Model Reduction and Neural Networks

Derniers papiers

• Vidar: Embodied Video Diffusion Model for Generalist Manipulation

  Yao Feng, Hengkai Tan, Xinyi Mao, Chendong Xiang, Guodong Liu, Shuhe Huang, Hang Su, Jun Zhu · 23 décembre 2025

  Scaling general-purpose manipulation to new robot embodiments remains challenging: each platform typically needs large, homogeneous demonstrations, and end-to-end pixel-to-action pipelines may degenerate under background and viewpoint shifts. Based on previous advances in video-based robot control, …

• Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems

  Quercus Hernandez, Max Win, Thomas C. O'Connor, Paulo E. Arratia, Nathaniel Trask · 23 décembre 2025

  Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropi…

• A Critical Assessment of Pattern Comparisons Between POD and Autoencoders in Intraventricular Flows

  Eneko Lazpita, Andr\'es Bell-Navas, Jes\'us Garicano-Mena, Petros Koumoutsakos, Soledad Le Clainche · 23 décembre 2025

  Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can support early detection of cardiac deterioration. Conventional vi…

• On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning

  Mahdi Mohammadigohari, Giuseppe Di Fatta, Giuseppe Nicosia, Panos M. Pardalos · 23 décembre 2025

  The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition numbers in the weight matrices and introducing a tailored Sobo…

• An Inverse Scattering Inspired Fourier Neural Operator for Time-Dependent PDE Learning

  Rixin Yu · 23 décembre 2025

  Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the Fourier Neural Operator (FNO) and Koopman-inspired extension…

• A Riemannian Optimization Perspective of the Gauss-Newton Method for Feedforward Neural Networks

  Semih Cayci · 23 décembre 2025

  In this work, we establish non-asymptotic convergence bounds for the Gauss-Newton method in training neural networks with smooth activations. In the underparameterized regime, the Gauss-Newton gradient flow in parameter space induces a Riemannian gradient flow on a low-dimensional embedded submanifo…

• Multimodal Neural Operators for Real-Time Biomechanical Modelling of Traumatic Brain Injury

  Anusha Agarwal, Dibakar Roy Sarkar, Somdatta Goswami · 23 décembre 2025

  Background: Traumatic brain injury (TBI) is a major global health concern with 69 million annual cases. While neural operators have revolutionized scientific computing, existing architectures cannot handle the heterogeneous multimodal data (anatomical imaging, scalar demographics, and geometric cons…

• A Surrogate-Augmented Symbolic CFD-Driven Training Framework for Accelerating Multi-objective Physical Model Development

  Yuan Fang, Fabian Waschkowski, Maximilian Reissmann, Richard D. Sandberg, Takuo Oda, Koichi Tanimoto · 23 décembre 2025

  Computational Fluid Dynamics (CFD)-driven training combines machine learning (ML) with CFD solvers to develop physically consistent closure models with improved predictive accuracy. In the original framework, each ML-generated candidate model is embedded in a CFD solver and evaluated against referen…

• RP-CATE: Recurrent Perceptron-based Channel Attention Transformer Encoder for Industrial Hybrid Modeling

  Haoran Yang, Yinan Zhang, Wenjie Zhang, Dongxia Wang, Peiyu Liu, Yuqi Ye, Kexin Chen, Wenhai Wang · 23 décembre 2025

  Nowadays, industrial hybrid modeling which integrates both mechanistic modeling and machine learning-based modeling techniques has attracted increasing interest from scholars due to its high accuracy, low computational cost, and satisfactory interpretability. Nevertheless, the existing industrial hy…

• Benchmarking neural surrogates on realistic spatiotemporal multiphysics flows

  Runze Mao, Rui Zhang, Xuan Bai, Tianhao Wu, Teng Zhang, Zhenyi Chen, Minqi Lin, Bocheng Zeng, Yangchen Xu, Yingxuan Xiang, Haoze Zhang, Shubham Goswami, Pierre A. Dawe, Yifan Xu, Zhenhua An, Mengtao Yan, Xiaoyi Lu, Yi Wang, Rongbo Bai, Haobu Gao, Xiaohang Fang, Han Li, Hao Sun, Zhi X. Chen · 23 décembre 2025

  Predicting multiphysics dynamics is computationally expensive and challenging due to the severe coupling of multi-scale, heterogeneous physical processes. While neural surrogates promise a paradigm shift, the field currently suffers from an "illusion of mastery", as repeatedly emphasized in top-tier…

• Self-Consistent Probability Flow for High-Dimensional Fokker-Planck Equations

  Xiaolong Wu, Qifeng Liao · 23 décembre 2025

  Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and the bottleneck of evaluating second-order diffusion terms. Existing deep learning approaches, such as Physics-Informed Neural Networks (…

• Convolutional-neural-operator-based transfer learning for solving PDEs

  Peng Fan, Guofei Pang · 23 décembre 2025

  Convolutional neural operator is a CNN-based architecture recently proposed to enforce structure-preserving continuous-discrete equivalence and enable the genuine, alias-free learning of solution operators of PDEs. This neural operator was demonstrated to outperform for certain cases some baseline m…

