a variational autoencoder with a novel contrastive head, both sharing the same feature encoder. Our open-set push-pull loss encourages normal samples to form a compact cluster in representation space, while using labeled anomalies solely as repulsive examples, making it well suited for class-imbalance and open-set conditions. Furthermore, we optimize the shared feature encoder using the Correlation-Reduced MGDA-UB algorithm to dynamically balance reconstruction and contrastive gradients. Experiments on Green Bank Telescope spectrograms show that OPP remains robust under increasing class imbalance and openness, and achieves the best ROC-AUC among the considered baselines

• Wang, Chentong; Gao, Jincheng; Zhu, Fei; Halimi, Abderrahim & Richard, Cedric (2026). DTU-Net: A Multi-Scale Dilated Transformer Network for Nonlinear Hyperspectral Unmixing. IEEE Transactions on Geoscience and Remote Sensing. 64. doi: 10.1109/tgrs.2026.3658361. Fulltekst i vitenarkiv Vis sammendrag

  Transformers have shown significant success in hyperspectral unmixing (HU). However, challenges remain. Transformer-based unmixing networks, built on vision transformer (ViT) or Swin transformer, struggle to effectively capture essential multiscale and long-range spatial correlations. In addition, these networks predominantly rely on the linear mixing model (LLM), lacking the flexibility to accommodate scenarios with significant nonlinear effects. To address these limitations, we propose a multiscale dilated transformer-based unmixing network for nonlinear HU (DTU-Net). Its encoder integrates two branches: a spatial branch mainly employing multiscale dilated attention (MSDA) to uniquely capture intricate multiscale and long-range spatial correlations via adaptive receptive fields, and a spectral branch utilizing 3-D-convolutional neural networks (CNNs) with channel attention. This design enables comprehensive extraction as well as integration of multilevel spatial and spectral features. The decoder is specifically designed to accommodate both linear and nonlinear mixing. It explicitly models the polynomial post-nonlinear mixing model (PPNMM) by learning nonlinear coefficients as pixel-wise features, which enhances interpretability by directly reflecting the pixel-level nonlinear mixing strength. Experiments on synthetic, ray tracing, and real datasets validate the effectiveness of the proposed DTU-Net, demonstrating its superior performance compared to both PPNMM-derived and advanced unmixing networks. The code is available at: https://github.com/ChentongWang/DTU-Net

• Yang, Ziye; Song, Xiang; Zhao, Min; Chen, Jie; Richard, Cédric & Cohen, Israel (2026). FASS: Discrete Fourier Transform Adapters for Speech Separation With Incremental Learning. IEEE Transactions on Audio, Speech and Language Processing. 34, s. 3116–3131. doi: 10.1109/taslpro.2026.3700032. Fulltekst i vitenarkiv Vis sammendrag

  Speech separation with incremental learning (SSIL), which facilitates the continuous adaptation of speech separation models to new languages, remains a critical yet underexplored area. In this paper, we propose a novel framework, termed discrete Fourier transform Adapters for Speech Separation with incremental learning (FASS), designed to mitigate catastrophic forgetting by training orthogonal Fourier-domain adapters using a parameter expansion-fusion strategy. This approach stems from our analysis of how acquiring new tasks interferes with retaining prior knowledge. Specifically, FASS converts sparse Fourier-domain parameters into dense parameter-domain weights via the inverse discrete Fourier transform (IDFT), which could preserve previous knowledge without necessitating task identifiers or additional storage. Furthermore, an extended variant, FASS-random (FASS-r), enhances scalability by randomly assigning indices to the learnable frequencies while maintaining theoretical performance. Comprehensive theoretical analyses and extensive experimental results substantiate the effectiveness of our approach.

• Cavallo, Andrea; Gao, Zhan & Isufi, Elvin (2026). Sparse Covariance Neural Networks. IEEE Transactions on Signal Processing. 74, s. 3077–3091. doi: 10.1109/tsp.2026.3714283. Fulltekst i vitenarkiv Vis sammendrag

  Covariance Neural Networks (VNNs) perform graph convolutions on the covariance matrix of input data to leverage correlation information as pairwise connections. They have achieved success in a multitude of applications such as neuroscience, financial forecasting, and sensor networks. However, the empirical covariance matrix on which VNNs operate typically contains spurious correlations, creating a mismatch with the actual covariance matrix that degrades VNNs’ performance and computational efficiency. To tackle this issue, we put forth Sparse coVariance Neural Networks (S-VNNs), a framework that applies sparsification techniques on the sample covariance matrix and incorporates the latter into the VNN architecture. We investigate the S-VNN when the underlying data covariance matrix is both sparse and dense. When the true covariance matrix is sparse, we propose hard and soft thresholding to improve the covariance estimation and reduce the computational cost. Instead, when the true covariance is dense, we propose a stochastic sparsification where data correlations are dropped in probability according to principled strategies. Besides performance and computation improvements, we show that S-VNNs are more stable to finite-sample covariance estimations than nominal VNNs and the analogous sparse principal component analysis. By analyzing the impact of sparsification on their behavior, we tie the S-VNN stability to the data distribution and sparsification approach. We support our theoretical findings with experimental results on a variety of application scenarios, ranging from brain data to human action recognition, and show an improved task performance, improved stability, and reduced computational time compared to alternatives.

• Javeed, Aurya S.; Kouri, Drew P. & Surowiec, Thomas (2026). Inference as risk identification. Computational Management Science. 23(2). doi: 10.1007/s10287-026-00572-7. Fulltekst i vitenarkiv Vis sammendrag

  Abstract The Bayes posterior solves the variational problem of maximizing the expected likelihood of the data minus the Kullback–Leibler divergence from the prior distribution. We generalize Bayesian inference from this variational point of view. In particular, we introduce a variational inference (VI) problem whose solutions we call posteriors and show that these posteriors are risk identifiers, i.e., subgradients of risk measures. This insight leads to: ( i ) rigorous results concerning the existence and asymptotics of posteriors, ( ii ) the ability to constrain the divergence from the prior—which motivates a measure-valued relaxation of M-estimation that we call coherent inference —and ( iii ) insights into VI problems derived from $$\phi$$ -divergences. These insights include semi-analytical expressions for posteriors and connections with utility theory. We use the semi-analytical expressions for $$\phi$$ -divergence posteriors to numerically solve a multi-armed bandit problem.

• Imkeller, Peter; Pamen, Olivier Menoukeu & Proske, Frank Norbert (2026). TAKAGI TYPE FUNCTIONS AND DYNAMICAL SYSTEMS: THE SMOOTHNESS OF THE SBR MEASURE AND THE EXISTENCE AND SMOOTHNESS OF LOCAL TIME. arXiv.org. doi: https:/arxiv.org/pdf/2107.07185v4. Fulltekst i vitenarkiv Vis sammendrag

  We investigate the occupation measures and local times of Takagi-type functions with roughness parameter γ, which are Hölder continuous with exponent H = log γ / log(1/2). Analytical insight is obtained by embedding these functions into a dynamical system related to the baker transform, whose global attractor is the graph of the Takagi function. The associated stable manifolds support Sinai-Bowen-Ruelle (SBR) measures, which we identify with the laws of certain symmetric Bernoulli convolutions. Dually, where duality is induced by time reversal, we derive a representation of the Takagi-type curves centred around the stable fibres in terms of Bernoulli convolutions, thereby relating SBR measures to occupation measures. While Bernoulli convolutions belong to the first Rademacher chaos, we show that the occupation measure is naturally represented as a functional in the second Rademacher chaos within the framework of non-Gaussian Malliavin calculus. Using a Fourier-analytic criterion together with variants of Weyl’s equidistribution theorem, we prove that Takagi-type curves admit square-integrable local times for γ = 2^(-1/m), m ≥ 7, and that the same conclusion holds for drifted Takagi curves for almost every γ ∈ (1/2, 1).

• Mirafzali, Ehsan; Proske, Frank Norbert & Marinescu, Razvan (2026). Logarithmic derivatives of variational and singular stochastic partial differential equations. arXiv.org. arXiv:2608.21805 (math). doi: https:/arxiv.org/pdf/2608.21805. Fulltekst i vitenarkiv Vis sammendrag

  For a stochastic partial differential equation posed on a Gelfand triple and satisfying the fully local monotone conditions of Röckner, Shang and Zhang, we compute the logarithmic derivative of the law of the solution at a fixed time along a prescribed direction of the state space. The formula is intrinsic, being expressed through the Hilbert-Schmidt Malliavin derivative Φr=DrX(t) and the covariance γt=∫t0ΦrΦ∗rdr alone, so that neither the inversion of the first variation used in finite dimensions nor uniform Malliavin-Sobolev bounds on the Tikhonov family are called upon. It is obtained from an integration-by-parts identity on an abstract Hilbert space, a Moore-Penrose construction of a covering field on Wiener space, and a trace formula for the Tikhonov limit, specialised to the equation through the representation Φr=Y(t,r)B(r,X(r)) of the Malliavin derivative by the first variation; the stochastic p-Laplacian and the two-dimensional Navier-Stokes equation are treated in detail. Beyond the variational class, a scalar reduction gives an integration-by-parts identity for the law of a pairing ⟨u(t),φ⟩ which passes to the renormalised limit for the singular equations of Bruned, Chandra, Chevyrev and Hairer, and which is represented by a logarithmic derivative under second-order Malliavin smoothness and negative-moment hypotheses.

