Model Reduction and Neural Networks

Derniers papiers

• DAE-HardNet: A Physics Constrained Neural Network Enforcing Differential-Algebraic Hard Constraints

  Rahul Golder, Bimol Nath Roy, M. M. Faruque Hasan · 8 décembre 2025

  Traditional physics-informed neural networks (PINNs) do not always satisfy physics based constraints, especially when the constraints include differential operators. Rather, they minimize the constraint violations in a soft way. Strict satisfaction of differential-algebraic equations (DAEs) to embed…

• CFO: Learning Continuous-Time PDE Dynamics via Flow-Matched Neural Operators

  Xianglong Hou, Xinquan Huang, Paris Perdikaris · 8 décembre 2025

  Neural operator surrogates for time-dependent partial differential equations (PDEs) conventionally employ autoregressive prediction schemes, which accumulate error over long rollouts and require uniform temporal discretization. We introduce the Continuous Flow Operator (CFO), a framework that learns…

• xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning

  Ze Tao, Darui Zhao, Fujun Liu, Ke Xu, Xiangsheng Hu · 8 décembre 2025

  Physics-informed neural networks (PINN) face significant challenges from spectral bias, which impedes their ability to model high-frequency phenomena and limits extrapolation performance. To address this, we introduce xLSTM-PINN, a novel architecture that performs representation-level spectral remod…

• Comparison of neural network training strategies for the simulation of dynamical systems

  Paul Strasser, Andreas Pfeffer, Jakob Weber, Markus Gurtner, Andreas K\"orner · 4 décembre 2025

  Neural networks have become a widely adopted tool for modeling nonlinear dynamical systems from data. However, the choice of training strategy remains a key design decision, particularly for simulation tasks. This paper compares two predominant strategies: parallel and series-parallel training. The …

• A Discrete Neural Operator with Adaptive Sampling for Surrogate Modeling of Parametric Transient Darcy Flows in Porous Media

  Zhenglong Chen, Zhao Zhang, Xia Yan, Jiayu Zhai, Piyang Liu, Kai Zhang · 4 décembre 2025

  This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to approximate the mapping between vector spaces of random parameter …

• Learning Fluid-Structure Interaction with Physics-Informed Machine Learning and Immersed Boundary Methods

  Afrah Farea, Saiful Khan, Reza Daryani, Emre Cenk Ersan, Mustafa Serdar Celebi · 4 décembre 2025

  Physics-informed neural networks (PINNs) have emerged as a promising approach for solving complex fluid dynamics problems, yet their application to fluid-structure interaction (FSI) problems with moving boundaries remains largely unexplored. This work addresses the critical challenge of modeling FSI…

• MathBode: Measuring the Stability of LLM Reasoning using Frequency Response

  Charles L. Wang · 4 décembre 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…

• Calibrating Geophysical Predictions under Constrained Probabilistic Distributions

  Zhewen Hou, Jiajin Sun, Subashree Venkatasubramanian, Peter Jin, Shuolin Li, Tian Zheng · 4 décembre 2025

  Machine learning (ML) has shown significant promise in studying complex geophysical dynamical systems, including turbulence and climate processes. Such systems often display sensitive dependence on initial conditions, reflected in positive Lyapunov exponents, where even small perturbations in short-…

• Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES

  Toby van Gastelen, Wouter Edeling, Benjamin Sanderse · 4 décembre 2025

  Machine learning-based closure models for LES have shown promise in capturing complex turbulence dynamics but often suffer from instabilities and physical inconsistencies. In this work, we develop a novel skew-symmetric neural architecture as closure model that enforces stability while preserving ke…

• ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics

  Julian Evan Chrisnanto, Nurfauzi Fadillah, Yulison Herry Chrisnanto · 4 décembre 2025

  Physics-Informed Neural Networks (PINNs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs). However, they notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent spectral bias of standard multilayer perceptron (MLP) archi…

• BlendedNet++: A Large-Scale Blended Wing Body Aerodynamics Dataset and Benchmark

  Nicholas Sung, Steven Spreizer, Mohamed Elrefaie, Matthew C. Jones, Faez Ahmed · 4 décembre 2025

  Despite progress in machine learning-based aerodynamic surrogates, the scarcity of large, field-resolved datasets limits progress on accurate pointwise prediction and reproducible inverse design for aircraft. We introduce BlendedNet++, a large-scale aerodynamic dataset and benchmark focused on blend…

• Dynamic Correction of Erroneous State Estimates via Diffusion Bayesian Exploration

  Yiwei Shi, Hongnan Ma, Mengyue Yang, Cunjia Liu, Weiru Liu · 4 décembre 2025

  In emergency response and other high-stakes societal applications, early-stage state estimates critically shape downstream outcomes. Yet, these initial state estimates-often based on limited or biased information-can be severely misaligned with reality, constraining subsequent actions and potentiall…

