Model Reduction and Neural Networks

Derniers papiers

• LFNO: Bridging Laplace and Fourier via Transient-Steady Decomposition

  Jeongun Ha, Sanga Yoon, Donghun Lee · 9 juin 2026

  We introduce the Laplace-Fourier Neural Operator (LFNO), a unified framework for modeling dynamical systems across transient and steady-state regimes by integrating the spectral advantages of Laplace and Fourier Neural Operators. LFNO employs a dual-branch architecture that explicitly decomposes sys…

• Stochastic Dimension Implicit Functional Projections for Global Integral Conservation in High-Dimensional PINNs

  Zhangyong Liang, Huanhuan Gao · 9 juin 2026

  Enforcing prescribed global integral constraints in mesh-free neural PDE solvers is challenging in high-dimensional domains. Existing projection methods for spatial integrals are often tied to fixed grids or uniform quadrature, which can conflict with randomly sampled physics-informed neural network…

• Fourier Neural Operators with rank-1 lattice points and hyperbolic cross

  Jakob Dilen, Alexander Keller, Frances Y. Kuo, Dirk Nuyens · 9 juin 2026

  The \emph{Fourier neural operator} (FNO) is a neural network architecture that learns mappings between function spaces. Its efficient implementation is based on the multi-dimensional Fourier transform. By deriving general regularity bounds for the FNO with respect to both the spatial and parametric …

• Mesh Graph Neural Network Framework for Accelerating Finite Element Simulation for Arbitrary Geometries

  Josiah D. Kunz, Kamal Choudhary · 9 juin 2026

  Finite element analysis (FEA) is essential for structural design but remains computationally expensive, particularly when evaluating multiple design iterations or load scenarios. Machine learning surrogate models offer a promising alternative, yet most approaches struggle with a critical limitation:…

• In-Context Learning of Stochastic Differential Equations with Foundation Inference Models

  Patrick Seifner, Kostadin Cvejoski, David Berghaus, Cesar Ojeda, Ramses J. Sanchez · 9 juin 2026

  Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery) of these functions from data is a central problem in machin…

• From inverse problems to neural operators: prediction, mechanism, and generalization of data-driven models

  Conor Rowan · 9 juin 2026

  Scientists have historically relied on mathematical models based on differential equations to relate system inputs -- forces, fluxes, or heat sources -- to outputs, such as displacement, velocity, concentration, and temperature. These models rely on deep domain knowledge to determine the form of the…

• Overcoming the Limits of Finite Difference Method; Physics-Informed Neural Network for Noisy High-Dimensional Heat Diffusion

  Shreesh Bhattarai, Harish Chandra Bhandari · 9 juin 2026

  High-dimensional transient heat diffusion under noisy boundary conditions exposes a fundamental limitation of classical numerical methods: accuracy degrades catastrophically where physical noise is unavoidable. This paper presents a Physics-Informed Neural Network (PINN) framework as a systematic so…

• A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction

  Kangkang Qi, Huiyu Yang, Keqi Ding, Yunpeng Wang, Yuntian Chen, Yuanwei Bin, Rikui Zhang, Jianchun Wang · 9 juin 2026

  High-fidelity computational fluid dynamics (CFD) is crucial to vehicle aerodynamic analysis, but its cost still constrains early-stage design exploration. Machine-learning-based surface-field prediction offers a faster alternative if the model can efficiently capture both global flow context and loc…

• Data-driven discovery of governing differential equations across physical systems

  Siyu Lou, Hao Xu, Wenguan Wang, Lu Lu, Hao Sun, Yang Liu, Linfeng Zhang, Dongxiao Zhang, Yuntian Chen · 9 juin 2026

  Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena. As a promising alternative to traditional first principles, data-driven differential equation discovery has attracted increasing attentio…

• Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems

  Karn Tiwari, Niladri Dutta, N M Anoop Krishnan, Prathosh A P · 9 juin 2026

  Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies. Graph neural networks (GNNs) provide a natural representation but typically rely on autoregressive rollouts and treat spatial and temporal dynamics separately, leading to error …

• Operator learning for solving Fokker-Planck equations with various initial conditions