• Agram, Nacira; Øksendal, Bernt Karsten; Proske, Frank Norbert & Tymochenko, Olena (2026). Optimal Stopping for Systems Driven by the Brownian Sheet. arXiv.org. arXiv:2603.12853 (math). doi: https:/arxiv.org/abs/2603.12853. Fulltekst i vitenarkiv Vis sammendrag

  We investigate optimal stopping problems for systems driven by the Brownian sheet. Our analysis is divided into two parts. In the first part, we derive explicit solutions to two optimal stopping problems for the exponentially discounted Brownian sheet. The first problem consists in determining the optimal two parameter first hitting point τ = (τ1,τ2) that maximizes E e−ρτ1τ2 h B(τ1,τ2), where ρ > 0 is a discount factor and h is a reward function. Restricting attention to first hitting points of levels, we obtain a closed form characterization of the optimal stopping threshold. In particular, for linear rewards h(y) = y, the optimal level is y= (2ρ)−1/2 . The second problem concerns optimal stopping of the integrated discounted Brownian sheet: E τ1 0 τ2 0 e−ρtxB(t,x) dtdx . We show that the optimal first hitting level is strictly positive, and provide an explicit representation of the value function in terms of the exponential integral function. The optimal threshold is characterized as the unique solution of a nonlinear equation derived from a Laplace transform identity for the product τ1τ2.The result is surprising, in view of the (well-known) fact that the solution of the corresponding one-parameter problem is to stop at the first time t when B(t) hits the negative level y=−(2ρ)−1/2 . In the second and main part of the paper, we develop a general potential theoretic framework for two parameter optimal stopping problems associated with stochastic partial differential equations (SPDEs) driven by the Brownian sheet. For a class of Itˆo sheets and time space homogeneous SPDEs, we prove that the value function is the least superharmonic majorant of the reward and that the optimal stopping point is given by the first exit point from the continuation region. This yields a general existence theorem for optimal stopping points in the plane, extending classical one parameter theory to the two parameter Brownian sheet setting.

• Mirafzali, Ehsan; Proske, Frank Norbert; Venturi, Daniele & Marinescu, Razvan (2026). SCORE-BASED DIFFUSION MODELS IN INFINITE DIMENSIONS: A MALLIAVIN CALCULUS PERSPECTIVE. Journal of Machine Learning for Modeling and Computing. 7(2). doi: https:/www.dl.begellhouse.com/download/article/7de76a605645f298/JMLMC0702(2)-63274.pdf. Fulltekst i vitenarkiv Vis sammendrag

  We study score-based diffusion modelling in infinite-dimensional separable Hilbert spaces through Malliavin calculus, extending the analysis of generative models beyond the finite-dimensional set- ting. The forward diffusion process is formulated as a linear stochastic partial differential equa- tion (SPDE) driven by space–time coloured noise with a trace-class covariance operator, ensuring well-posedness in arbitrary spatial dimensions. Building on Malliavin calculus and an infinite- dimensional extension of the Bismut–Elworthy–Li formula, we derive a closed-form expression for the logarithmic derivative of the transition measure along Cameron–Martin directions, which serves as the natural infinite-dimensional analogue of the score function. Our operator-theoretic approach preserves the intrinsic geometry of Hilbert spaces and accommodates general trace-class operators, thereby incorporating spatially correlated noise without assuming semigroup invertibility. We vali- date the derived score formula numerically for several classes of linear SPDEs in both one and two spatial dimensions using spectral methods.

• Compagnoni, Enea Monzio; Islamov, Rustem; Proske, Frank Norbert; Lucchi, Aurelien; Orvieto, Antonio & Gorbunov, Eduard (2026). On the Interaction of Batch Noise, Adaptivity, and Compression, under (L0, L1)-Smoothness: An SDE Approach. Proceedings of Machine Learning Research (PMLR). ICML 2026. doi: https:/openreview.net/attachment?id=Pmsc4yytlf&name=pdf. Fulltekst i vitenarkiv Vis sammendrag

  Distributed stochastic optimization intertwines (i) stochastic gradient noise, (ii) communication compression, and (iii) adaptive/normalized updates. While each factor has been studied in isolation, their joint effect under realistic assumptions remains poorly understood. In this work, we develop a unified theoretical framework for Distributed Compressed SGD (DCSGD) and its sign variant Distributed SignSGD (DSignSGD) under the recently introduced (L0,L1)- smoothness condition. From a conceptual perspective, we show that the first- and second-order modified equations from the literature do not accurately model the discrete-time stepsize/stability restrictions, especially under (L0,L1)-smoothness. From a technical perspective, we propose new first-order SDEs by carefully incorporating curvature-dependent terms into their drift: This helps capture the fine-grained relationship between learning rate restrictions, gradient noise, compression, and the geometry of the loss landscape. Importantly, we do so under general gradient noise assumptions, including heavy-tailed and affine-variance regimes, which extend beyond the classical bounded-variance setting. Our results suggest that normalizing the updates of DCSGD emerges as a natural condition for stability, with the degree of normalization precisely determined by the gradient noise structure, the landscape’s regularity, and the compression rate. In contrast, DSignSGD converges even under heavy-tailed noise with standard learning rate schedules. Together, these findings offer both new theoretical insights and perspectives, and practical guidance.

• Benth, Fred Espen; Ortiz-Latorre, Salvador & Tarquini, Leonardo (2026). Signature McKean-Vlasov stochastic differential equations. arXiv. doi: 10.48550/ARXIV.2606.22964. Fulltekst i vitenarkiv Vis sammendrag

  McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric p-rough path lift of its solution, with $p\in(2,3)$. After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean-Vlasov SDEs. Finally, we consider the associated particle system and propagation of chaos is established.

• Lozano, Pere Diaz & Nunno, Giulia Di (2026). Hölder regularity for backward stochastic Volterra integral equations and applications to numerical schemes. arXiv.org. doi: 10.48550/ARXIV.2607.04012. Fulltekst i vitenarkiv Vis sammendrag

  We prove a Hölder-type regularity estimate for the martingale integrand of a backward stochastic Volterra integral equation (BSVIE). The estimate is formulated in Lp(Ω) after averaging in L2 over the first time variable, and gives an averaged Hölder estimate of order 1/2 in the second time variable. Our approach is based on the approximation of the BSVIE by a system of BSDEs. For this system, we establish a uniform regularity estimate for the martingale component using Malliavin calculus, and then pass to the limit to obtain the result for the BSVIE. We allow for a general Malliavin differentiable free term and generator. In particular, neither is assumed to come from a forward stochastic differential equation or to have a specific functional form. We also propose an explicit Euler scheme for the approximating BSDE system and show that the regularity estimate yields a convergence rate for the resulting discrete approximation of the BSVIE.

• Lozano, Pere Diaz & Kloster, Thomas K. (2026). A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration. arXiv.org. doi: 10.48550/ARXIV.2602.16232. Fulltekst i vitenarkiv Vis sammendrag

  Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

• Liu, Kang; Wang, Ziqi & Zuazua, Enrique (2026). Nonlinear equilibrium transitions in a potential game model for federated learning. Physica D : Non-linear phenomena. 495. doi: 10.1016/j.physd.2026.135288. Fulltekst i vitenarkiv Vis sammendrag

  In federated learning (FL), a central server typically allocates training efforts to clients. However, from a market-oriented perspective, clients may independently choose their training efforts based on rational self-interest. To study this setting, we propose a potential game framework in which each client’s payoff is determined by its individual effort and the rewards provided by the server. The rewards are influenced by the collective efforts of all clients and can be modulated by a reward factor. We first establish the existence of Nash equilibria (NEs) and then investigate their uniqueness in a stationary setting. We show that the NEs depend nonlinearly on the reward factor and exhibit a nonsmooth transition at a critical value, where the stationary potential loses strict curvature, leading to nonunique NEs and a jump between low-effort and high-effort branches. Furthermore, we prove the convergence of the best-response algorithm for computing NEs in our FL game. Finally, we apply the clients’ rational efforts derived from the NEs to FL training with various datasets and models, thereby validating the effectiveness of the identified critical reward factor.

• Bratterud, Alfred; Dankel, Gisle Mikal Nitter; Farajianzadeh, Mohammadamin; Groves, John; Juan, Chengyi & Suetterlein, Joshua [Vis alle 9 forfattere av denne artikkelen] (2026). No Atomics, No Problem. Developing a RAG Pipeline for Shared CXL Memory. IEEE transactions on computers. 75(4), s. 1291–1308. doi: 10.1109/tc.2026.3667821. Fulltekst i vitenarkiv Vis sammendrag

  We share early experiments with software development for shared CXL memory on the H3 Falcon C5022 CXL switch. We describe how the different stages in the development of a commercial RAG pipeline were impacted by the presence of CXL memory. All of Wikipedia is split into 46 million text passages which are embedded into a high-dimensional embedding space and subjected to heavy load in single- and multi-host experiments. We observe significant performance advantages available to DuckDB and Faiss without changing the software; we measure up to 12x latency reduction with real workloads and 40x reduction with synthetic workloads on CXL, compared to the same queries run with demand paging on NVMe. We explain the current challenges of working with two disjoint cache coherency domains and explain how the Fabric-Attached Memory File System (famfs) and famfs producer-consumer queues provide synchronization patterns without atomic operations on current x86 CPUs. We then discuss open challenges remaining for high performance atomics and locking mechanisms in shared memory. Lastly we show how famfs page-level interleaving enables near-linear throughput scaling when a second host serves queries from the same Faiss index on shared fabric-attached memory and how shared memory allocations can be orchestrated by Kubernetes in a full vertical RAG deployment.

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• Moreno, Emilio Ruiz; Konstantinos, Slavakis, & Beferull-Lozano, Baltasar (2026). [2609.16472] Online Gradient Computation for Warping Gaussian Process Transformations. arxiv.org. Fulltekst i vitenarkiv Vis sammendrag

  Warped Gaussian processes (GPs) handle non-Gaussian observations by mapping them into a latent standard GP via a parametric transformation called warping. Existing online variants either optimize the warping parameters periodically rather than sequentially, or sacrifice analytical tractability and computational efficiency for higher model expressivity. In this paper, we avoid these compromises. To achieve this, we first show that the gradient of the instantaneous negative log-likelihood of a warped GP admits an exact recursive computation. Based on this result, we propose a novel online method for warped GPs that jointly updates the latent GP moments and optimizes the warping parameters. Finally, we validate our method on an existing benchmark adapted to an online formulation.