• Consistent Projection of Langevin Dynamics: Preserving Thermodynamics and Kinetics in Coarse-Grained Models

  Vahid Nateghi, Lara Neureither, Selma Moqvist, Carsten Hartmann, Simon Olsson, Feliks N\"uske · 4 décembre 2025

  Coarse graining (CG) is an important task for efficient modeling and simulation of complex multi-scale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general underdamped Langevin dynamics. Following the Zwanzig projec…

• Model Recovery at the Edge under Resource Constraints for Physical AI

  Bin Xu, Ayan Banerjee, Sandeep K. S. Gupta · 3 décembre 2025

  Model Recovery (MR) enables safe, explainable decision making in mission-critical autonomous systems (MCAS) by learning governing dynamical equations, but its deployment on edge devices is hindered by the iterative nature of neural ordinary differential equations (NODEs), which are inefficient on FP…

• Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements

  Ibrahim Laiche, Mokrane Boudaoud, Patrick Gallinari, Pascal Morin · 3 décembre 2025

  This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification of physically consistent models, which are essential for mod…

• MSPT: Efficient Large-Scale Physical Modeling via Parallelized Multi-Scale Attention

  Pedro M. P. Curvo, Jan-Willem van de Meent, Maksim Zhdanov · 2 décembre 2025

  A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the Multi-Scale Patch Transformer (MSPT), an architecture that com…

• Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets

  Adrienne M. Propp, Mauro Perego, Eric C. Cyr, Anthony Gruber, Amanda A. Howard, Alexander Heinlein, Panos Stinis, Daniel M. Tartakovsky · 2 décembre 2025

  Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks that demand hundreds or thousands of evaluations. We develop a physics-inspired graph neural network (GNN) surrogate that…

• High-dimensional Mean-Field Games by Particle-based Flow Matching

  Jiajia Yu, Junghwan Lee, Yao Xie, Xiuyuan Cheng · 2 décembre 2025

  Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications, including optimal transport (OT) and generative models. Despit…

• ECO: Energy-Constrained Operator Learning for Chaotic Dynamics with Boundedness Guarantees

  Andrea Goertzen, Sunbochen Tang, Navid Azizan · 2 décembre 2025

  Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems are dissipative and ergodic, motivating data-driven models …

• Koopman operators with intrinsic observables in rigged reproducing kernel Hilbert spaces

  Isao Ishikawa, Yuka Hashimoto, Masahiro Ikeda, Yoshinobu Kawahara · 2 décembre 2025

  This paper presents a novel approach for estimating the Koopman operator defined on a reproducing kernel Hilbert space (RKHS) and its spectra. We propose an estimation method, what we call Jet Extended Dynamic Mode Decomposition (JetEDMD), leveraging the intrinsic structure of RKHS and the geometric…

• Finite Operator Learning: Bridging Neural Operators and Numerical Methods for Efficient Parametric Solution and Optimization of PDEs

  Shahed Rezaei, Reza Najian Asl, Kianoosh Taghikhani, Ahmad Moeineddin, Michael Kaliske, Markus Apel · 2 décembre 2025

  We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single framework. We can parametrically solve partial differential equa…

• Learning with Physical Constraints

  Miguel A. Mendez, Jan van Den Berghe, Manuel Ratz, Matilde Fiore, Lorenzo Schena · 2 décembre 2025

  This chapter provides three tutorial exercises on physics-constrained regression. These are implemented as toy problems that seek to mimic grand challenges in (1) the super-resolution and data assimilation of the velocity field in image velocimetry, (2) data-driven turbulence modeling, and (3) syste…

• Stabilizing black-box model selection with the inflated argmax

  Melissa Adrian, Jake A. Soloff, Rebecca Willett · 2 décembre 2025

  Model selection is the process of choosing from a class of candidate models given data. For instance, methods such as the LASSO and sparse identification of nonlinear dynamics (SINDy) formulate model selection as finding a sparse solution to a linear system of equations determined by training data. …

• L2RU: a Structured State Space Model with prescribed L2-bound

  Leonardo Massai, Muhammad Zakwan, Giancarlo Ferrari-Trecate · 2 décembre 2025

  Structured state-space models (SSMs) have recently emerged as a powerful architecture at the intersection of machine learning and control, featuring layers composed of discrete-time linear time-invariant (LTI) systems followed by pointwise nonlinearities. These models combine the expressiveness of d…

• Guided Unconditional and Conditional Generative Models for Super-Resolution and Inference of Quasi-Geostrophic Turbulence

  Anantha Narayanan Suresh Babu, Akhil Sadam, Pierre F. J. Lermusiaux · 2 décembre 2025

  Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy. We apply four generative diffusion modeling approaches to super-resolution and inference of forced two-dimensional quasi-geostrophic turbulence on the beta-plane from coarse, sparse, and gappy …