Model Reduction and Neural Networks

Derniers papiers

• Physics-informed deep learning and compressive collocation for high-dimensional diffusion-reaction equations: practical existence theory and numerics

  Simone Brugiapaglia, Nick Dexter, Samir Karam, Weiqi Wang · 12 novembre 2025

  On the forefront of scientific computing, Deep Learning (DL), i.e., machine learning with Deep Neural Networks (DNNs), has emerged a powerful new tool for solving Partial Differential Equations (PDEs). It has been observed that DNNs are particularly well suited to weakening the effect of the curse o…

• Natural gradient and parameter estimation for quantum Boltzmann machines

  Dhrumil Patel, Mark M. Wilde · 12 novembre 2025

  Thermal states play a fundamental role in various areas of physics, and they are becoming increasingly important in quantum information science, with applications related to semi-definite programming, quantum Boltzmann machine learning, Hamiltonian learning, and the related task of estimating the pa…

• Automatic Grid Updates for Kolmogorov-Arnold Networks using Layer Histograms

  Jamison Moody, James Usevitch · 12 novembre 2025

  Kolmogorov-Arnold Networks (KANs) are a class of neural networks that have received increased attention in recent literature. In contrast to MLPs, KANs leverage parameterized, trainable activation functions and offer several benefits including improved interpretability and higher accuracy on learnin…

• Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics

  Hojin Kim, Varun Shankar, Venkatasubramanian Viswanathan, Romit Maulik · 12 novembre 2025

  Differentiable physical simulators are proving to be valuable tools for developing data-driven models for computational fluid dynamics (CFD). In particular, these simulators enable end-to-end training of machine learning (ML) models embedded within CFD solvers. This paradigm enables novel algorithms…

• Data-assimilated model-informed reinforcement learning

  Defne E. Ozan, Andrea N\'ovoa, Georgios Rigas, Luca Magri · 11 novembre 2025

  The control of spatio-temporally chaos is challenging because of high dimensionality and unpredictability. Model-free reinforcement learning (RL) discovers optimal control policies by interacting with the system, typically requiring observations of the full physical state. In practice, sensors often…

• SVDQuant: Absorbing Outliers by Low-Rank Components for 4-Bit Diffusion Models

  Muyang Li, Yujun Lin, Zhekai Zhang, Tianle Cai, Xiuyu Li, Junxian Guo, Enze Xie, Chenlin Meng, Jun-Yan Zhu, Song Han · 11 novembre 2025

  Diffusion models can effectively generate high-quality images. However, as they scale, rising memory demands and higher latency pose substantial deployment challenges. In this work, we aim to accelerate diffusion models by quantizing their weights and activations to 4 bits. At such an aggressive lev…

• Zero-Shot Function Encoder-Based Differentiable Predictive Control

  Hassan Iqbal, Xingjian Li, Tyler Ingebrand, Adam Thorpe, Krishna Kumar, Ufuk Topcu, J\'an Drgo\v{n}a · 11 novembre 2025

  We introduce a differentiable framework for zero-shot adaptive control over parametric families of nonlinear dynamical systems. Our approach integrates a function encoder-based neural ODE (FE-NODE) for modeling system dynamics with a differentiable predictive control (DPC) for offline self-supervise…

• A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series

  Xuyang Li, John Harlim, Romit Maulik · 11 novembre 2025

  Accurate forecasting of complex high-dimensional dynamical systems from observational data is essential for several applications across science and engineering. A key challenge, however, is that real-world measurements are often corrupted by noise, which severely degrades the performance of data-dri…

• Learning Stochastic Multiscale Models

  Andrew F. Ilersich, Prasanth B. Nair · 11 novembre 2025

  The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at the finest relevant scales, leading to a high-dimensional st…

• Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learning

  Kianoosh Taghikhani, Yusuke Yamazaki, Jerry Paul Varghese, Markus Apel, Reza Najian Asl, Shahed Rezaei · 11 novembre 2025

  We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to approximate the nonlinear parametric solutionof the governing e…

• Attention on flow control: transformer-based reinforcement learning for lift regulation in highly disturbed flows

  Zhecheng Liu (University of California, Los Angeles), Jeff D. Eldredge (University of California, Los Angeles) · 11 novembre 2025

  A linear flow control strategy designed for weak disturbances may not remain effective in sequences of strong disturbances due to nonlinear interactions, but it is sensible to leverage it for developing a better strategy. In the present study, we propose a transformer-based reinforcement learning (R…

• Transolver is a Linear Transformer: Revisiting Physics-Attention through the Lens of Linear Attention

  Wenjie Hu, Sidun Liu, Peng Qiao, Zhenglun Sun, Yong Dou · 11 novembre 2025

  Recent advances in Transformer-based Neural Operators have enabled significant progress in data-driven solvers for Partial Differential Equations (PDEs). Most current research has focused on reducing the quadratic complexity of attention to address the resulting low training and inference efficiency…