• Lozano, Pere Diaz; Nunno, Giulia Di & Ortiz-Latorre, Salvador (2026). Backward stochastic equations and martingale modelling. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  This thesis is concerned with numerical methods and regularity properties for backward stochastic equations, together with martingale modelling in mathematical finance. The main tools are Wiener chaos expansions and Malliavin calculus. The first part focuses on backward stochastic differential equations (BSDEs). We develop numerical methods that do not require the terminal condition to be given as a function of a forward diffusion, as is often assumed in the literature. Instead, the terminal condition is represented through its Wiener chaos expansion. This leads to two related approaches: an operator-based Euler scheme that approximates the map sending terminal conditions to BSDE solutions, and a chaos-based Euler scheme in which conditional expectations and martingale integrands are computed through finite chaos projections. Convergence results are obtained for both methods. In the second part, we apply the same Wiener chaos point of view to financial modelling. Starting from the no-arbitrage requirement that discounted prices should be martingales under a risk-neutral measure, we construct an over-parameterized square-integrable martingale model by parameterizing its terminal value through a finite Wiener chaos expansion. The resulting model is arbitrage-free by construction, dense in the space of square-integrable martingales, and can be efficiently calibrated to implied volatility surfaces. The final part of the thesis studies backward stochastic Volterra integral equations (BSVIEs). We establish Hölder-type regularity estimates for the martingale integrand, both for the original BSVIE and for a system of approximating BSDEs. These estimates are then used to prove a convergence rate for an explicit Euler-type approximation of the BSVIE.

• Castellacci, Fulvio; Tommaso, Ciarli,; Yuan, Gao,; Marianna, Marino,; Giacomo, Marzi, & Massimo, Riccaboni, [Vis alle 8 forfattere av denne artikkelen] (2026). [2607.24879] Generative Artificial Intelligence in Scientific Research: Individual Benefits, Collective Risks, and a Framework for Responsible Research with AI. arXiv:2511.05625 . Fulltekst i vitenarkiv Vis sammendrag

  Abstract page for arXiv paper 2607.24879: Generative Artificial Intelligence in Scientific Research: Individual Benefits, Collective Risks, and a Framework for Responsible Research with AI

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• Ebrahimi-Fard, Kurusch & Harang, Fabian Andsem (2026). Trondheim. The Geometry of Data – Why Machine Learning Needs Signatures – ECMI. Fulltekst i vitenarkiv Vis sammendrag

  Introduction: Think of scribbling a digit on a digital tablet. You might write the number '3' slowly, with hesitations, or quickly in a single burst. To a computer analyzing the raw chronological data stream, these two actions look completely different. Yet, the geometric shape -- the path created -- remains identical. This simple example highlights a fundamental challenge in modern machine learning. While state-of-the-art systems perform impressively on static data, they often struggle when data becomes irregular, highly structured, or subject to time-warping. The bottleneck is rarely the learning algorithm itself, but rather the representation of the data. To achieve robustness against distortions like re-sampling or rotation, we need features that respect the underlying geometry of the signal.

• Benth, Fred Espen (2026). Managing weather risk across time and space. Fulltekst i vitenarkiv
• Moe, Signe (2026). AI assisted route optimization. Fulltekst i vitenarkiv Vis sammendrag

  Retail faces complicated logistic problems that AI—or, more broadly speaking, quantitative researchers—can solve with innovative solutions. Objective: Minimize total transportation costs.

• Antil, Harbir (2026). Digital Twins, Generative AI, and Beyond: A PDE-Constrained Optimization Perspective. doi: https:/www.siam.org/media/lgrf0meb/jmm26_flyer_v4.pdf. Fulltekst i vitenarkiv Vis sammendrag

  Digital Twins (DTs) are adaptive, real-time virtual replicas of physical systems that integrate physics-based models, sensor data, and intelligent decisionmaking. At their core, DTs can be rigorously framed within PDE–constrained optimization (PDECO). This talk develops a unified PDECO framework for state estimation and control, leveraging adjoint-based methods in both deterministic and stochastic settings. To address the challenges of infinite-dimensional, large-scale optimization, we introduce novel function-space trust-region and augmented Lagrangian algorithms, and explore the role of randomized methods in dynamic PDECO. A central theme is a new connection between PDECO and Generative AI: score-based generative models can be interpreted as backward-in-time PDEs, linking ill-posed inverse problems, stability analysis, and modern machine learning. This perspective bridges physics-informed modeling with data-driven synthesis, opening the door to, for instance, score-based Digital Twins. Applications span a wide range of domains, including structural and biomedical systems—from bridges and dams to aneurysm modeling, optimal insulation, electromagnetic cloaking, light bending, fusion, and neuromorphic computing. Together, these examples highlight a pathway toward predictive, adaptive, and trustworthy Digital Twins and AI technologies.

• Antil, Harbir (2026). Digital Twins, Generative AI, and Beyond: A PDE-Constrained Optimization Perspective. doi: https:/www.lsu.edu/cct/news/scala2026.php. Fulltekst i vitenarkiv Vis sammendrag

  Digital Twins (DTs) are adaptive, real-time virtual replicas of physical systems that integrate physics-based models, sensor data, and intelligent decision-making. At their core, DTs can be rigorously framed within PDE–constrained optimization (PDECO). This talk develops a unified PDECO framework for state estimation and control, leveraging adjoint-based methods in both deterministic and stochastic settings. To address the challenges of infinite-dimensional, large-scale optimization, we introduce novel function-space trust-region and augmented Lagrangian algorithms and explore the role of randomized methods in dynamic PDECO. A central theme is a new connection between PDECO and Generative AI: score-based generative models can be interpreted as backward-in-time PDEs, linking ill-posed inverse problems, stability analysis, and modern machine learning. This perspective bridges physicsinformed modeling with data-driven synthesis, opening the door to, for instance, score based Digital Twins. Applications span a wide range of domains, including structural and biomedical systems—from bridges and dams to aneurysm modeling, optimal insulation, electromagnetic cloaking, light bending, fusion, and neuromorphic computing. Together, these examples highlight a pathway toward predictive, adaptive, and trustworthy Digital Twins and AI technologies.

• Antil, Harbir (2026). Digital Twins and Structural Health Monitoring. doi: https:/cps-vo.org/group/digital-twins-for-federal-highways. Fulltekst i vitenarkiv Vis sammendrag

  Presentation at the USDOT and NSF Digital Twins Workshop

• Antil, Harbir (2026). Digital Twins, Generative AI, and Beyond: A PDE-Constrained Optimization Perspective. doi: https:/cse.umn.edu/math/deep-learning-meets-pde-workshop-talk-titles-and-abstracts-0. Fulltekst i vitenarkiv Vis sammendrag

  Digital Twins (DTs) are adaptive, real-time virtual replicas of physical systems that integrate physics-based models, sensor data, and intelligent decision-making. At their core, DTs can be rigorously framed within PDE–constrained optimization (PDECO). This talk develops a unified PDECO framework for state estimation and control, leveraging adjoint-based methods in both deterministic and stochastic settings. To address the challenges of infinite-dimensional, large-scale optimization, we introduce novel function-space trust-region and augmented Lagrangian algorithms, and explore the role of randomized methods in dynamic PDECO. A central theme is a new connection between PDECO and Generative AI: score-based generative models can be interpreted as backward-in-time PDEs, linking ill-posed inverse problems, stability analysis, and modern machine learning. This perspective bridges physics-informed modeling with data-driven synthesis, opening the door to, for instance, score-based Digital Twins. Applications span a wide range of domains, including structural and biomedical systems—from bridges and dams to aneurysm modeling, optimal insulation, electromagnetic cloaking, light bending, fusion, and neuromorphic computing. Together, these examples highlight a pathway toward predictive, adaptive, and trustworthy Digital Twins and AI technologies.

• Antil, Harbir (2026). Digital Twins and Beyond: A PDE-Constrained Optimization Perspective. doi: https:/mod.fau.eu/mlpdes26/. Fulltekst i vitenarkiv Vis sammendrag

  Digital Twins (DTs) are adaptive, real-time virtual replicas of physical systems that integrate physics-based models, sensor data, and intelligent decision-making. At their core, DTs can be rigorously framed within PDEconstrained optimization (PDECO). This talk develops a unified PDECO framework for state estimation and control, leveraging adjoint-based methods in both deterministic and stochastic settings. To address the challenges of infinite-dimensional, large-scale optimization, we introduce novel function-space trust-region and augmented Lagrangian algorithms, and explore the role of randomized methods in dynamic PDECO. Applications span a wide range of domains, including structural and biomedical systems--from bridges and dams to aneurysm modeling, optimal insulation, electromagnetic cloaking, light bending, fusion, and neuromorphic computing. Together, these examples highlight a pathway toward predictive, adaptive, and trustworthy Digital Twins and AI technologies.

• Antil, Harbir (2026). Risk-Aware Digital Twins for Biomedical and Engineering Systems: A PDE-Constrained Optimization Perspective. doi: https:/compbiomed.net/wp-content/uploads/2026/06/CMBE2026_Programme_22062026.pdf. Fulltekst i vitenarkiv Vis sammendrag

  Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. Their reliability requires more than simulation or machine learning: it requires physics-based models, scalable optimization, uncertainty quantification, and risk-aware decision support. This talk presents a PDE-constrained optimization perspective on trustworthy digital twins, with emphasis on both applications and theoretical foundations. We discuss how digital twins lead to large-scale inverse, control, and design problems constrained by PDEs, and how adjoint methods, inexact trust-region algorithms, and augmented Lagrangian techniques provide scalable tools for model updating and decision-making. A central theme is uncertainty: digital twins must operate with noisy data, incomplete boundary conditions, uncertain parameters, and rare but consequential events. Risk-aware formulations, including CVaR-type objectives and robust perspectives, provide a principled framework for such settings. Applications include patient-specific aneurysm modeling, structural digital twins for bridges, thermal design, sensing, graph-based control, and Maxwell-based systems.

