Model Reduction and Neural Networks

Derniers papiers

• KANs need curvature: penalties for compositional smoothness

  James Bagrow · 5 mai 2026

  Kolmogorov-Arnold networks (KANs) offer a potent combination of accuracy and interpretability, thanks to their compositions of learnable univariate activation functions. However, the activations of well-fitting KANs tend to exhibit pathologically high-curvature oscillations, making them difficult to…

• From Euler to Dormand-Prince: ODE Solvers for Flow Matching Generative Models

  Hao Xiao · 5 mai 2026

  Sampling from Flow Matching generative models requires solving an ordinary differential equation (ODE) whose computational cost is dominated by neural network forward passes. We derive four classical ODE solvers -- Euler, Explicit Midpoint, Classical Runge-Kutta (RK4), and Dormand-Prince 5(4) -- fro…

• Isotropic Fourier Neural Operators

  Michael F. Staddon · 5 mai 2026

  Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within the model are Fourier layers, which apply linear transformat…

• Exact Loop Controllers for ReLU Realization of Homogeneous Curve Refinements

  Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur · 5 mai 2026

  We study homogeneous refinement operators \((V\gamma)(t)=\sum_{j\in\mathbb Z}A_j\gamma(Mt-j)\), acting on compactly supported continuous piecewise linear curves \(\gamma:\mathbb R\to\mathbb R^p\), where \(M\ge2\) and only finitely many matrices \(A_j\in\mathbb R^{p\times p}\) are nonzero. We prove t…

• An ALE-Consistent Graph Neural Operator-Transformer Framework for Fluid-Structure Interaction

  Shihang Zhao, Mart\'in Saravia, Haokui Jiang, Zhiyang Xue, Shunxiang Cao · 5 mai 2026

  We propose an arbitrary Lagrangian-Eulerian (ALE)-consistent machine learning framework for long-term fluid-structure interaction (FSI) prediction on deforming unstructured meshes. Specifically, the fluid dynamics are modeled by a surrogate that combines a graph neural operator (GNO) with a vision T…

• Physics-Informed Neural Learning for State Reconstruction and Parameter Identification in Coupled Greenhouse Climate Dynamics

  Sani Biswas, Khursheed J. Ansari, Md. Nasim Akhtar · 5 mai 2026

  Physics-informed neural networks (PINNs) have recently emerged as a promising framework for integrating data-driven learning with physical knowledge. In this work, we propose a coupled PINN approach for the joint reconstruction of indoor temperature and humidity dynamics in greenhouse environments, …

• ZNO: Stable Rational Neural Operators in the Z-Domain for Discrete-Time Dynamic

  Xianli Zhu, Jia Yin · 5 mai 2026

  We introduce the Z-Domain Neural Operator (ZNO), a causal neural operator whose layers are stable low-rank multiple-input multiple-output (MIMO) rational filters parameterized directly in the $z$-plane. ZNO addresses a limitation of existing operator learning methods, many of which are primarily tai…

• Mesh Based Simulations with Spatial and Temporal awareness

  Paul Garnier, Vincent Lannelongue, Elie Hachem · 5 mai 2026

  Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical bottleneck in the field: while architectures have advanced signif…

• Learning Koopman operators for coupled systems via information on governing equations of subsystems

  Tatsuya Naoi, Jun Ohkubo · 5 mai 2026

  Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic methods based on the Koopman operator have attracted attention…

• Variational Matrix-Learning Fourier Networks for Parametric Multiphysics Surrogates

  Xinyu Li, Jianhua Zhang, Liang Chen · 5 mai 2026

  Multiphysics simulation is critical for system-technology co-optimization (STCO) in chiplet-based design, but repeated finite-element solutions of PDE-governed problems are computationally expensive in parametric design exploration. This paper proposes a variational matrix-learning Fourier network (…

• Cell-induced densification and tether formation in fibrous extracellular matrices with biomimetic physics-informed neural networks

  Anci Lin, Zhiwen Zhang, Wenju Zhao · 5 mai 2026

  Nonconvex multi-well energies in cell-induced phase transitions give rise to fine-scale microstructures, low-regularity transition layers and sharp interfaces, all of which pose numerical challenges for physics-informed learning. Here we introduce biomimetic physics-informed neural networks (Bio-PIN…

• Chebyshev-Augmented One-Shot Transfer Learning for PINNs on Nonlinear Differential Equations

  Yiqi Rao, Pavlos Protopapas · 5 mai 2026

  Physics-Informed Neural Networks (PINNs) offer a flexible paradigm for solving differential equations by embedding governing laws into the training objective. A persistent limitation is instance specificity: standard PINNs typically require retraining for each new forcing term, boundary/initial cond…

