Model Reduction and Neural Networks

Derniers papiers

• Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces

  Nicolas Hoischen, Petar Bevanda, Stefan Sosnowski, Sandra Hirche, Boris Houska · 3 novembre 2025

  This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only a control penalty function and constraints a…

• FMint-SDE: A Multimodal Foundation Model for Accelerating Numerical Simulation of SDEs via Error Correction

  Jiaxin Yuan, Haizhao Yang, Maria Cameron · 3 novembre 2025

  Fast and accurate simulation of dynamical systems is a fundamental challenge across scientific and engineering domains. Traditional numerical integrators often face a trade-off between accuracy and computational efficiency, while existing neural network-based approaches typically require training a …

• Domain decomposition architectures and Gauss-Newton training for physics-informed neural networks

  Alexander Heinlein, Taniya Kapoor · 3 novembre 2025

  Approximating the solutions of boundary value problems governed by partial differential equations with neural networks is challenging, largely due to the difficult training process. This difficulty can be partly explained by the spectral bias, that is, the slower convergence of high-frequency compon…

• Hysteresis Activation Function for Efficient Inference

  Moshe Kimhi, Idan Kashani, Avi Mendelson, Chaim Baskin · 31 octobre 2025

  The widely used ReLU is favored for its hardware efficiency, {as the implementation at inference is a one bit sign case,} yet suffers from issues such as the ``dying ReLU'' problem, where during training, neurons fail to activate and constantly remain at zero, as highlighted by Lu et al. Traditional…

• Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training

  Hong Wang, Haiyang Xin, Jie Wang, Xuanze Yang, Fei Zha, Huanshuo Dong, Yan Jiang · 31 octobre 2025

  Pre-training has proven effective in addressing data scarcity and performance limitations in solving PDE problems with neural operators. However, challenges remain due to the heterogeneity of PDE datasets in equation types, which leads to high errors in mixed training. Additionally, dense pre-traini…

• Scaling Up Liquid-Resistance Liquid-Capacitance Networks for Efficient Sequence Modeling

  M\'onika Farsang, Ramin Hasani, Daniela Rus, Radu Grosu · 30 octobre 2025

  We present LrcSSM, a $\textit{non-linear}$ recurrent model that processes long sequences as fast as today's linear state-space layers. By forcing its Jacobian matrix to be diagonal, the full sequence can be solved in parallel, giving $\mathcal{O}(TD)$ time and memory and only $\mathcal{O}(\log T)$ s…

• Meshless solutions of PDE inverse problems on irregular geometries

  James V. Roggeveen, Michael P. Brenner · 30 octobre 2025

  Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral bases on arbitrary spatiotemporal domains, whereby the basis …

• Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutions

  Naoki Kiyohara, Edward Johns, Yingzhen Li · 30 octobre 2025

  Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between arbitrary time points. We introduce Neural Stochastic Flows (NSFs…

• LieSolver: A PDE-constrained solver for IBVPs using Lie symmetries

  Ren\'e P. Klausen, Ivan Timofeev, Johannes Frank, Jonas Naujoks, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek · 30 octobre 2025

  We introduce a method for efficiently solving initial-boundary value problems (IBVPs) that uses Lie symmetries to enforce the associated partial differential equation (PDE) exactly by construction. By leveraging symmetry transformations, the model inherently incorporates the physical laws and learns…

• Hierarchical Physics-Embedded Learning for Spatiotemporal Dynamical Systems

  Xizhe Wang, Xiaobin Song, Qingshan Jia, Hongbo Zhao, Benben Jiang · 30 octobre 2025

  Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first principles, due to their inherent complexity, characterized b…

• MathBode: Understanding LLM Reasoning with Dynamical Systems

  Charles L. Wang · 29 octobre 2025

  This paper presents MathBode, a dynamic diagnostic for mathematical reasoning in large language models (LLMs). Instead of one-shot accuracy, MathBode treats each parametric problem as a system: we drive a single parameter sinusoidally and fit first-harmonic responses of model outputs and exact solut…

• Enforcing boundary conditions for physics-informed neural operators

  Niklas G\"oschel, Sebastian G\"otschel, Daniel Ruprecht · 29 octobre 2025

  Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partial differential equations. Boundary conditions can be enforced either weakly by penalizing deviations in the loss functio…

• Physics-Informed Extreme Learning Machine (PIELM): Opportunities and Challenges

  He Yang, Fei Ren, Hai-Sui Yu, Xiaohui Chen, Pei-Zhi Zhuang · 29 octobre 2025

  We are very delighted to see the fast development of physics-informed extreme learning machine (PIELM) in recent years for higher computation efficiency and accuracy in physics-informed machine learning. As a summary or review on PIELM is currently not available, we would like to take this opportuni…