• Antil, Harbir (2026). Risk-Aware Digital Twins for Biomedical and Engineering Systems: A PDE-Constrained Optimization Perspective. doi: https:/www.linkedin.com/posts/harbir-antil-3181014_pdes-optimization-numericalanalysis-ugcPost-7476110055491325952-_q_R/. Fulltekst i vitenarkiv Vis sammendrag

  Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. Their reliability requires more than simulation or machine learning: it requires physics-based models, scalable optimization, uncertainty quantification, and risk-aware decision support. This talk presents a PDE-constrained optimization perspective on trustworthy digital twins, with emphasis on both applications and theoretical foundations. We discuss how digital twins lead to large-scale inverse, control, and design problems constrained by PDEs, and how adjoint methods, inexact trust-region algorithms, and augmented Lagrangian techniques provide scalable tools for model updating and decision-making. A central theme is uncertainty: digital twins must operate with noisy data, incomplete boundary conditions, uncertain parameters, and rare but consequential events. Risk-aware formulations, including CVaR-type objectives and robust perspectives, provide a principled framework for such settings. Applications include patient-specific aneurysm modeling, structural digital twins for bridges, thermal design, sensing, graph-based control, and Maxwell-based systems.

• Antil, Harbir (2026). Risk-Aware Digital Twins for Biomedical and Engineering Systems: A PDE-Constrained Optimization Perspective. doi: https:/uryasev.github.io/conferences/uryasev70/program/. Fulltekst i vitenarkiv Vis sammendrag

  Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. Their reliability requires more than simulation or machine learning: it requires physics-based models, scalable optimization, uncertainty quantification, and risk-aware decision support. This talk presents a PDE-constrained optimization perspective on trustworthy digital twins, with emphasis on both applications and theoretical foundations. We discuss how digital twins lead to large-scale inverse, control, and design problems constrained by PDEs, and how adjoint methods, inexact trust-region algorithms, and augmented Lagrangian techniques provide scalable tools for model updating and decision-making. A central theme is uncertainty: digital twins must operate with noisy data, incomplete boundary conditions, uncertain parameters, and rare but consequential events. Risk-aware formulations, including CVaR-type objectives and robust perspectives, provide a principled framework for such settings. Applications include patient-specific aneurysm modeling, structural digital twins for bridges, thermal design, sensing, graph-based control, and Maxwell-based systems.

• Antil, Harbir (2026). Risk-Aware Digital Twins for Biomedical and Engineering Systems: A PDE-Constrained Optimization Perspective. doi: https:/bioengineering.gmu.edu/research/seminars. Fulltekst i vitenarkiv Vis sammendrag

  Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. Their reliability requires more than simulation or machine learning: it requires physics-based models, scalable optimization, uncertainty quantification, and risk-aware decision support. This talk presents a PDE-constrained optimization perspective on trustworthy digital twins, with emphasis on both applications and theoretical foundations. We discuss how digital twins lead to large-scale inverse, control, and design problems constrained by PDEs, and how adjoint methods, inexact trust-region algorithms, and augmented Lagrangian techniques provide scalable tools for model updating and decision-making. A central theme is uncertainty: digital twins must operate with noisy data, incomplete boundary conditions, uncertain parameters, and rare but consequential events. Risk-aware formulations, including CVaR-type objectives and robust perspectives, provide a principled framework for such settings. Applications include patient-specific aneurysm modeling, structural digital twins for bridges, thermal design, sensing, graph-based control, and Maxwell-based systems.

• Antil, Harbir (2026). Risk-Aware Digital Twins for Biomedical and Engineering Systems: A PDE-Constrained Optimization Perspective. doi: https:/events.wayne.edu/2026/09/23/risk-aware-digital-twins-for-biomedical-and-engineering-systems-107872. Fulltekst i vitenarkiv Vis sammendrag

  Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. Their reliability requires more than simulation or machine learning: it requires physics-based models, scalable optimization, uncertainty quantification, and risk-aware decision support. This talk presents a PDE-constrained optimization perspective on trustworthy digital twins, with emphasis on both applications and theoretical foundations. We discuss how digital twins lead to large-scale inverse, control, and design problems constrained by PDEs, and how adjoint methods, inexact trust-region algorithms, and augmented Lagrangian techniques provide scalable tools for model updating and decision-making. A central theme is uncertainty: digital twins must operate with noisy data, incomplete boundary conditions, uncertain parameters, and rare but consequential events. Risk-aware formulations, including CVaR-type objectives and robust perspectives, provide a principled framework for such settings. Applications include patient-specific aneurysm modeling, structural digital twins for bridges, thermal design, sensing, graph-based control, and Maxwell-based systems.

• Antil, Harbir (2026). Risk-Aware Digital Twins for Biomedical and Engineering System: A PDE-Constrained Optimization Perspective. doi: https:/mathematics.fsu.edu/event/risk-aware-digital-twins-biomedical-and-engineering-system-pde-constrained-optimization. Fulltekst i vitenarkiv Vis sammendrag

  Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. Their reliability requires more than simulation or machine learning: it requires physics-based models, scalable optimization, uncertainty quantification, and risk-aware decision support. This talk presents a PDE-constrained optimization perspective on trustworthy digital twins, with emphasis on both applications and theoretical foundations. We discuss how digital twins lead to large-scale inverse, control, and design problems constrained by PDEs, and how adjoint methods, inexact trust-region algorithms, and augmented Lagrangian techniques provide scalable tools for model updating and decision-making. A central theme is uncertainty: digital twins must operate with noisy data, incomplete boundary conditions, uncertain parameters, and rare but consequential events. Risk-aware formulations, including CVaR-type objectives and robust perspectives, provide a principled framework for such settings. Applications include patient-specific aneurysm modeling, structural digital twins for bridges, thermal design, sensing, graph-based control, and Maxwell-based systems.

• Battistin, Claudia; Dingsør, Liv; Røstad, Lillian; Kriken, Olav Sindre & Wold, Erik (2026). Importance of close collaboration between research and industry, and how to best utilize Norwegian data in this work. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Panel discussion led by Claudia Battistin, during the Business & Industry Day at the SURE-AI Annual Conference; bridging the academic discussion with practical debate on implementation and innovation in business and industry.

• Thürer, Benjamin & Richardson, Andrew (2026). Vessel Destination Prediction as a Leading Indicator for Energy Markets. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Ship movements provide important insight into the energy market: vessels transport energy commodities (oil, gas, coal), support infrastructure construction (e.g., pipeline-laying vessels), and maintain offshore assets (e.g., offshore wind farms). Predicting a ship's destination, therefore, enables short-term energy market forecasting and has been used lately for predicting recovery of the Middle East Crisis. However, self-reported AIS destinations are often missing, inconsistent, or unreliable and require data modelling. At Rystad Energy, we collect, preprocess, and model AIS vessel-tracking data at scale. To support this, we use modern geospatial techniques to cluster and compress raw AIS positions into spatial clusters which, in turn, can build out a global spatial routing system based on Uber H3 hexagons. These routes serve as input features to a linear regression model that estimates destination likelihood by matching a vessel's current trajectory against historical route patterns. We combine this spatial model with the vessel's self-reported AIS destination using a decision-tree-based ensemble, allowing the model to compensate for unreliable self-reporting with learned route behavior. The resulting ensemble model trained for LNG ships achieves a port prediction accuracy of 0.30, 0.43, and 0.60 once a vessel has completed 0%, 33%, and 66% of its journey, respectively. This computationally lightweight model outperforms the self-reported AIS destination alone and exceeds chance (0.03 at 332 LNG ports) significantly.

• Surowiec, Thomas (2026). RALES: A Risk-Averse Augmented Lagrangian Equality-constrained SQP Method for Optimization with General Constraints. Fulltekst i vitenarkiv Vis sammendrag

  Recent advances in augmented Lagrangian methods for infinite-dimensional constrained optimization have significantly broadened this classical algorithmic framework. However, cutting-edge approaches like ALESQP were not designed to handle the nonsmooth composite objective functions typically found in risk-averse stochastic optimization models. Conversely, methods such as the primal-dual risk minimization (PD-Risk) algorithm, developed for minimizing structured nonsmooth risk measures, do not account for simulation-based equality constraints or complex geometric constraints. We remedy this gap by fusing PD-Risk with ALESQP to introduce a new method: RALES. RALES is a provably convergent algorithm designed to solve risk-averse optimization problems that incorporate both simulation-based equality constraints and general convex set constraints. The method specifically addresses the computational challenges posed by nonsmooth coherent risk measures, such as Average Value-at-Risk (AVaR). It achieves this by utilizing a risk-averse augmented Lagrangian functional that maintains Fréchet differentiability via epiregularization of the nonsmooth functionals using the previous dual variables in the regularization terms. By integrating this functional with a composite-step trust-region SQP solver, RALES effectively decomposes the problem into manageable components. Simulation-based constraints are handled via inexact, matrix-free linear system solves, while general convex constraints are managed through the augmented Lagrangian. A distinguishing feature of the algorithm is its use of a decoupled penalty parameter update scheme (adapted from the ALESQP framework) during an initial calibration phase of K iterations. This allows the framework to adaptively learn appropriate scalings for heterogeneous sets of constraints. We provide a rigorous convergence analysis for minimizers and dual variables in an ideal setting, and stationary points in a more general, computationally relevant setting. Finally, we illustrate the method's performance and viability through numerical experiments on high-dimensional problems.

• Surowiec, Thomas (2026). RALES: A Risk-Averse Augmented Lagrangian Equality-constrained SQP Method for Optimization with General Constraints. Fulltekst i vitenarkiv
• Surowiec, Thomas (2026). A Brief Tour of Risk-Averse PDE-Constrained Optimization: From models to data-driven stability. Fulltekst i vitenarkiv
• Surowiec, Thomas & Kirkeby, Adrian (2026). Én feil, og alt kollapser. doi: https:/www.morgenbladet.no/ideer/en-feil-og-alt-kollapser/10233893. Fulltekst i vitenarkiv
• Surowiec, Thomas (2026). From Mathematical Foundations to New Technologies: SURE-AI's Path to Sustainable, Risk-Averse, and Ethical AI. Fulltekst i vitenarkiv
• Surowiec, Thomas; Riegler, Michael & Kirkeby, Adrian (2026). Vi trenger ikke høyere temperatur i KI-debatten. doi: https:/www.morgenbladet.no/ideer/vi-trenger-ikke-hoyere-temperatur-i-ki-debatten/10355409. Fulltekst i vitenarkiv
• Moe, Signe (2026). AI in Retail: Use cases and ongoing work at REMA 1000. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Presnetaion at the Business & Industry Day during the SURE-AI Annual Conference; bridging the academic discussion with practical debate on implementation and innovation in business and industry.

