Model Reduction and Neural Networks

Derniers papiers

• Sinkhorn-Drifting Generative Models

  Ping He, Om Khangaonkar, Hamed Pirsiavash, Yikun Bai, Soheil Kolouri · 16 mars 2026

  We establish a theoretical link between the recently proposed "drifting" generative dynamics and gradient flows induced by the Sinkhorn divergence. In a particle discretization, the drift field admits a cross-minus-self decomposition: an attractive term toward the target distribution and a repulsive…

• Surrogates for Physics-based and Data-driven Modelling of Parametric Systems: Review and New Perspectives

  Matteo Giacomini, Pedro D\'iez · 16 mars 2026

  Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a wide range of applications, including optimisation, control…

• Adaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems

  Dibyajyoti Chakraborty, Hojin Kim, Romit Maulik · 16 mars 2026

  High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are deterministic, for example when neural operators are involved. However, …

• Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs

  Zhangyong Liang, Ji Zhang · 16 mars 2026

  Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable. The problem becomes even more severe when the model must also predict beyond the training time range. Existing methods u…

• A Spectral Revisit of the Distributional Bellman Operator under the Cram\'er Metric

  Keru Wang, Yixin Deng, Yao Lyu, Stephen Redmond, Shengbo Eben Li · 16 mars 2026

  Distributional reinforcement learning (DRL) studies the evolution of full return distributions under Bellman updates rather than focusing on expected values. A classical result is that the distributional Bellman operator is contractive under the Cram\'er metric, which corresponds to an $L^2$ geometr…

• FastLSQ: Solving PDEs in One Shot via Fourier Features with Exact Analytical Derivatives

  Antonin Sulc · 16 mars 2026

  We present FastLSQ, a framework for PDE solving and inverse problems built on trigonometric random Fourier features with exact analytical derivatives. Trigonometric features admit closed-form derivatives of any order in $\calO(1)$, enabling graph-free operator assembly without autodiff. Linear PDEs:…

• Bases of Steerable Kernels for Equivariant CNNs: From 2D Rotations to the Lorentz Group

  Alan Garbarz · 16 mars 2026

  We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different symmetry groups and for feature maps of arbitrary tensor type. A m…

• Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws

  Kaushik Bhattacharya, Lianghao Cao, Andrew Stuart · 16 mars 2026

  History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation …

• Inverse Neural Operator for ODE Parameter Optimization

  Zhi-Song Liu, Wenqing Peng, Helmi Toropainen, Ammar Kheder, Andreas Rupp, Holger Froning, Xiaojie Lin, Michael Boy · 13 mars 2026

  We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a differentiable surrogate that reconstructs full ODE trajectories from ar…

• Context-dependent manifold learning: A neuromodulated constrained autoencoder approach

  J\'er\^ome Adriaens (Neuroengineering Lab, Department of Electrical Engineering and Computer Science, University of Li\`ege), Guillaume Drion (Neuroengineering Lab, Department of Electrical Engineering and Computer Science, University of Li\`ege), Pierre Sacr\'e (Neuroengineering Lab, Department of Electrical Engineering and Computer Science, University of Li\`ege) · 13 mars 2026

  Constrained autoencoders (cAE) provide a successful path towards interpretable dimensionality reduction by enforcing geometric structure on latent spaces. However, standard cAEs cannot adapt to varying physical parameters or environmental conditions without conflating these contextual shifts with th…

• Ill-Conditioning in Dictionary-Based Dynamic-Equation Learning: A Systems Biology Case Study

  Yuxiang Feng, Niall M Mangan, Manu Jayadharan · 13 mars 2026

  Data-driven discovery of governing equations from time-series data provides a powerful framework for understanding complex biological systems. Library-based approaches that use sparse regression over candidate functions have shown considerable promise, but they face a critical challenge when candida…

• Hypercomplex Widely Linear Processing: Fundamentals for Quaternion Machine Learning

  Sayed Pouria Talebi, Clive Cheong Took · 13 mars 2026

  Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the success of quaternions. The most useful feature of quaternions li…

• Deep Eigenspace Network for Parametric Non-self-adjoint Eigenvalue Problems

  H. Li, J. Sun, Z. Zhang · 13 mars 2026

  We consider operator learning for efficiently solving parametric non-self-adjoint eigenvalue problems. To overcome the spectral instability and mode switching associated with non-self-adjoint operators, we choose to learn the eigenspace rather than individual eigenfunctions. In particular, we propos…

• Structure-Aware Epistemic Uncertainty Quantification for Neural Operator PDE Surrogates

  Haoze Song, Zhihao Li, Mengyi Deng, Xin Li, Duyi Pan, Zhilu Lai, Wei Wang · 13 mars 2026

