Model Reduction and Neural Networks

Derniers papiers

• Sparse maximal update parameterization: A holistic approach to sparse training dynamics

  Nolan Dey, Shane Bergsma, Joel Hestness · 4 février 2026

  Several challenges make it difficult for sparse neural networks to compete with dense models. First, setting a large fraction of weights to zero impairs forward and gradient signal propagation. Second, sparse studies often need to test multiple sparsity levels, while also introducing new hyperparame…

• Koopman Autoencoders with Continuous-Time Latent Dynamics for Fluid Dynamics Forecasting

  Rares Grozavescu, Pengyu Zhang, Etienne Meunier, Mark Girolami · 4 février 2026

  Data-driven surrogate models have emerged as powerful tools for accelerating the simulation of turbulent flows. However, classical approaches which perform autoregressive rollouts often trade off between strong short-term accuracy and long-horizon stability. Koopman autoencoders, inspired by Koopman…

• Ultra Fast PDE Solving via Physics Guided Few-step Diffusion

  Cindy Xiangrui Kong, Yueqi Wang, Haoyang Zheng, Weijian Luo, Guang Lin · 4 février 2026

  Diffusion-based models have demonstrated impressive accuracy and generalization in solving partial differential equations (PDEs). However, they still face significant limitations, such as high sampling costs and insufficient physical consistency, stemming from their many-step iterative sampling mech…

• Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs

  Benjamin D. Shaffer, Shawn Koohy, Brooks Kinch, M. Ani Hsieh, Nathaniel Trask · 4 février 2026

  We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we introduce General-Geometry Neural Whitney Forms (Geo-NeW): a …

• Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach

  Naoki Sato, Hideaki Iiduka · 4 février 2026

  Deep equilibrium models (DEQs) achieve infinitely deep network representations without stacking layers by exploring fixed points of layer transformations in neural networks. Such models constitute an innovative approach that achieves performance comparable to state-of-the-art methods in many large-s…

• Learnable Koopman-Enhanced Transformer-Based Time Series Forecasting with Spectral Control

  Ali Forootani, Raffaele Iervolino · 4 février 2026

  This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman variants-scalar-gated, per-mode gated, MLP-shaped spectral mapping, and low-ran…

• Manifold-Constrained Energy-Based Transition Models for Offline Reinforcement Learning

  Zeyu Fang, Zuyuan Zhang, Mahdi Imani, Tian Lan · 4 février 2026

  Model-based offline reinforcement learning is brittle under distribution shift: policy improvement drives rollouts into state--action regions weakly supported by the dataset, where compounding model error yields severe value overestimation. We propose Manifold-Constrained Energy-based Transition Mod…

• Optimization and Generation in Aerodynamics Inverse Design

  Huaguan Chen, Ning Lin, Luxi Chen, Rui Zhang, Wenbing Huang, Chongxuan Li, Hao Sun · 4 février 2026

  Inverse design with physics-based objectives is challenging because it couples high-dimensional geometry with expensive simulations, as exemplified by aerodynamic shape optimization for drag reduction. We revisit inverse design through two canonical solutions, the optimal design point and the optima…

• SymPlex: A Structure-Aware Transformer for Symbolic PDE Solving

  Yesom Park, Annie C. Lu, Shao-Ching Huang, Qiyang Hu, Y. Sungtaek Ju, Stanley Osher · 4 février 2026

  We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as tree-structured decision-making and optimizes candidate solutions using…

• naPINN: Noise-Adaptive Physics-Informed Neural Networks for Recovering Physics from Corrupted Measurement

  Hankyeol Kim, Pilsung Kang · 4 février 2026

  Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data. However, their performance degrades significantly under complex measurement noise and gross outliers. To address this issue, we propose the Noise-A…

• Multi-Level Monte Carlo Training of Neural Operators

  James Rowbottom, Stefania Fresca, Pietro Lio, Carola-Bibiane Sch\"onlieb, Nicolas Boull\'e · 4 février 2026

  Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually, expensive to train for large-scale problems at high-resoluti…

• Equilibrium Propagation for Non-Conservative Systems

  Antonino Emanuele Scurria, Dimitri Vanden Abeele, Bortolo Matteo Mognetti, Serge Massar · 4 février 2026

  Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning. In its original formulation it is limited to conservative systems, $\textit{i.e.}$ to dynamics which derive from an energy function. Given their im…

• Geometry-Preserving Neural Architectures on Manifolds with Boundary

  Karthik Elamvazhuthi, Shiba Biswal, Kian Rosenblum, Arushi Katyal, Tianli Qu, Grady Ma, Rishi Sonthalia · 4 février 2026