• Wold, Erik (2026). Introducing AI-consumption of data in a Data-as-a-Service company. An AI journey. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Presentation at the Business & Industry Day during the SURE-AI Annual Conference; bridging the academic discussion with practical debate on implementation and innovation in business and industry.

• Richard, Cèdric (2026). Non-parametric change-point detection using Reproducing Kernel Hilbert Spaces (RKHS) and Pearson Chi2 divergence. doi: https:/ppgeti.ufc.br/pt/author/ppgeti/page/6/. Fulltekst i vitenarkiv Vis sammendrag

  Plenary talk at the Graduate Program in Teleinformatics Engineering at the Federal University of Ceará, Fortaleza, Brasil

• Richard, Cèdric (2026). L’IA au service de l’observation de notre environnement (AI in the service of environmental observation). doi: https:/www.oca.eu/en/. Fulltekst i vitenarkiv Vis sammendrag

  Plenary talk at the Research Support Staff Day, Observatoire de la Côte d’Azur

• Viselli, Andrea (2026). Roundtable on AI & Electricity markets. doi: https:/www.bi.no/en/about-bi/events/2026/september/workshop-on-transition-in-a-changing-world/. Fulltekst i vitenarkiv
• Iacone, Fabrizio & Viselli, Andrea (2026). Robust forecast evaluation under extreme shocks. doi: https:/andreaviselli.it/dm-dashboard/#simulation. Fulltekst i vitenarkiv Vis sammendrag

  We address forecast evaluation in the presence of extreme, one-off shocks, such as the impact of Covid-19 on GDP. Conventional predictive ability tests may have no power under such brief but severe instabilities, potentially overlooking the superior accuracy of forecasts during normal periods. To remove this effect, we propose winsorizing forecast errors to neutralize the influence of extreme events. Using the US Survey of Professional Forecasters for real GDP growth, we illustrate how this approach uncovers superior performance that standard tests would otherwise fail to detect.

• Zuazua, Enrique (2026). Control and Machine Learning: A Mathematical Journey. doi: https:/dcn.nat.fau.eu/bnu-control-and-machine-learning-a-mathematical-journey/. Fulltekst i vitenarkiv Vis sammendrag

  On March 19, 2026, Prof. Enrique Zuazua presented as keynote speaker at the 30th lecture of its Mathematics Forum “Control and Machine Learning: A Mathematical Journey” hosted by the BNU, Beijing Normal University, China. In his talk, Prof. Zuazua traced the historical development of control theory, from the origins of cybernetics, introduced by Ampère and later expanded by Wiener, to its modern connections with artificial intelligence (AI). He emphasized how control theory provides a rigorous mathematical framework for understanding regulation and communication in both natural and engineered systems. A central theme of the lecture was the deep connection between control systems and contemporary machine learning. He highlighted how mathematical principles underpinning control theory are increasingly shaping AI methodologies, enabling advances in modeling, prediction, and technological innovation. Through examples and applications, he illustrated the transformative impact of integrating control theory with machine learning, offering a forward-looking perspective on the future of applied mathematics. After an engaging discussion on questions about AI, mathematical modeling, and the evolving role of mathematics in scientific discovery, Prof. Zuazua highlighted how mathematics remains a fundamental driver of innovation, particularly as new challenges emerge in the era of artificial intelligence.

• Zuazua, Enrique (2026). Machine Learning, Control Theory and PDEs. doi: https:/congreso-internacional-fcm-unmsm-grabaciones-certificacion.onhercules.app/. Fulltekst i vitenarkiv
• Zuazua, Enrique (2026). Machine Learning from an Applied Mathematician’s Perspective. doi: https:/sites.google.com/unitn.it/mfml-2026/home?authuser=0. Fulltekst i vitenarkiv Vis sammendrag

  Machine Learning has emerged as one of the most transformative forces in contemporary science and technology. In this three-lecture series, I will discuss Machine Learning through the lens of applied mathematics, emphasizing its connections with control theory, partial differential equations, and numerical analysis. In the first lecture, we will revisit the historical and conceptual links between Machine Learning and Systems Control (Cybernetics). This point of view allows us to reinterpret representation and expressivity properties of deep neural networks in terms of ensemble or simultaneous controllability of neural differential equations. The second lecture will focus on the use of neural network architectures as numerical approximation tools. We will consider, as a guiding example, the classical Dirichlet problem for the Laplace equation, formulated via energy minimization under neural-network constraints. Particular attention will be paid to the lack of convexity and coercivity in the resulting optimization problems. We will show how relaxation techniques may restore convexity at the price of losing coercivity, and we will discuss the mathematical implications of this trade-off for analysis and computation. In the third lecture, we will present a PDE-based perspective on generative diffusion models. Their convergence can be reinterpreted in terms of the asymptotic behavior of Fokker–Planck equations driven by the so-called score vector field. We will explain how classical tools, such as Li-Yau-type differential inequalities for positive solutions of the heat equation, provide insight into the regularization and convergence properties of these models. The series will conclude with a discussion of open problems and promising directions for future research at the interface of control theory, PDEs, numerical analysis, and modern Machine Learning.

• Zuazua, Enrique (2026). Machine Learning, PDEs and Control. doi: https:/www.icm2026.org/event/ac193975-5d24-4628-8c30-ddb23de19a8b/catalog?environment=P2. Fulltekst i vitenarkiv Vis sammendrag

  Traditional applied mathematics provides a natural framework for understanding several of the fundamental mechanisms underlying modern Artificial Intelligence. In this talk, we will show how control notions and methods, such as simultaneous and ensemble controllability, shed light on the classification and representation capabilities of deep neural networks, leading to an interpretation of learning as a control problem. The second part of the talk will focus on generative AI. We will show how classical diffusion processes and their associated partial differential equations provide a mathematical perspective on modern generative models, revealing generation as a controlled reversal of heat flow. Finally, we will address the use of neural networks as computational tools for the approximation of complex systems. In this context, new phenomena emerge, including situations in which physical states converge while the corresponding network parameters escape to infinity, revealing a gap between the well-posedness of the underlying mathematical problem and that of its neural parametrization. These examples illustrate how control theory, partial differential equations, probability, approximation theory, and scientific computing are becoming increasingly intertwined in shaping the mathematical foundations of AI. They also point toward significant mathematical challenges, both in understanding modern AI and in adapting these methodologies to specialized scientific, engineering, and biomedical applications.

• Zuazua, Enrique (2026). Control and Machine Learning: A Mathematical Journey. doi: https:/www.youtube.com/watch?v=eH5pvsaVoas. Fulltekst i vitenarkiv Vis sammendrag

  Control theory, also known as cybernetics, a term first introduced by Ampère and later popularized by Norbert Wiener, studies regulation and communication in animals and machines. Its roots can be traced back to antiquity and to the enduring human ambition to design mechanisms capable of acting autonomously, thereby extending both freedom and efficiency. The goals of control systems resonate strongly with those of modern Artificial Intelligence (AI). This connection highlights not only the deep unity of mathematics but also its remarkable power to model natural phenomena and shape technological innovation. In this lecture, Prof. Zuazua traces the historical development of control theory, highlights some of its fundamental mathematical principles, and explores key links to contemporary machine learning paradigms. The lecture also presents representative applications and success stories illustrating the transformative interplay between control and learning.

• Zuazua, Enrique (2026). Classical PDE ideas in modern AI: Gaussian variational ansatzes and diffusion dynamics. doi: https:/sites.google.com/view/thinstructures7/home-page?authuser=0. Fulltekst i vitenarkiv Vis sammendrag

  The talk discusses two examples at the interface between PDEs, the calculus of variations, and machine learning. The first one concerns Gaussian ansatz approximations of elliptic variational problems, with links to universal approximation and energy minimization. A central goal is to understand the unexpected efficiency of these methods, even though, from the viewpoint of classical rigorous analysis, they may at first seem destined to fail. The second one, based on joint work with Kang Liu (Dijon), concerns diffusion-based generative AI. In this setting, the heat equation and related diffusion dynamics provide a natural PDE framework for understanding and designing modern generative methods in AI. The aim is to show how classical analytical tools remain central to emerging questions in AI, and how the rapid development of machine learning is opening fascinating new problems in PDEs.

• Cuchiero, Christa (2026). Dynamic universal approximation and optimal control for path-dependent systems via signature SDEs. doi: https:/rgosa.net/conferences/cosa-2026/conference-program/. Fulltekst i vitenarkiv Vis sammendrag

  Many applications in generative time series modeling, particularly in finance, require stochastic dynamics that are genuinely path-dependent and non-Markovian. From a numerical perspective, the most natural route is to lift path dependence to an enlarged state space, thereby obtaining a Markovian approximation of the original dynamics. Among such lifts, signature SDEs provide a canonical and model-agnostic choice, building on the strong algebraic and approximation-theoretic properties of path signatures, which form a universal and non-parametric feature set for paths. We explain how this leads to dynamic universal approximation results for generic non-Markovian SDEs. We also show how the resulting finite-dimensional signature SDEs can be used in optimal control problems with path-dependent dynamics and objectives, reducing, for instance, the infinite-dimensional Hamilton-Jacobi-Bellman PDE to a computationally much simpler Riccati ODE.