• Equation-Free Digital Twins for Nonlinear Structural Dynamics

  Mohammad Mahdi Abaei, Ahmad BahooToroody, Arttu Poloj\"arvi, Heikki Remes, Ulf Tyge Tygesen, Mikko Suominen, Michael Beer · 5 mai 2026

  Monitoring high-dimensional engineering structures in extreme environments is limited by non-stationary excitation, nonlinear structural kinematics, and stochastic forcing. Traditional model-based and black-box data-driven methods often struggle to resolve these dynamics in real time, particularly u…

• Meta-learning Structure-Preserving Dynamics

  Cheng Jing, Uvini Balasuriya Mudiyanselage, Woojin Cho, Minju Jo, Anthony Gruber, Kookjin Lee · 5 mai 2026

  Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative behavior. However, these models are typically trained on a per-confi…

• Adaptation of AI-accelerated CFD Simulations to the IPU platform

  P. Rosciszewski, A. Krzywaniak, S. Iserte, K. Rojek, P. Gepner · 4 mai 2026

  Intelligence Processing Units (IPU) have proven useful for many AI applications. In this paper, we evaluate them within the emerging field of \emph{AI for simulation}, where traditional numerical simulations are supported by artificial intelligence approaches. We focus specifically on a program for …

• Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics

  Satoshi Noguchi, Yoshinobu Kawahara · 4 mai 2026

  We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivarianc…

• Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries

  Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu · 4 mai 2026

  This paper deals with solving the 2D Helmholtz equation on non-parametric domains, leveraging a physics-informed neural operator network based on the DeepONet framework. We consider a 2D square domain with an inclusion of arbitrary boundary geometry at its center. This inclusion acts as a scatterer …

• A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions

  Matteo Raviola, Benjamin Peherstorfer · 4 mai 2026

  Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We interpret this non-uniqueness as a gauge freedom: nullspace directions that leave the time derivative unchanged can…

• RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics

  Bojun Zhang, Huiyu Yang, Yunpeng Wang, Yuntian Chen, Yuanwei Bin, Rikui Zhang, Jianchun Wang · 4 mai 2026

  Rapid aerodynamic evaluation is crucial for modern vehicle design, yet existing neural operators struggle to capture intricate spatial correlations. We propose the rotary-enhanced transformer operator (RETO), a novel neural solver featuring a dual-stage spatial awareness mechanism: sinusoidal-cosine…

• HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs

  Jinpai Zhao, Nishant Panda, Yen Ting Lin, Eirik Valseth, Diane Oyen, Clint Dawson · 4 mai 2026

  We introduce HyCOP, a modular framework that learns parametric PDE solution operators by composing simple modules (advection, diffusion, learned closures, boundary handling) in a query-conditioned way. Rather than learning a monolithic map, HyCOP learns a policy over short programs - which module to…

• Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems

  Mengke Zhao, Guang-Xing Li, Duo Xu, Keping Qiu · 4 mai 2026

  Complex physical systems, from supersonic turbulence to the macroscopic structure of the universe, are governed by continuous multiscale dynamics. While modern machine learning architectures excel at mapping the high-dimensional observables of these systems, it remains unclear whether they internali…

• PILIR: Physics-Informed Local Implicit Representation

  Jianfeng Li, Feng Wang, Ke Tang · 4 mai 2026

  Physics-Informed Neural Networks have become a powerful mesh-free method for solving partial differential equations, but their performance is often limited by spectral bias. Specifically, in standard MLPs used in PINNs, the global parameter coupling causes the model to prioritize learning low-freque…

• Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks

  Beomchul Park, Minsu Koh, Heejo Kong, Seong-Whan Lee · 1 mai 2026

  Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function. In parameterized PDE families, variations in coefficients or boundary/initial conditions define distinct tasks. This makes training individual PI…

• Green Physics-Informed Machine Learning Models For Structural Health Monitoring

  Daisy R Bradley, Elizabeth J Cross · 1 mai 2026

  Machine learning continues to emerge as an important tool to be utilised within structural engineering and structural health monitoring, due to its ability to accurately and quickly perform both regression and classification tasks. However, a purely data driven approach has its limitations, particul…

• An adaptive wavelet-based PINN for problems with localized high-magnitude source

  Himanshu Pandey, Ratikanta Behera · 1 mai 2026

  In recent years, physics-informed neural networks (PINNs) have gained significant attention for solving differential equations, although they suffer from two fundamental limitations, namely, spectral bias inherent in neural networks and loss imbalance arising from multiscale phenomena. This paper pr…