  Neural operators (NOs) provide fast, resolution-invariant surrogates for mapping input fields to PDE solution fields, but their predictions can exhibit significant epistemic uncertainty due to finite data, imperfect optimization, and distribution shift. For practical deployment in scientific computi…

• UniPINN: A Unified PINN Framework for Multi-task Learning of Diverse Navier-Stokes Equations

  Dengdi Sun, Jie Chen, Xiao Wang, Jin Tang · 12 mars 2026

  Physics-Informed Neural Networks (PINNs) have shown promise in solving incompressible Navier-Stokes equations, yet existing approaches are predominantly designed for single-flow settings. When extended to multi-flow scenarios, these methods face three key challenges: (1) difficulty in simultaneously…

• Panda: A pretrained forecast model for chaotic dynamics

  Jeffrey Lai, Anthony Bao, William Gilpin · 12 mars 2026

  Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained on individual time series, or foundation mode…

• MCMC Informed Neural Emulators for Uncertainty Quantification in Dynamical Systems

  Heikki Haario, Zhi-Song Liu, Martin Simon, Hendrik Weichel · 12 mars 2026

  Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model parameters is available. Here we study the common opposite situa…

• Gradient Flow Drifting: Generative Modeling via Wasserstein Gradient Flows of KDE-Approximated Divergences

  Jiarui Cao, Zixuan Wei, Yuxin Liu · 12 mars 2026

  We reveal a precise mathematical framework about a new family of generative models which we call Gradient Flow Drifting. With this framework, we prove an equivalence between the recently proposed Drifting Model and the Wasserstein gradient flow of the forward KL divergence under kernel density estim…

• Dynamics-Informed Deep Learning for Predicting Extreme Events

  Eirini Katsidoniotaki, Themistoklis P. Sapsis · 12 mars 2026

  Predicting extreme events in high-dimensional chaotic dynamical systems remains a fundamental challenge, as such events are rare, intermittent, and arise from transient dynamical mechanisms that are difficult to infer from limited observations. Accordingly, real-time forecasting calls for precursors…

• Factorized Neural Implicit DMD for Parametric Dynamics

  Siyuan Chen, Zhecheng Wang, Yixin Chen, Yue Chang, Peter Yichen Chen, Eitan Grinspun, Jonathan Panuelos · 12 mars 2026

  A data-driven, model-free approach to modeling the temporal evolution of physical systems mitigates the need for explicit knowledge of the governing equations. Even when physical priors such as partial differential equations are available, such systems often reside in high-dimensional state spaces a…

• Flow Field Reconstruction via Voronoi-Enhanced Physics-Informed Neural Networks with End-to-End Sensor Placement Optimization

  Renjie Xiao, Bingteng Sun, Yiling Chen, Lin Lu, Qiang Du, Junqiang Zhu · 11 mars 2026

  (short version abstract, full in article)High-fidelity flow field reconstruction is important in fluid dynamics, but it is challenged by sparse and spatiotemporally incomplete sensor measurements, as well as failures of pre-deployed measurement points that can invalidate pre-trained reconstruction m…

• Upper Generalization Bounds for Neural Oscillators

  Zifeng Huang, Konstantin M. Zuev, Yong Xia, Michael Beer · 11 mars 2026

  Neural oscillators that originate from the second-order ordinary differential equations (ODEs) have shown competitive performance in learning mappings between dynamic loads and responses of complex nonlinear structural systems. Despite this empirical success, theoretically quantifying the generaliza…

• Correction of Transformer-Based Models with Smoothing Pseudo-Projector

  Vitaly Bulgakov · 11 mars 2026

  The pseudo-projector is a lightweight modification that can be integrated into existing language models and other neural networks without altering their core architecture. It can be viewed as a hidden-representation corrector that reduces sensitivity to noise by suppressing directions induced by lab…

• The Coupling Within: Flow Matching via Distilled Normalizing Flows

  David Berthelot, Tianrong Chen, Jiatao Gu, Marco Cuturi, Laurent Dinh, Bhavik Chandna, Michal Klein, Josh Susskind, Shuangfei Zhai · 11 mars 2026

  Flow models have rapidly become the go-to method for training and deploying large-scale generators, owing their success to inference-time flexibility via adjustable integration steps. A crucial ingredient in flow training is the choice of coupling measure for sampling noise/data pairs that define th…

• NN-OpInf: an operator inference approach using structure-preserving composable neural networks

  Eric Parish, Anthony Gruber, Patrick Blonigan, Irina Tezaur · 10 mars 2026

  We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns latent dynamics from snapshot data, enforcing local operator stru…