• Cuchiero, Christa (2026). Dynamic universal approximation and optimal control for non-Markovian systems via signature stochastic differential equations. doi: https:/www.ekf.vsb.cz/mme/en/. Fulltekst i vitenarkiv Vis sammendrag

  Many applications in generative time series modeling, particularly in finance, require stochastic dynamics that are genuinely path-dependent and non-Markovian. Classical Markovian state-space models are often too restrictive to capture memory effects, delayed responses, volatility feedback, and other features generated by the past trajectory of the system. From a numerical perspective, the most natural route is to lift path dependence to an enlarged state space, thereby obtaining a Markovian approximation of the original dynamics. Among such lifts, signature stochastic differential equations (SDEs) provide a canonical and model-agnostic choice, building on the strong algebraic and approximation-theoretic properties of path signatures, which form a universal and non-parametric feature set for paths. We explain how this leads to dynamic universal approximation results for generic non-Markovian SDEs. We also show how the resulting finite-dimensional signature SDEs can be used in optimal control problems with path-dependent dynamics and objectives, reducing, for instance, the infinite-dimensional Hamilton-Jacobi-Bellman PDE to a much simpler Riccati ODE.

• Cuchiero, Christa (2026). Dynamic universal approximation and optimal control for path-dependent systems via signature SDEs. doi: https:/iccf26.web.ox.ac.uk/. Fulltekst i vitenarkiv Vis sammendrag

  Many applications in generative time series modeling, particularly in finance, require stochastic dynamics that are genuinely path-dependent and non-Markovian. From a numerical perspective, the most natural route is to lift path dependence to an enlarged state space, thereby obtaining a Markovian approximation of the original dynamics. Among such lifts, signature SDEs provide a canonical and model-agnostic choice, building on the strong algebraic and approximation-theoretic properties of path signatures, which form a universal and non-parametric feature set for paths. We explain how this leads to dynamic universal approximation results for generic non-Markovian SDEs. We also show how the resulting finite-dimensional signature SDEs can be used in optimal control problems with path-dependent dynamics and objectives, reducing, for instance, the infinite-dimensional Hamilton-Jacobi-Bellman PDE to a computationally much simpler Riccati ODE.

• Cuchiero, Christa (2026). Dynamic universal approximation and modeling with signature SDEs. doi: https:/www.bacheliercongress.com/2026/. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by generative AI inspired modeling, we investigate the mathematical foundations of neural and signature stochastic differential equations (SDEs). In these models, the coefficients of the SDE are parameterized either by neural networks or by functions of the path signature, leveraging their well-known universal approximation properties. While such classical universal approximation results concern static functions, our focus is on dynamic universal approximation at the level of the SDE solutions. We show that any standard SDE as well as path-dependent SDE can be approximated by a suitable neural or signature SDE, respectively. For signature SDEs, this requires the development of a dedicated well-posedness theory. Building on this foundation, we prove in particular that SDEs whose coefficients are entire functions of the signature serve as dynamic universal approximators for path-dependent SDEs. Since these signature SDEs exhibit an affine structure with respect to the lifted signature state, this result implies universality of affine processes within the class of Itô-processes. We also outline how a similar approach can be used to tackle generic path-dependent optimal control problems.

• Cuchiero, Christa (2026). Modeling with neural SPDEs: data-driven Heath-Jarrow-Morton models. doi: https:/probabilitypalermo2026.unipa.it/. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by recent advances in AI inspired generative modeling, we investigate the mathematical foundations and universal approximation properties of neural stochastic partial differential equations (SPDEs) of Heath–Jarrow–Morton (HJM) type, whose coefficients are parameterized by function-valued neural networks. Building on this framework, we then propose a fully data-driven HJM model for the forward interest rate dynamics. Specifically, we consider dynamics driven by linear functionals of the yield curve, such as a finite collection of representative forward rates, possibly augmented by observable macroeconomic factors whose characteristics can be directly estimated from market data. The volatility structure is parameterized via artificial neural networks, naturally leading to a neural SPDE formulation. The neural network parameters are learned from historical yield curve data, yielding an arbitrage-free and data-driven framework for the generation and prediction of yield curves. We demonstrate the proposed deep learning methodology by reconstructing and forecasting the Euro area yield curves.

• Cuchiero, Christa (2026). Generative AI for Finance: Dynamic universal approximation and modeling with neural and signature SDEs (Phd Course). doi: https:/quantitative-finance-conference-2026.pages.dev/summer-school. Fulltekst i vitenarkiv Vis sammendrag

  Generative AI has recently transformed a wide range of fields by enabling the modeling of complex and high-dimensional datasets as well as the synthesis of new content. In finance, it offers a modern approach to scenario generation, for instance through market simulators and return generators. This talk explores the key characteristics of generative AI models, including autoencoders, GANs, diffusion models, as well as neural and signature stochastic differential equations (SDEs) - with a particular focus on the latter two. We delve into the mathematical foundations of neural and signature SDEs, emphasizing especially their universal approximation capabilities. As financial applications we present a Bayesian calibration approach to neural SDEs, a data-driven version of the Heath–Jarrow–Morton framework for interest rate modeling, and signature-based asset price models calibrated jointly to VIX and SPX options

• Cuchiero, Christa (2026). Dynamic universal approximation and modeling with neural and signature SDEs. doi: https:/www.lorentzcenter.nl/mathematics-and-machines-from-brown-to-sustainable-finance.html. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by generative AI inspired modeling, we investigate the mathematical foundations of neural and signature stochastic differential equations (SDEs). In these models, the coefficients of the SDE are parameterized either by neural networks or by functions of the path signature, leveraging their well-known universal approximation properties. While such classical universal approximation results concern static functions, our focus is on dynamic universal approximation at the level of the SDE solutions. We show that any standard SDE as well as path-dependent SDE can be approximated by a suitable neural or signature SDE, respectively. For signature SDEs, this requires the development of a dedicated well-posedness theory. Building on this foundation, we prove in particular that SDEs whose coefficients are entire functions of the signature serve as dynamic universal approximators for path-dependent SDEs. Since these signature SDEs exhibit an affine structure with respect to the lifted signature state, this result implies universality of affine processes within the class of Itô-processes. We also outline how a similar approach can be used to tackle generic path-dependent optimal control problems.

• Cuchiero, Christa (2026). Dynamic universal approximation and modeling with neural and signature SDEs. doi: https:/www.mathematik.uni-konstanz.de/forschung/kolloquien-und-oberseminare/detailansicht-fb-kolloquium/termin/mathematisches-kolloquium-dynamic-universal-approximation-and-modeling-with-neural-and-signature-sdes/. Fulltekst i vitenarkiv
• Cuchiero, Christa (2026). Dynamic universal approximation and modeling with neural and signature SDEs. doi: https:/stochasticcontrol.org/smc/. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by generative AI inspired modeling, we investigate the mathematical foundations of neural and signature stochastic differential equations (SDEs). In these models, the coefficients of the SDE are parameterized either by neural networks or by functions of the path signature, leveraging their well-known universal approximation properties. While such classical universal approximation results concern static functions, our focus is on dynamic universal approximation at the level of the SDE solutions. We show that any standard SDE as well as path-dependent SDE can be approximated by a suitable neural or signature SDE, respectively. For signature SDEs, this requires the development of a dedicated well-posedness theory. Building on this foundation, we prove in particular that SDEs whose coefficients are entire functions of the signature serve as dynamic universal approximators for path-dependent SDEs. Since these signature SDEs exhibit an affine structure with respect to the lifted signature state, this result implies universality of affine processes within the class of Itô-processes. We also outline how a similar approach can be used to tackle generic path-dependent optimal control problems.

• Cuchiero, Christa (2026). Dynamic universal approximation and modeling with neural and signature SDEs. doi: https:/memotef.web.uniroma1.it/it/women-mathematical-finance-workshop-february-12-13-2026. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by generative AI inspired modeling, we investigate the mathematical foundations of neural and signature stochastic differential equations (SDEs). In these models, the coefficients of the SDE are parameterized either by neural networks or by functions of the path signature, leveraging their well-known universal approximation properties. While such classical universal approximation results concern static functions, our focus is on dynamic universal approximation at the level of the SDE solutions. We show that any standard SDE as well as path-dependent SDE can be approximated by a suitable neural or signature SDE, respectively. For signature SDEs, this requires the development of a dedicated well-posedness theory. Building on this foundation, we prove in particular that SDEs whose coefficients are entire functions of the signature serve as dynamic universal approximators for path-dependent SDEs. Since these signature SDEs exhibit an affine structure with respect to the lifted signature state, this result implies universality of affine processes within the class of Itô-processes. We also outline how a similar approach can be used to tackle generic path-dependent optimal control problems.

• Cuchiero, Christa (2026). Dynamic universal approximation and modeling with neural and signature SDEs. doi: https:/www.esi.ac.at/events/e581/. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by generative AI inspired modeling, we investigate the mathematical foundations of neural and signature stochastic differential equations (SDEs). In these models, the coefficients of the SDE are parameterized either by neural networks or by functions of the path signature, leveraging their well-known universal approximation properties. While such classical universal approximation results concern static functions, our focus is on dynamic universal approximation at the level of the SDE solutions. We show that any standard SDE as well as path-dependent SDE can be approximated by a suitable neural or signature SDE, respectively. For signature SDEs, this requires the development of a dedicated well-posedness theory. Building on this foundation, we prove in particular that SDEs whose coefficients are entire functions of the signature serve as dynamic universal approximators for path-dependent SDEs. Since these signature SDEs exhibit an affine structure with respect to the lifted signature state, this result implies universality of affine processes within the class of Itô-processes. We also outline how a similar approach can be used to tackle generic path-dependent optimal control problems.

