Model Reduction and Neural Networks

Derniers papiers

• TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation

  Dibyajyoti Nayak, Somdatta Goswami · 20 novembre 2025

  Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms: fixed-horizon rollouts, which predict full spatiotemporal so…

• Learning in Compact Spaces with Approximately Normalized Transformer

  J\"org K. H. Franke, Urs Spiegelhalter, Marianna Nezhurina, Jenia Jitsev, Frank Hutter, Michael Hefenbrock · 20 novembre 2025

  The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization and normalization techniques that usually require tuning add…

• CODE: A global approach to ODE dynamics learning

  Nils Wildt, Daniel M. Tartakovsky, Sergey Oladyshkin, Wolfgang Nowak · 20 novembre 2025

  Ordinary differential equations (ODEs) are a conventional way to describe the observed dynamics of physical systems. Scientists typically hypothesize about dynamical behavior, propose a mathematical model, and compare its predictions to data. However, modern computing and algorithmic advances now en…

• Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation

  Victorita Dolean, Daria Hrebenshchykova, St\'ephane Lanteri, Victor Michel-Dansac · 20 novembre 2025

  Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing partial differential equations (PDEs) such as the Helmholtz e…

• A Physics Informed Machine Learning Framework for Optimal Sensor Placement and Parameter Estimation

  Georgios Venianakis, Constantinos Theodoropoulos, Michail Kavousanakis · 20 novembre 2025

  Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that provide the maximum amount of information about the unknown para…

• Optimal Control of Nonlinear Systems with Unknown Dynamics

  Wenjian Hao, Paulo C. Heredia, Shaoshuai Mou · 20 novembre 2025

  This paper presents a data-driven method to find a closed-loop optimal controller, which minimizes a specified infinite-horizon cost function for systems with unknown dynamics. Suppose the closed-loop optimal controller can be parameterized by a given class of functions, hereafter referred to as the…

• Algebraformer: A Neural Approach to Linear Systems

  Pietro Sittoni, Francesco Tudisco · 19 novembre 2025

  Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are ill-conditioned. Existing numerical methods for ill-conditioned …

• FoilDiff: A Hybrid Transformer Backbone for Diffusion-based Modelling of 2D Airfoil Flow Fields

  Kenechukwu Ogbuagu, Sepehr Maleki, Giuseppe Bruni, Senthil Krishnababu · 19 novembre 2025

  The accurate prediction of flow fields around airfoils is crucial for aerodynamic design and optimisation. Computational Fluid Dynamics (CFD) models are effective but computationally expensive, thus inspiring the development of surrogate models to enable quicker predictions. These surrogate models c…

• Enforcing hidden physics in physics-informed neural networks

  Nanxi Chen, Sifan Wang, Rujin Ma, Airong Chen, Chuanjie Cui · 19 novembre 2025

  Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, despite their foundational role, the hidden irreversibility implied by the Second Law of Thermodynam…

• Derivative of the truncated singular value and eigen decomposition

  Jan Naumann · 19 novembre 2025

  Recently developed applications in the field of machine learning and computational physics rely on automatic differentiation techniques, that require stable and efficient linear algebra gradient computations. This technical note provides a comprehensive and detailed discussion of the derivative of t…

• Extended Physics Informed Neural Network for Hyperbolic Two-Phase Flow in Porous Media

  Saif Ur Rehman, Wajid Yousuf · 19 novembre 2025

  The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains a central challenge in computational science due to the presence of steep gradients, discontinuities, and multiscale structures that make conventional discretization-based solvers computationally demanding. P…

• Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems

  Amanda A. Howard, Bruno Jacob, Sarah Helfert, Alexander Heinlein, Panos Stinis · 18 novembre 2025

  Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensive to train, even for relatively small networks. Inspired by finite basis physics-informed neural networks (FBPINNs), in…

• Diffusion Models: A Mathematical Introduction

  Sepehr Maleki, Negar Pourmoazemi · 18 novembre 2025

  We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we construct denoising diffusion probabilistic models from first prin…

• Scalable learning of macroscopic stochastic dynamics

  Mengyi Chen, Pengru Huang, Kostya S. Novoselov, Qianxiao Li · 18 novembre 2025

  Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to first-principles methods to build accurate macroscopic models from…

• Sumudu Neural Operator for ODEs and PDEs

  Ben Zelenskiy, Saibilila Abudukelimu, George Flint, Kevin Zhu, Sunishchal Dev · 18 novembre 2025

