Model Reduction and Neural Networks

Derniers papiers

• Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)

  Tiffany Fan, Murray Cutforth, Marta D'Elia, Alexandre Cortiella, Alireza Doostan, Eric Darve · 1 décembre 2025

  Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational Autoencoder (GM-VAE) framework designed to address this by int…

• Probabilistic Digital Twin for Misspecified Structural Dynamical Systems via Latent Force Modeling and Bayesian Neural Networks

  Sahil Kashyap, Rajdip Nayek · 1 décembre 2025

  This work presents a probabilistic digital twin framework for response prediction in dynamical systems governed by misspecified physics. The approach integrates Gaussian Process Latent Force Models (GPLFM) and Bayesian Neural Networks (BNNs) to enable end-to-end uncertainty-aware inference and predi…

• Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems

  Enzo Nicol\'as Spotorno, Josafat Leal Filho, Ant\^onio Augusto Fr\"ohlich · 1 décembre 2025

  This paper presents a framework for physics-informed learning in complex cyber-physical systems governed by differential equations with both unknown dynamics and algebraic invariants. First, we formalize the Hybrid Recurrent Physics-Informed Neural Network (HRPINN), a general-purpose architecture th…

• CORGI: GNNs with Convolutional Residual Global Interactions for Lagrangian Simulation

  Ethan Ji, Yuanzhou Chen, Arush Ramteke, Fang Sun, Tianrun Yu, Jai Parera, Wei Wang, Yizhou Sun · 1 décembre 2025

  Partial differential equations (PDEs) are central to dynamical systems modeling, particularly in hydrodynamics, where traditional solvers often struggle with nonlinearity and computational cost. Lagrangian neural surrogates such as GNS and SEGNN have emerged as strong alternatives by learning from p…

• Resolving Sharp Gradients of Unstable Singularities to Machine Precision via Neural Networks

  Yongji Wang, Tristan L\'eger, Ching-Yao Lai, Tristan Buckmaster · 1 décembre 2025

  Recent work introduced a robust computational framework combining embedded mathematical structures, advanced optimization, and neural network architecture, leading to the discovery of multiple unstable self-similar solutions for key fluid dynamics equations, including the Incompressible Porous Media…

• Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decomposition

  Yuanhong Chen, Federico Pichi, Zhen Gao, Gianluigi Rozza · 1 décembre 2025

  Graph autoencoders have gained attention in nonlinear reduced-order modeling of parameterized partial differential equations defined on unstructured grids. Despite they provide a geometrically consistent way of treating complex domains, applying such architectures to parameterized dynamical systems …

• FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networks

  Chenhui Xu, Dancheng Liu, Amir Nassereldine, Jinjun Xiong · 1 décembre 2025

  Physics Informed Neural Networks (PINNs) often exhibit failure modes in which the PDE residual loss converges while the solution error stays large, a phenomenon traditionally blamed on local optima separated from the true solution by steep loss barriers. We challenge this understanding by demonstrat…

• Test Time Training for AC Power Flow Surrogates via Physics and Operational Constraint Refinement

  Panteleimon Dogoulis, Mohammad Iman Alizadeh, Sylvain Kubler, Maxime Cordy · 1 décembre 2025

  Power Flow (PF) calculation based on machine learning (ML) techniques offer significant computational advantages over traditional numerical methods but often struggle to maintain full physical consistency. This paper introduces a physics-informed test-time training (PI-TTT) framework that enhances t…

• AdS/Deep-Learning made easy II: neural network-based approaches to holography and inverse problems

  Hyun-Sik Jeong, Hanse Kim, Keun-Young Kim, Gaya Yun, Hyeonwoo Yu, Kwan Yun · 1 décembre 2025

  We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving non-linear differential equations of motion. First, we introduc…

• A Flat Minima Perspective on Understanding Augmentations and Model Robustness

  Weebum Yoo, Sung Whan Yoon · 1 décembre 2025

  Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruption, adversarial attacks, and domain shifts. Data augmentation is one of the prevalent and effective ways to enhance robustness. Despite the great success of augmentations in…

• MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems

  Minghao Han, Kiwan Wong, Adrian Wing-Keung Law, Xunyuan Yin · 1 décembre 2025

  In this work, we propose a meta-learning-based Koopman modeling and predictive control approach for nonlinear systems with parametric uncertainties. An adaptive deep meta-learning-based modeling approach, called Meta Adaptive Koopman Operator (MAKO), is proposed. Without knowledge of the parametric …

• Towards a Foundation Model for Partial Differential Equations Across Physics Domains

  Eduardo Soares, Emilio Vital Brazil, Victor Shirasuna, Breno W. S. R. de Carvalho, Cristiano Malossi · 1 décembre 2025

  We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral tokenization, physics-aware conditioning, and a Mamba-based st…

• LILAD: Learning In-context Lyapunov-stable Adaptive Dynamics Models

  Amit Jena, Na Li, Le Xie · 1 décembre 2025

  System identification in control theory aims to approximate dynamical systems from trajectory data. While neural networks have demonstrated strong predictive accuracy, they often fail to preserve critical physical properties such as stability and typically assume stationary dynamics, limiting their …