• Beferull-Lozano, Baltasar (2026). SURE-AI Centre for Sustainable, Risk-averse and Ethical AI. Progress, status and outlook. Fulltekst i vitenarkiv Vis sammendrag

  Status update presentation of the SURE-AI Centre to the RCN Portfolio Board for Enabling Technologies

• Beferull-Lozano, Baltasar (2026). SURE-AI Centre for Sustainable, Risk-averse and Ethical AI. Fulltekst i vitenarkiv Vis sammendrag

  Short presentation of SURE-AI Centre for Sustainable, Risk-averse and Ethical AI

• Beferull-Lozano, Baltasar (2026). SURE-AI Centre for Sustainable, Risk-averse and Ethical AI. Fulltekst i vitenarkiv Vis sammendrag

  Presentation of the SURE-AI Centre for Sustainable, Risk-averse and Ethical AI and possibilities for collaboration

• Ortiz-Latorre, Salvador (2026). Heston-Hawkes stochastic volatility model: Change of measure and Thiele's PIDE. Fulltekst i vitenarkiv
• Ortiz-Latorre, Salvador (2026). Convergence in law for quasi-linear SPDEs. Fulltekst i vitenarkiv
• Nunno, Giulia Di (2026). Uncertainties in risk evaluation for long term horizons and computational aspects. doi: https:/www.bacheliercongress.com/2026/eventi.unibo.it/bachelier.html. Fulltekst i vitenarkiv Vis sammendrag

  Long and short-horizons must be treated differently in monetary risk-evaluations. Horizon-risk and h-longevity are identified to capture this. We clarify that classical dynamic risk measures are subject to horizon-risk exposure, and propose to work with fully-dynamic risk-measures. In long horizons, also interest rate uncertainty cannot be underestimated. We combine these aspect working with cash non-additive dynamic risk-measures via BSDEs and generalised shortfalls. We take steps in the numerical quantification relying on a novel use of Wiener-Ito chaos expansions and proposing DeepO BSDEs schemes.

• Nunno, Giulia Di (2026). Malliavin calculus in Sandwich Volterra Volatility models. Fulltekst i vitenarkiv Vis sammendrag

  Sandwich Volterra Volatility models are capturing both the long-memory and rough features of volatility, while also complying with stylised facts observed in volatility markets. Within the analysis of this family, we see how Malliavin calculus has been instrumental to characterise the behaviour of these processes. As supplement, we also discuss generalised product and chain rule.

• Nunno, Giulia Di (2026). BSDEs and Operator Deep BSDEs for dynamic risk evaluation. doi: https:/www.ucc.ie/en/stochastica/events/stochasticadirectionsworkshopapril2026/. Fulltekst i vitenarkiv Vis sammendrag

  Backward SDEs (BSDEs) have been used for dynamic risk measurement, we revise the framework and value of a dynamic risk evaluation. We also indicate some shortcomings, particularly related to the evaluation of risk at different time horizon, introduced as horizon-risk. For this reason we introduce the concept of fully-dynamic risk measurement and show how it is still easily related to BSDEs. As illustration we consider variation to the entropic case as well as we introduce the hq-entropic risk measure inspired by Tsallis general entropy. We discuss computational methods from an operator point of view, proposing an Operator Deep BSDE approach.

• Nunno, Giulia Di (2026). Capturing horizon risk and interest rate uncertainty. doi: https:/sites.google.com/view/mf-osaka/home?authuser=1. Fulltekst i vitenarkiv Vis sammendrag

  Horizon risk is introduced as the evaluation of the exposure to potentially erroneous risk measurement when using a risk measure that is not adequate to the actual time horizon of the position. We clarify that classical dynamic risk measures are subject to horizon risk, so we propose to work with fully-dynamic risk measures, which are then designed to capture horizon risk and evaluate it in terms of an index of h-longevity. For this we use backward stochastic differential equations. In a financial context, we combine horizon risk with interest rates uncertainty, thus we also propose a cash non-additive version of fully- dynamic risk measures. We construct such risk measures via backward stochastic differential equations or via a generalisation of shortfall-type representation. As illustration, we introduce the class of hq-entropic risk measures.

• Gancia, Gino; Mittal, Shivika; Nunno, Giulia Di; Castellacci, Fulvio & Beferull-Lozano, Baltasar (2026). SURE-AI@STAR Workshop on the Environmental Cost of AI. doi: https:/www.mn.uio.no/math/english/research/groups/risk-stochastics/events/seminars/SURE-AI@STARWorkshop-CostAI.html. Fulltekst i vitenarkiv
• Tarquini, Leonardo (2026). Signature McKean-Vlasov stochastic differential equations. doi: https:/sites.google.com/unipv.it/apmp2026/home-page. Fulltekst i vitenarkiv Vis sammendrag

  McKean--Vlasov-type stochastic differential equations (SDEs) are characterised by coefficients depending on both the state and the law of the solution. In our work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric p-rough path lift of its solution, with p ∈ (2,3). After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean–Vlasov SDEs. Finally, we consider the associated particle system and establish propagation of chaos. This is a joint work with F.E. Benth (BI Norwegian Business School and University of Oslo) and S. Ortiz-Latorre (University of Oslo).

• Lozano, Pere Diaz (2026). Deep operator BSDE: A numerical scheme to approximate solution operators. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by dynamic risk measures and conditional g-expectations, in this work we propose a numerical method to approximate the solution operator given by a backward stochastic differential equation (BSDE). The main ingredients for this are the Wiener chaos decomposition and the classical Euler scheme for BSDEs. We show convergence of this scheme under very mild assumptions, and provide a rate of convergence in more restrictive cases. We then implement it using neural networks, and we present several numerical examples where we can check the accuracy of the method.

• Lozano, Pere Diaz (2026). A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration. Fulltekst i vitenarkiv Vis sammendrag

  Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

• Lozano, Pere Diaz (2026). A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration. Fulltekst i vitenarkiv Vis sammendrag

  Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.

• Lozano, Pere Diaz (2026). An Euler scheme for BSDEs via the Wiener chaos decomposition. Fulltekst i vitenarkiv Vis sammendrag

  The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each time step. We propose an implementation based on the Wiener chaos decomposition to approximate these quantities. In contrast to many numerical schemes that rely on a finite-dimensional Markovian representation, our approach accommodates arbitrary FT-measurable square-integrable terminal conditions. We provide a comprehensive convergence analysis under additional Malliavin regularity assumptions and illustrate the method on several numerical examples, including genuinely non-Markovian problems arising, for instance, in the pricing and hedging of contingent claims under rough-volatility models.

• D'Ecclesiis, Enrico; Castellacci, Fulvio & Ahmadi, Arash (2026). Validating LLM-generated synthetic survey samples: A use-dependent multi-dimensional framework for social-science applications. Fulltekst i vitenarkiv
• Castellacci, Fulvio & D'Ecclesiis, Enrico (2026). AI: Optimist or Skeptic? The Role of Trust in EU Institutions in Shaping Attitudes Toward AI. Fulltekst i vitenarkiv
• Harang, Fabian Andsem (2026). SURE-AI@NORA.AI. doi: https:/www.nora.ai/nora-events/annual-conference-2026/program2026.html. Fulltekst i vitenarkiv Vis sammendrag

  A presentation at the NORA Annual Conference on the SURE-AI Centre. The centre will conduct interdisciplinary research on designing AI to be sustainable, risk-aware and ethical; bringing together mathematicians, statisticians and engineers, together with economists, social scientists and humanities researchers.

• Harang, Fabian Andsem (2026). Forskning uten for mye press og stress | CAS. [Internet]. https://cas-nor.no/news/forskning-uten-mye-press-og-stress. Fulltekst i vitenarkiv Vis sammendrag

  – Året ved CAS var et spennende år, vi kunne virkelig fordype oss. Det var veldig annerledes enn å jobbe på universitet til vanlig, der man underviser litt, forsker litt, veileder litt, gjør mye administrativt arbeid og skriver søknader. Hvor mye tid har man egentlig da til å fordype seg i egne forskningsinteresser? CAS ga oss frihet og rom til å forske, sier Fabian Harang.

• Nunno, Giulia Di (2026). On Sandwiched Volterra Volatility Models. Fulltekst i vitenarkiv Vis sammendrag

  Sandwiched Volterra Volatility (SVV) models are a class of dynamics capable of capturing both the long-memory and rough features of volatility, while also complying with several stylized facts observed in volatility markets. At the same time, price dynamics with SVV volatility remain sufficiently tractable to allow for a rigorous and explicit analysis of pricing and hedging of financial assets. We present an overview of these models, highlighting their main features and potential applications. While pricing aspects are briefly discussed, the main focus of the talk is on the quadratic hedging of financial derivatives within this framework, providing insights into the computational challenges associated with the optimal hedging strategy.

• Nunno, Giulia Di (2026). Quadratic hedging in Sandwiched Volterra Volatility Models. Fulltekst i vitenarkiv Vis sammendrag

  Sandwiched Volterra Volatility (SVV) models are a class of dynamics capable of capturing both the long-memory and rough features of volatility, while also complying with several stylized facts observed in volatility markets. At the same time, price dynamics with SVV volatility remain sufficiently tractable to allow for a rigorous and explicit analysis of pricing and hedging of financial assets. We present an overview of these models, highlighting their main features and potential applications. While pricing aspects are briefly discussed, the main focus of the talk is on the quadratic hedging of financial derivatives within this framework, providing insights into the computational challenges associated with the optimal hedging strategy. The explicit optimal hedging solution is characterized via the non-anticipating derivative, and its numerical implementation is addressed through Markovian approximations.