• Unlocking Out-of-Distribution Generalization in Dynamics through Physics-Guided Augmentation

  Fan Xu, Hao Wu, Kun Wang, Nan Wang, Qingsong Wen, Xian Wu, Wei Gong, Xibin Zhao · 29 octobre 2025

  In dynamical system modeling, traditional numerical methods are limited by high computational costs, while modern data-driven approaches struggle with data scarcity and distribution shifts. To address these fundamental limitations, we first propose SPARK, a physics-guided quantitative augmentation p…

• Efficient Global-Local Fusion Sampling for Physics-Informed Neural Networks

  Jiaqi Luo, Shixin Xu, Zhouwang Yang · 29 octobre 2025

  The accuracy of Physics-Informed Neural Networks (PINNs) critically depends on the placement of collocation points, as the PDE loss is approximated through sampling over the solution domain. Global sampling ensures stability by covering the entire domain but requires many samples and is computationa…

• STNet: Spectral Transformation Network for Solving Operator Eigenvalue Problem

  Hong Wang, Jiang Yixuan, Jie Wang, Xinyi Li, Jian Luo, Huanshuo Dong · 29 octobre 2025

  Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to address this challenge by iteratively updating neural networks…

• A data free neural operator enabling fast inference of 2D and 3D Navier Stokes equations

  Junho Choi, Teng-Yuan Chang, Namjung Kim, Youngjoon Hong · 29 octobre 2025

  Ensemble simulations of high-dimensional flow models (e.g., Navier Stokes type PDEs) are computationally prohibitive for real time applications. Neural operators enable fast inference but are limited by costly data requirements and poor generalization to 3D flows. We present a data-free operator net…

• A Physics-informed Multi-resolution Neural Operator

  Sumanta Roy, Bahador Bahmani, Ioannis G. Kevrekidis, Michael D. Shields · 29 octobre 2025

  The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to obtain in some real-world engineering applications. These datas…

• Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers

  Nima Hosseini Dashtbayaz, Hesam Salehipour, Adrian Butscher, Nigel Morris · 28 octobre 2025

  Reduced-order modeling (ROM) of time-dependent and parameterized differential equations aims to accelerate the simulation of complex high-dimensional systems by learning a compact latent manifold representation that captures the characteristics of the solution fields and their time-dependent dynamic…

• Koopman Eigenfunction-Based Identification and Optimal Nonlinear Control of Turbojet Engine

  David Grasev · 28 octobre 2025

  Gas turbine engines are complex and highly nonlinear dynamical systems. Deriving their physics-based models can be challenging because it requires performance characteristics that are not always available, often leading to many simplifying assumptions. This paper discusses the limitations of convent…

• Analysis of accuracy and efficiency of neural networks to simulate Navier-Stokes fluid flows with obstacles

  Rui Hespanha, Elliot McGuire, Jo\~ao Hespanha · 28 octobre 2025

  Conventional fluid simulations can be time consuming and energy intensive. We researched the viability of a neural network for simulating incompressible fluids in a randomized obstacle-heavy environment, as an alternative to the numerical simulation of the Navier-Stokes equation. We hypothesized tha…

• Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domains

  Gareth Hardwick, Haizhao Yang · 28 octobre 2025

  Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive representations for traditional numerical methods and lead to d…

• An Introductory Guide to Koopman Learning

  Matthew J. Colbrook, Zlatko Drma\v{c}, Andrew Horning · 28 octobre 2025

  Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman learning, emphasizing rigorously convergent data-driven meth…

• Towards Deep Physics-Informed Kolmogorov-Arnold Networks

  Spyros Rigas, Fotios Anagnostopoulos, Michalis Papachristou, Georgios Alexandridis · 28 octobre 2025

  Since their introduction, Kolmogorov-Arnold Networks (KANs) have been successfully applied across several domains, with physics-informed machine learning (PIML) emerging as one of the areas where they have thrived. In the PIML setting, Chebyshev-based physics-informed KANs (cPIKANs) have become the …

• Predicting symbolic ODEs from multiple trajectories

  Yakup Emre \c{S}ahin, Niki Kilbertus, S\"oren Becker · 28 octobre 2025

  We introduce MIO, a transformer-based model for inferring symbolic ordinary differential equations (ODEs) from multiple observed trajectories of a dynamical system. By combining multiple instance learning with transformer-based symbolic regression, the model effectively leverages repeated observatio…