  We introduce the Sumudu Neural Operator (SNO), a neural operator rooted in the properties of the Sumudu Transform. We leverage the relationship between the polynomial expansions of transform pairs to decompose the input space as coefficients, which are then transformed into the Sumudu Space, where t…

• Trace Regularity PINNs: Enforcing $\mathrm{H}^{\frac{1}{2}}(\partial \Omega)$ for Boundary Data

  Doyoon Kim, Junbin Song · 18 novembre 2025

  We propose an enhanced physics-informed neural network (PINN), the Trace Regularity Physics-Informed Neural Network (TRPINN), which enforces the boundary loss in the Sobolev-Slobodeckij norm $H^{1/2}(\partial \Omega)$, the correct trace space associated with $H^1(\Omega)$. We reduce computational co…

• Spectral Bias Mitigation via xLSTM-PINN: Memory-Gated Representation Refinement for Physics-Informed Learning

  Ze Tao, Darui Zhao, Fujun Liu, Ke Xu, Xiangsheng Hu · 18 novembre 2025

  Physics-informed learning for PDEs is surging across scientific computing and industrial simulation, yet prevailing methods face spectral bias, residual-data imbalance, and weak extrapolation. We introduce a representation-level spectral remodeling xLSTM-PINN that combines gated-memory multiscale fe…

• Attention-Enhanced Convolutional Autoencoder and Structured Delay Embeddings for Weather Prediction

  Amirpasha Hedayat, Karthik Duraisamy · 18 novembre 2025

  Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range weather prediction and investigates fundamental questions in dimen…

• Adaptive Graph Rewiring to Mitigate Over-Squashing in Mesh-Based GNNs for Fluid Dynamics Simulations

  Sangwoo Seo, Hyunsung Kim, Jiwan Kim, Chanyoung Park · 18 novembre 2025

  Mesh-based simulation using Graph Neural Networks (GNNs) has been recognized as a promising approach for modeling fluid dynamics. However, the mesh refinement techniques which allocate finer resolution to regions with steep gradients can induce the over-squashing problem in mesh-based GNNs, which pr…

• Conformal Online Learning of Deep Koopman Linear Embeddings

  Ben Gao, Jordan Patracone, St\'ephane Chr\'etien, Olivier Alata · 18 novembre 2025

  We introduce Conformal Online Learning of Koopman embeddings (COLoKe), a novel framework for adaptively updating Koopman-invariant representations of nonlinear dynamical systems from streaming data. Our modeling approach combines deep feature learning with multistep prediction consistency in the lif…

• INC: An Indirect Neural Corrector for Auto-Regressive Hybrid PDE Solvers

  Hao Wei, Aleksandra Franz, Bjoern List, Nils Thuerey · 18 novembre 2025

  When simulating partial differential equations, hybrid solvers combine coarse numerical solvers with learned correctors. They promise accelerated simulations while adhering to physical constraints. However, as shown in our theoretical framework, directly applying learned corrections to solver output…

• Mesh-based Super-resolution of Detonation Flows with Multiscale Graph Transformers

  Shivam Barwey, Pinaki Pal · 18 novembre 2025

  Super-resolution flow reconstruction using state-of-the-art data-driven techniques is valuable for a variety of applications, such as subgrid/subfilter closure modeling, accelerating spatiotemporal forecasting, data compression, and serving as an upscaling tool for sparse experimental measurements. …

• From Black-Box to White-Box: Control-Theoretic Neural Network Interpretability

  Jihoon Moon · 18 novembre 2025

  Deep neural networks achieve state of the art performance but remain difficult to interpret mechanistically. In this work, we propose a control theoretic framework that treats a trained neural network as a nonlinear state space system and uses local linearization, controllability and observability G…

• Method of Manufactured Learning for Solver-free Training of Neural Operators

  Arth Sojitra, Omer San · 18 novembre 2025

  Training neural operators to approximate mappings between infinite-dimensional function spaces often requires extensive datasets generated by either demanding experimental setups or computationally expensive numerical solvers. This dependence on solver-based data limits scalability and constrains ex…

• Fast Equivariant Imaging: Acceleration for Unsupervised Learning via Augmented Lagrangian and Auxiliary PnP Denoisers

  Guixian Xu, Jinglai Li, Junqi Tang · 18 novembre 2025

  In this work, we propose Fast Equivariant Imaging (FEI), a novel unsupervised learning framework to rapidly and efficiently train deep imaging networks without ground-truth data. From the perspective of reformulating the Equivariant Imaging based optimization problem via the method of Lagrange multi…