  Li Zeng, Xiaoliang Wan, Yaobin Wang, Fabio Nobile, Tao Zhou · 9 juin 2026

  The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics. In this work, we propose a conditional normalizing flow-based physics-informed neural network (PINN) framework for efficiently a…

• Mitigating the Contractivity Trap in Diffusion ODEs via Stein Stabilization

  Shigui Li, Delu Zeng · 9 juin 2026

  A fundamental tension exists in the large-step inference of diffusion models via their deterministic probability flow ordinary differential equation (PF-ODE) trajectories, which we identify as the contractivity trap: efficient inference favors large step sizes, while aggressive steps and highly expr…

• GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators

  Jason Sulskis, Sathya Ravi · 9 juin 2026

  We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space. Exis…

• Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime

  Weinan Wang, Bowen Gang, Hao Deng · 9 juin 2026

  In this paper, we propose a perturbation-based conformal prediction framework for uncertainty quantification in operator learning, with a focus on the 2D Navier--Stokes equations. While neural operators provide fast surrogates for expensive PDE solvers, they do not by themselves provide calibrated u…

• Reachability and asymptotics of Gaussian Transformer dynamics

  Albert Alcalde, Zhengping Ji, Enrique Zuazua · 9 juin 2026

  We formulate data propagation through the Transformer, the machine learning architecture powering large language models, as a nonlinear control system on the space of probability measures. For the mean-field Transformer model with self-attention and affine feed-forward layers, we prove that Gaussian…

• Architecture Shapes Transfer Specificity in Implicit Neural Representations

  D Yang Eng · 8 juin 2026

  Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using c…

• Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series

  S. V. Manivelan, Andrei Velichko, I. Manimehan · 8 juin 2026

  Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics. We propose a geometry-guided machine learning framework that unifies predictive trajectory divergence with macroscopic attractor morphology to track abrupt regime …

• Finite Element-Based Material Learning via Automatic Differentiation: Learning constitutive neural network models from full-field deformation data

  Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka · 5 juin 2026

  The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters. Existing approa…

• Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming

  Shah Pallav Dhanendrakumar, Saikat Pal, Sitikantha Roy · 5 juin 2026

  Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning. Mechanistic models provide valuable scientific insight into the disorders, but in practice they are of…

• From Ticks to Flows: Dynamics of Neural Reinforcement Learning in Continuous Environments

  Saket Tiwari, Tejas Kotwal, George Konidaris · 4 juin 2026

  We present a novel theoretical framework for deep reinforcement learning (RL) in continuous environments by modeling the problem as a continuous-time stochastic process, drawing on insights from stochastic control. Building on previous work, we introduce a viable model of actor-critic algorithm that…

• Bagged Polynomial Regression and Neural Networks

  Sylvia Klosin, Jaume Vives-i-Bastida · 4 juin 2026

  Climate and environmental applications increasingly rely on high-dimensional prediction from remote sensing and other scientific data. Neural networks (NN) can deliver strong accuracy in these settings, but they are often hard to audit and hard to align with domain knowledge. As an alternative, we p…

• Learning Control-Affine Reduced-Order Models via Autoencoders

  Ali Mjalled, Martin M\"onnigmann · 4 juin 2026

  We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state…

• Nonlocal Mean Field Schr\"{o}dinger Bridge with Learned Interactions

  Daisuke Inoue, Mathieu Lauri\`ere, Dante Kalise · 4 juin 2026

  The Schr\"odinger Bridge Problem constructs a stochastic process that connects an initial distribution to a terminal distribution with minimum energy. This work considers its mean-field extension, the Mean-Field Schr\"odinger Bridge, for interacting particle systems. With nonlocal interactions, eval…

• PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems

  Ismail Hassaballa, Mircea Lazar · 4 juin 2026

  Hybrid models that combine physics-based and data-driven components have shown strong potential for achieving accuracy and interpretability in control applications. While recent methods have made progress in incorporating physical consistency, challenges remain in scalability, robustness to noise, a…

• Curvature-aware dynamic precision approach for physics-informed neural networks

  Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn, Taniya Kapoor · 4 juin 2026

  Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, recent studies show that PINN optimisation is sensitive to numerical precision. Existing implemen…