• Physics-Informed Design of Input Convex Neural Networks for Consistency Optimal Transport Flow Matching

  Fanghui Song, Zhongjian Wang, Jiebao Sun · 11 novembre 2025

  We propose a consistency model based on the optimal-transport flow. A physics-informed design of partially input-convex neural networks (PICNN) plays a central role in constructing the flow field that emulates the displacement interpolation. During the training stage, we couple the Hamilton-Jacobi (…

• Physics-Guided Machine Learning for Uncertainty Quantification in Turbulence Models

  Minghan Chu, Weicheng Qian · 11 novembre 2025

  Predicting the evolution of turbulent flows is central across science and engineering. Most studies rely on simulations with turbulence models, whose empirical simplifications introduce epistemic uncertainty. The Eigenspace Perturbation Method (EPM) is a widely used physics-based approach to quantif…

• AutoHood3D: A Multi-Modal Benchmark for Automotive Hood Design and Fluid-Structure Interaction

  Vansh Sharma, Harish Jai Ganesh, Maryam Akram, Wanjiao Liu, Venkat Raman · 11 novembre 2025

  This study presents a new high-fidelity multi-modal dataset containing 16000+ geometric variants of automotive hoods useful for machine learning (ML) applications such as engineering component design and process optimization, and multiphysics system surrogates. The dataset is centered on a practical…

• Walsh-Hadamard Neural Operators for Solving PDEs with Discontinuous Coefficients

  Giorrgio M. Cavallazzi, Miguel Perex Cuadrado, Alfredo Pinelli · 11 novembre 2025

  Neural operators have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). However, standard spectral methods based on Fourier transforms struggle with problems involving discontinuous coefficients due to the Gibbs phenomenon and poor representation of …

• Self-adaptive weighting and sampling for physics-informed neural networks

  Wenqian Chen, Amanda Howard, Panos Stinis · 10 novembre 2025

  Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and efficiency. In this work, we introduce a hybrid adaptive sampling …

• Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulators

  Naveen Raj Manoharan, Hassan Iqbal, Krishna Kumar · 10 novembre 2025

  Graph network-based simulators (GNS) have demonstrated strong potential for learning particle-based physics (such as fluids, deformable solids, and granular flows) while generalizing to unseen geometries due to their inherent inductive biases. However, existing models are typically trained for a sin…

• DeepPAAC: A New Deep Galerkin Method for Principal-Agent Problems

  Michael Ludkovski, Changgen Xie, Zimu Zhu · 7 novembre 2025

  We consider numerical resolution of principal-agent (PA) problems in continuous time. We formulate a generic PA model with continuous and lump payments and a multi-dimensional strategy of the agent. To tackle the resulting Hamilton-Jacobi-Bellman equation with an implicit Hamiltonian we develop a no…

• Deep Dictionary-Free Method for Identifying Linear Model of Nonlinear System with Input Delay

  Patrik Val\'abek, Marek Wadinger, Michal Kvasnica, Martin Klau\v{c}o · 7 novembre 2025

  Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail in these contexts, necessitating innovative approaches. Thi…

• Uncertainties in Physics-informed Inverse Problems: The Hidden Risk in Scientific AI

  Yoh-ichi Mototake, Makoto Sasaki · 7 novembre 2025

  Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize physical systems. This framework enables data-driven understan…

• Physics-Informed Neural Networks and Neural Operators for Parametric PDEs: A Human-AI Collaborative Analysis

  Zhuo Zhang, Xiong Xiong, Sen Zhang, Yuan Zhao, Xi Yang · 7 novembre 2025

  PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter space exploration prohibitively expensive. Recent machine learn…

• ODE approximation for the Adam algorithm: General and overparametrized setting

  Steffen Dereich, Arnulf Jentzen, Sebastian Kassing · 7 novembre 2025

  The Adam optimizer is currently presumably the most popular optimization method in deep learning. In this article we develop an ODE based method to study the Adam optimizer in a fast-slow scaling regime. For fixed momentum parameters and vanishing step-sizes, we show that the Adam algorithm is an as…

• Quamba2: A Robust and Scalable Post-training Quantization Framework for Selective State Space Models

  Hung-Yueh Chiang, Chi-Chih Chang, Natalia Frumkin, Kai-Chiang Wu, Mohamed S. Abdelfattah, Diana Marculescu · 7 novembre 2025

  State Space Models (SSMs) are emerging as a compelling alternative to Transformers because of their consistent memory usage and high performance. Despite this, scaling up SSMs on cloud services or limited-resource devices is challenging due to their storage requirements and computational power. To o…

• Projection Methods for Operator Learning and Universal Approximation

  Emanuele Zappala · 7 novembre 2025

  We obtain a new universal approximation theorem for continuous (possibly nonlinear) operators on arbitrary Banach spaces using the Leray-Schauder mapping. Moreover, we introduce and study a method for operator learning in Banach spaces $L^p$ of functions with multiple variables, based on orthogonal …