• Harang, Fabian Andsem (2026). What collaborating with Rema 1000 has taught me. About useful research – and learning the work first. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv
• Moreno, Emilio Ruiz (2026). A primer on risk-aware reinforcement learning. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv
• Abeele, Jeriek Paul Van den (2026). AI for a safer and smarter tomorrow. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv
• Gregersen, Thomas (2026). AI in payment systems. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv
• Lorenzo, Paolo Di; Barbarossa, Sergio & Isufi, Elvin (2026). Topological Signal Processing and Learning. doi: https:/eusipco2026.org/special-sessions/. Fulltekst i vitenarkiv Vis sammendrag

  Many modern datasets exhibit complex relational structures that cannot be properly described using traditional Euclidean models. In recent years, graph signal processing and geometric deep learning have provided powerful frameworks for processing signals defined on irregular domains such as networks. However, many real-world systems involve higher-order interactions among groups of entities, which cannot be adequately captured by pairwise relations. Examples include multi-agent coordination, social group interactions, biological networks, and infrastructure systems where flows occur along network links. To model these interactions, researchers have recently turned to topological representations such as simplicial complexes and cell complexes, which naturally capture multiway relationships. This tutorial introduces the emerging framework of Topological Signal Processing and Learning, which generalizes graph signal processing and graph neural networks to signals defined over higher-order structures. The tutorial presents the fundamental tools needed to represent, process, and learn from topological signals using concepts from algebraic topology and signal processing. We begin by reviewing relational inductive biases and the foundations of graph signal processing. We then introduce topological representations of data, including simplicial complexes and the associated algebraic operators such as incidence matrices and Hodge Laplacians. Building on these tools, we present signal processing methods for topological signals, including filtering, sampling, representation, and dictionary learning. Finally, we discuss emerging learning architectures based on simplicial convolutions that extend graph neural networks to higher-order domains. The tutorial combines theoretical insights with illustrative applications and recent research results, providing attendees with a clear overview of this rapidly growing research direction.

• Goodman, Jacob & Jasa, Hajg (2026). Riemannian Metric Preconditioning for Trajectory Tracking. Fulltekst i vitenarkiv Vis sammendrag

  Given a Riemannian metric g and a one-form, we introduce a reward metric via a rank-one update of g with this one-form, which makes certain directions of motion "cheaper" to travel along. We derive an explicit formula for the difference tensor between the Levi–Civita connections of the original and reward metrics. We then use this to formulate a preconditioned intrinsic trajectory-tracking law for affine connection control systems on Riemannian manifolds. The approach is applied to an underactuated rigid-body system on SE(3), and we compare it with an unmodified geometric tracking controller in a maze navigation problem.

• Harang, Fabian Andsem; Pettersen, Klas Henning; Kostøl, Andreas Ravndal; Nærland, Tine Uberg & Ingul, Marte (2026). Er fremtiden med KI bærekraftig? En diskusjon om energi, økonomi og demokrati. Fulltekst i vitenarkiv Vis sammendrag

  Panelsamtale som undersøker samfunnsmessig bærekraft og reelle kostnader og konsekvenser av KI-revolusjonen - vår tids største teknologiskifte.

• Solheim, Øyvind Bugge (2026). Norwegians’ use of generative AI. Fulltekst i vitenarkiv Vis sammendrag

  How do Norwegians' use generative AI?

• Antil, Harbir (2026). Reliable Digital Twins for Biomedical and Engineering Systems: A PDE-Constrained Optimization Perspective. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Digital twins are adaptive virtual representations of physical systems that are updated by data and used to support prediction, monitoring, and decision-making. In biomedical applications, they may represent patients, organs, vascular systems, hospital workflows, or digital populations for treatment planning and virtual trials. Their reliability requires more than data and machine learning: it depends on physics-based models, scalable optimization algorithms, and uncertainty-aware decision support. This talk presents a PDE-constrained optimization perspective on reliable digital twins for biomedical and engineering systems. We begin with medical digital twins, focusing on patient-specific aneurysm modeling, where incomplete boundary conditions, uncertain inflow profiles, and truncated geometries can strongly affect clinically relevant flow quantities. Adjoint-based sensitivity analysis provides a principled way to quantify these effects and guide model improvement. The same framework extends to structural health monitoring, thermal design, neuromorphic sensing, graph-based control, and Maxwell-based digital twins. Across these examples, PDE-constrained optimization provides a common language for state estimation, parameter identification, control, sensor placement, and model updating. The central message is that trustworthy digital twins are not merely data-driven models; they are optimization-driven, uncertainty-aware, structure-preserving computational systems that close the loop between measurements, prediction, and decisions.

• Richard, Cédric (2026). Listening to the City: Repurposing Telecom Fibers for Massive-Scale Traffic Sensing with AI. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Telecommunication optical fibers—traditionally used only for data transmission—can be transformed into dense, city-scale arrays of seismo-acoustic sensors. This talk presents recent advances demonstrating how Distributed Acoustic Sensing (DAS), combined with machine learning and statistical signal-processing methods, enables real-time monitoring of traffic flow, environmental activity, and infrastructure integrity with meter-level spatial resolution over tens to hundreds of kilometers. By exploiting vibrations generated by vehicles, construction operations, and natural phenomena, DAS turns existing fiber networks into continuous, scalable, and infrastructure-free sensing platforms. I will show how these signals can be processed to extract actionable information in complex urban environments, and how such systems pave the way for safer and more sustainable cities.

• Ni, Hao (2026). Diffusion distillation via signatures and parallelisation. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Diffusion and score-based generative models rely on many sequential model evaluations, making both sampling and trajectory generation computationally expensive. This talk presents two complementary approaches to address these bottlenecks. SigDEG is a principled distillation framework grounded in stochastic Taylor expansions and rough path theory. By representing Brownian path information through partial signatures, it replaces multiple fine solver steps with a single coarse update, reducing inference cost. ParaSig complements this by accelerating teacher trajectory generation with the Parareal algorithm, exploiting parallelism in time to reduce the simulation cost resulted from the teacher model.

• Cuchiero, Christa (2026). Dynamic universal approximation and modeling with signature stochastic differential equations. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Motivated by generative AI inspired modeling, we investigate the mathematical foundations of signature stochastic differential equations (SDEs). In these models, the coefficients of the SDE are parameterized by functions of the path signature, leveraging their well-known universal approximation properties. While such classical universal approximation results concern static functions, our focus is on dynamic universal approximation at the level of the SDE solutions. We show that essentially any path-dependent SDE can be approximated by a suitable signature SDE. This requires the development of a dedicated well-posedness theory. Building on this foundation, we prove in particular that SDEs whose coefficients are entire functions of the signature serve as dynamic universal approximators for path-dependent SDEs. Since these signature SDEs exhibit an affine structure with respect to the lifted signature state, this result implies universality of affine processes within the class of Itô-processes. We also outline how a similar approach can be used to tackle generic path-dependent optimal control problems.

• Medina-Cetina, Zenon (2026). Probabilistic Simulation of Risk Scenarios. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  A new set of theory and methods of Artificial Intelligence called Bayesian Risk Networks for Decision-Making are presented for the first time. These are introduce using a simple application where the fundamental elements required to make systematic optimal decisions are outlined. Risk here is defined as the sequence of events needed to make an informed decision: a driving event, a system posed by the driving event, and the impact on the system (i.e., social, economic, and/or environmental). This approach includes the definition of a subject’s, organization’s, and/or process’s current, best, and worst risk scenarios, representing cause-effect relations of all participating variables and its degree of uncertainty when thought as interdependent systems. Knowing a system’s current risk scenario vs. its best, and worst, probabilistically, allows one to assess the ‘distance’ from the current state of risk to its worst in terms of probability metrics, providing an ‘initial condition’ to make a decision (i.e., it is not the same to know that the system’s state of risk is closer to the best risk scenario than to be closer to the worst risk scenario, while knowing the degree of confidence representing each risk scenario). This emerging risk-based approach is thought to revolutionize how AI optimal decision-making should be represented and quantified, using the Bayesian unique features to simulate forward (prognosis) and inverse (diagnosis) risk scenarios, and its updating capabilities as data becomes available to inform a system’s state of risk.

• Ortega, Antonio (2026). Machine Learning on Graphs: Combining Local and Global Information. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Conventional graph machine learning techniques rely heavily on simple message-passing algorithms, thereby avoiding the complexity of computing eigendecompositions on large-scale graphs. However, these approaches require a large number of layers to aggregate information from poorly connected parts of the graph, leading to phenomena such as oversmoothing and oversquashing. Solutions to this problem in the literature include graph rewiring and the use of transformers, which enable the creation of long-range connections. As an alternative, we propose a local-to-global approach (L2GNet) in which the graph is first analyzed, and the learning architecture is adapted to its structure. Specifically, after identifying graph clusters, we decompose the global graph Fourier transform into localized (cluster-based) terms and aggregation terms based on Cauchy matrices. This enables spectral analysis within each cluster (avoiding oversmoothing), while making connections across clusters simple (avoiding oversquashing). Our experimental results demonstrate that we can achieve results comparable to transformer architectures with far fewer learnable parameters.

• Isufi, Elvin (2026). Relational Learning with Covariance Information. doi: https:/www.sure-ai.no/events/sure-ai-annual-conference-2026/. Fulltekst i vitenarkiv Vis sammendrag

  Covariance information is commonly used in machine learning to reveal data interdependencies such as network topology inference (e.g., graphical lasso) and dimensionality reduction (e.g., Principal Component Analysis (PCA)). However, such information is often only the first step in a machine learning pipeline that is performed separately from the task. Because of finite-data estimation errors, we end up working with a sample covariance matrix that leads to uncertainties in its spectrum. For example, PCA is notoriously unstable to covariance estimation errors, i.e., small data perturbations might lead to large changes in principal directions. To address this, coVariance Neural Networks (VNNs) were introduced. These networks perform graph convolutions on the sample covariance matrix, an operation that, similarly to PCA, modulates the data principal components, but with enhanced representation power and greater stability against covariance estimation errors. However, in sparse, high-dimensional settings with limited data, covariance estimation is particularly difficult, which hinders VNNs’ performance despite their stability. Sparse VNNs overcome this by using theoretically grounded covariance sparsification, which improves stability, reduces the impact of spurious correlations on performance and improves computation and memory efficiency. The success of VNNs motivates their extension to different settings. SpatioTemporal VNNs, for instance, process multivariate time series by applying graph convolutions on the online estimated covariance and temporal convolutions over time, achieving stability to estimation errors in both covariance and model parameters due to streaming data. Finally, VNNs’ stability promotes fairness in datasets with poorly represented groups. Building on this, Fair VNNs leverage equitable covariance estimates and fairness penalties in the loss function to ensure a more balanced treatment of these groups.

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