• Spatially Aware Dictionary-Free Eigenfunction Identification for Modeling and Control of Nonlinear Dynamical Systems

  David Grasev · 1 décembre 2025

  A new approach to data-driven discovery of Koopman eigenfunctions without a pre-defined set of basis functions is proposed. The approach is based on a reference trajectory, for which the Koopman mode amplitudes are first identified, and the Koopman mode decomposition is transformed to a new basis, w…

• Hybrid coupling with operator inference and the overlapping Schwarz alternating method

  Irina Tezaur, Eric Parish, Anthony Gruber, Ian Moore, Christopher Wentland, Alejandro Mota · 27 novembre 2025

  This paper presents a novel hybrid approach for coupling subdomain-local non-intrusive Operator Inference (OpInf) reduced order models (ROMs) with each other and with subdomain-local high-fidelity full order models (FOMs) with using the overlapping Schwarz alternating method (O-SAM). The proposed me…

• Going with the Speed of Sound: Pushing Neural Surrogates into Highly-turbulent Transonic Regimes

  Fabian Paischer, Leo Cotteleer, Yann Dreze, Richard Kurle, Dylan Rubini, Maurits Bleeker, Tobias Kronlachner, Johannes Brandstetter · 27 novembre 2025

  The widespread use of neural surrogates in automotive aerodynamics, enabled by datasets such as DrivAerML and DrivAerNet++, has primarily focused on bluff-body flows with large wakes. Extending these methods to aerospace, particularly in the transonic regime, remains challenging due to the high leve…

• Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints

  Utkarsh Utkarsh, Pengfei Cai, Alan Edelman, Rafael Gomez-Bombarelli, Christopher Vincent Rackauckas · 27 novembre 2025

  Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as conservation laws (linear and nonlinear) and physical consistencies,…

• Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems

  Fleur Hendriks, Ond\v{r}ej Roko\v{s}, Martin Do\v{s}k\'a\v{r}, Marc G. D. Geers, Vlado Menkovski · 27 novembre 2025

  Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models struggle to capture this multiplicity, averaging over solutions and failing to represent lower-symmetry ou…

• Deceptron: Learned Local Inverses for Fast and Stable Physics Inversion

  Aaditya L. Kachhadiya · 27 novembre 2025

  Inverse problems in the physical sciences are often ill-conditioned in input space, making progress step-size sensitive. We propose the Deceptron, a lightweight bidirectional module that learns a local inverse of a differentiable forward surrogate. Training combines a supervised fit, forward-reverse…

• A Physics-Informed U-net-LSTM Network for Data-Driven Seismic Response Modeling of Structures

  Sutirtha Biswas, Kshitij Kumar Yadav · 27 novembre 2025

  Accurate and efficient seismic response prediction is essential for the design of resilient structures. While the Finite Element Method (FEM) remains the standard for nonlinear seismic analysis, its high computational demands limit its scalability and real time applicability. Recent developments in …

• SUPN: Shallow Universal Polynomial Networks

  Zachary Morrow, Michael Penwarden, Brian Chen, Aurya Javeed, Akil Narayan, John D. Jakeman · 27 novembre 2025

  Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are popular methods for function approximation due to their flexibility and expressivity. However, they typically require a large number of trainable parameters to produce a suitable approximation. Beyond making the resulting network …

• Force Prompting: Video Generation Models Can Learn and Generalize Physics-based Control Signals

  Nate Gillman, Charles Herrmann, Michael Freeman, Daksh Aggarwal, Evan Luo, Deqing Sun, Chen Sun · 27 novembre 2025

  Recent advances in video generation models have sparked interest in world models capable of simulating realistic environments. While navigation has been well-explored, physically meaningful interactions that mimic real-world forces remain largely understudied. In this work, we investigate using phys…

• Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations

  Tingkai Xue, Chin Chun Ooi, Zhengwei Ge, Fong Yew Leong, Hongying Li, Chang Wei Kang · 27 novembre 2025

  Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This work presents a hybrid physics-neural model that predicts s…

• Inference-Time Alignment of Diffusion Models via Evolutionary Algorithms

  Purvish Jajal, Nick John Eliopoulos, Benjamin Shiue-Hal Chou, George K. Thiruvathukal, James C. Davis, Yung-Hsiang Lu · 27 novembre 2025

  Diffusion models are state-of-the-art generative models, yet their samples often fail to satisfy application objectives such as safety constraints or domain-specific validity. Existing techniques for alignment require gradients, internal model access, or large computational budgets resulting in high…

• ENMA: Tokenwise Autoregression for Generative Neural PDE Operators

  Armand Kassa\"i Koupa\"i, Lise Le Boudec, Louis Serrano, Patrick Gallinari · 27 novembre 2025

  Solving time-dependent parametric partial differential equations (PDEs) remains a fundamental challenge for neural solvers, particularly when generalizing across a wide range of physical parameters and dynamics. When data is uncertain or incomplete-as is often the case-a natural approach is to turn …