  Preserving geometric structure is important in learning. We propose a unified class of geometry-aware architectures that interleave geometric updates between layers, where both projection layers and intrinsic exponential map updates arise as discretizations of projected dynamical systems on manifold…

• Sparse identification of nonlinear dynamics with library optimization mechanism: Recursive long-term prediction perspective

  Ansei Yonezawa, Heisei Yonezawa, Shuichi Yahagi, Itsuro Kajiwara, Shinya Kijimoto, Hikaru Taniuchi, Kentaro Murakami · 3 février 2026

  The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given basis functions. A major challenge in SINDy is the design of a l…

• Learning Heat-based Equations in Self-similar variables

  Shihao Wang, Qipeng Qian, Jingquan Wang · 3 février 2026

  We study solution learning for heat-based equations in self-similar variables (SSV). We develop an SSV training framework compatible with standard neural-operator training. We instantiate this framework on the two-dimensional incompressible Navier-Stokes equations and the one-dimensional viscous Bur…

• Learning Operators through Coefficient Mappings in Fixed Basis Spaces

  Chuqi Chen, Yang Xiang, Weihong Zhang · 3 février 2026

  Operator learning has emerged as a promising paradigm for approximating solution operators of partial differential equations (PDEs). However, conventional approaches typically rely on pointwise function discretizations, which often suffer from the curse of dimensionality, mesh dependence, and prohib…

• WAKESET: A Large-Scale, High-Reynolds Number Flow Dataset for Machine Learning of Turbulent Wake Dynamics

  Zachary Cooper-Baldock, Paulo E. Santos, Russell S. A. Brinkworth, Karl Sammut · 3 février 2026

  Machine learning (ML) offers transformative potential for computational fluid dynamics (CFD), promising to accelerate simulations, improve turbulence modelling, and enable real-time flow prediction and control-capabilities that could fundamentally change how engineers approach fluid dynamics problem…

• Parametrization of subgrid scales in long-term simulations of the shallow-water equations using machine learning and convex limiting

  Md Amran Hossan Mojamder, Zhihang Xu, Min Wang, Ilya Timofeyev · 3 février 2026

  We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local parametrization that uses a four-point computational stencil, w…

• Stabilizing Fixed-Point Iteration for Markov Chain Poisson Equations

  Yang Xu, Vaneet Aggarwal · 3 février 2026

  Poisson equations underpin average-reward reinforcement learning, but beyond ergodicity they can be ill-posed, meaning that solutions are non-unique and standard fixed point iterations can oscillate on reducible or periodic chains. We study finite-state Markov chains with $n$ states and transition m…

• EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations

  Hamidreza Eivazi, Jendrik-Alexander Tr\"oger, Stefan Wittek, Stefan Hartmann, Andreas Rausch · 3 février 2026

  Multiscale problems are ubiquitous in physics. Numerical simulations of such problems by solving partial differential equations (PDEs) at high resolution are computationally too expensive for many-query scenarios, such as uncertainty quantification, remeshing applications, and topology optimization.…

• FluxNet: Learning Capacity-Constrained Local Transport Operators for Conservative and Bounded PDE Surrogates

  Zishuo Lan, Junjie Li, Lei Wang, Jincheng Wang · 3 février 2026

  Autoregressive learning of time-stepping operators offers an effective approach to data-driven PDE simulation on grids. For conservation laws, however, long-horizon rollouts are often destabilized when learned updates violate global conservation and, in many applications, additional state bounds suc…

• Adaptive Momentum and Nonlinear Damping for Neural Network Training

  Aikaterini Karoni, Rajit Rajpal, Benedict Leimkuhler, Gabriel Stoltz · 3 février 2026

  We propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape curvature to maintain stability without sacrificing convergence …

• Training-free score-based diffusion for parameter-dependent stochastic dynamical systems

  Minglei Yang, Sicheng He · 3 février 2026

  Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of machine learning methods in learning SDE dynamics, existing…

• Multimodal Scientific Learning Beyond Diffusions and Flows

  Leonardo Ferreira Guilhoto, Akshat Kaushal, Paris Perdikaris · 3 février 2026

  Scientific machine learning (SciML) increasingly requires models that capture multimodal conditional uncertainty arising from ill-posed inverse problems, multistability, and chaotic dynamics. While recent work has favored highly expressive implicit generative models such as diffusion and flow-based …

• Generative AI-enhanced Probabilistic Multi-Fidelity Surrogate Modeling Via Transfer Learning

  Jice Zeng, David Barajas-Solano, Hui Chen · 3 février 2026

  The performance of machine learning surrogates is critically dependent on data quality and quantity. This presents a major challenge, as high-fidelity (HF) data is often scarce and computationally expensive to acquire, while low-fidelity (LF) data is abundant but less accurate. To address this data …