• The Best of Both Worlds: Hybridizing Neural Operators and Solvers for Stable Long-Horizon Inference

  Rajyasri Roy, Dibyajyoti Nayak, Somdatta Goswami · 23 décembre 2025

  Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings. Neural operator (NO) surrogates offer fast inference across para…

• The Stochastic Occupation Kernel (SOCK) Method for Learning Stochastic Differential Equations

  Michael L. Wells, Kamel Lahouel, Bruno Jedynak · 22 décembre 2025

  We present a novel kernel-based method for learning multivariate stochastic differential equations (SDEs). The method follows a two-step procedure: we first estimate the drift term function, then the (matrix-valued) diffusion function given the drift. Occupation kernels are integral functionals on a…

• On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions

  Chloe H. Choi, Andrea Zanoni, Daniele E. Schiavazzi, Alison L. Marsden · 22 décembre 2025

  Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posteri…

• More Consistent Accuracy PINN via Alternating Easy-Hard Training

  Zhaoqian Gao, Min Yanga · 22 décembre 2025

  Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by finite element methods are widely adopted, recent research sugge…

• BumpNet: A Sparse Neural Network Framework for Learning PDE Solutions

  Shao-Ting Chiu, Ioannis G. Kevrekidis, Ulisses Braga-Neto · 22 décembre 2025

  We introduce BumpNet, a sparse neural network framework for PDE numerical solution and operator learning. BumpNet is based on meshless basis function expansion, in a similar fashion to radial-basis function (RBF) networks. Unlike RBF networks, the basis functions in BumpNet are constructed from ordi…

• Learning solution operator of dynamical systems with diffusion maps kernel ridge regression

  Jiwoo Song, Daning Huang, John Harlim · 22 décembre 2025

  Many scientific and engineering systems exhibit complex nonlinear dynamics that are difficult to predict accurately over long time horizons. Although data-driven models have shown promise, their performance often deteriorates when the geometric structures governing long-term behavior are unknown or …

• MINPO: Memory-Informed Neural Pseudo-Operator to Resolve Nonlocal Spatiotemporal Dynamics

  Farinaz Mostajeran, Aruzhan Tleubek, Salah A Faroughi · 22 décembre 2025

  Many physical systems exhibit nonlocal spatiotemporal behaviors described by integro-differential equations (IDEs). Classical methods for solving IDEs require repeatedly evaluating convolution integrals, whose cost increases quickly with kernel complexity and dimensionality. Existing neural solvers …

• Regularized Random Fourier Features and Finite Element Reconstruction for Operator Learning in Sobolev Space

  Xinyue Yu, Hayden Schaeffer · 22 décembre 2025

  Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically justified approximations that require less training than stand…

• Learning vertical coordinates via automatic differentiation of a dynamical core

  Tim Whittaker, Seth Taylor, Elsa Cardoso-Bihlo, Alejandro Di Luca, Alex Bihlo · 22 décembre 2025

  Terrain-following coordinates in atmospheric models often imprint their grid structure onto the solution, particularly over steep topography, where distorted coordinate layers can generate spurious horizontal and vertical motion. Standard formulations, such as hybrid or SLEVE coordinates, mitigate t…

• HydroGym: A Reinforcement Learning Platform for Fluid Dynamics

  Christian Lagemann, Sajeda Mokbel, Miro Gondrum, Mario R\"uttgers, Jared Callaham, Ludger Paehler, Samuel Ahnert, Nicholas Zolman, Kai Lagemann, Nikolaus Adams, Matthias Meinke, Wolfgang Schr\"oder, Jean-Christophe Loiseau, Esther Lagemann, Steven L. Brunton · 22 décembre 2025

  Modeling and controlling fluid flows is critical for several fields of science and engineering, including transportation, energy, and medicine. Effective flow control can lead to, e.g., lift increase, drag reduction, mixing enhancement, and noise reduction. However, controlling a fluid faces several…

• Training Deep Physics-Informed Kolmogorov-Arnold Networks

  Spyros Rigas, Fotios Anagnostopoulos, Michalis Papachristou, Georgios Alexandridis · 22 décembre 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 …

• Can Transformers overcome the lack of data in the simulation of history-dependent flows?

  P. Urdeitx, I. Alfaro, D. Gonzalez, F. Chinesta, E. Cueto · 19 décembre 2025

  It is well known that the lack of information about certain variables necessary for the description of a dynamical system leads to the introduction of historical dependence (lack of Markovian character of the model) and noise. Traditionally, scientists have made up for these shortcomings by designin…

• PILA: Physics-Informed Low Rank Augmentation for Interpretable Earth Observation

  Yihang She, Andrew Blake, Clement Atzberger, Adriano Gualandi, Srinivasan Keshav · 19 décembre 2025

  Physically meaningful representations are essential for Earth Observation (EO), yet existing physical models are often simplified and incomplete. This leads to discrepancies between simulation and observations that hinder reliable forward model inversion. Common approaches to EO inversion either ign…