Méthode de quadrature pour les PINNs fondée théoriquement sur la hessienne des résiduels

• URL: http://arxiv.org/abs/2506.20441v1
• Date: Wed, 25 Jun 2025 13:49:53 GMT
• Title: Méthode de quadrature pour les PINNs fondée théoriquement sur la hessienne des résiduels
• Authors: Antoine Caradot, Rémi Emonet, Amaury Habrard, Abdel-Rahim Mezidi, Marc Sebban,
• Abstract summary: Physics-informed Neural Networks (PINNs) have emerged as an efficient way to learn surrogate neural solvers of PDEs.<n>We propose a new quadrature method for approximating definite integrals based on the hessian of the considered function.
• Score: 11.912466054588327
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physics-informed Neural Networks (PINNs) have emerged as an efficient way to learn surrogate neural solvers of PDEs by embedding the physical model in the loss function and minimizing its residuals using automatic differentiation at so-called collocation points. Originally uniformly sampled, the choice of the latter has been the subject of recent advances leading to adaptive sampling refinements. In this paper, we propose a new quadrature method for approximating definite integrals based on the hessian of the considered function, and that we leverage to guide the selection of the collocation points during the training process of PINNs.

Related papers

• Provably Accurate Adaptive Sampling for Collocation Points in Physics-informed Neural Networks [11.912466054588327]
  Physics-informed Neural Networks (PINN) have emerged as an efficient way to learn surrogate solvers.<n>We introduce a provably accurate sampling method for collocation points based on the Hessian of the PDE residuals.
  arXiv  Detail & Related papers  (2025-04-01T15:45:08Z)
• Plane-Wave Decomposition and Randomised Training; a Novel Path to Generalised PINNs for SHM [0.0]
  We introduce a formulation of Physics-Informed Neural Networks (PINNs)<n>PINNs are based on learning the form of the Fourier decomposition, and a training methodology based on a spread of randomly chosen boundary conditions.
  arXiv  Detail & Related papers  (2025-03-31T21:37:18Z)
• An Adaptive Collocation Point Strategy For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method [1.2289361708127877]
  We propose an adaptive collocation point selection strategy utilizing the QR Discrete Empirical Interpolation Method (QR-DEIM)<n>Our results on benchmark PDEs, including the wave, Allen-Cahn, and Burgers' equations, demonstrate that our QR-DEIM-based approach improves PINN accuracy compared to existing methods.
  arXiv  Detail & Related papers  (2025-01-13T21:24:15Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• RoPINN: Region Optimized Physics-Informed Neural Networks [66.38369833561039]
  Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) This paper proposes and theoretically studies a new training paradigm as region optimization. A practical training algorithm, Region Optimized PINN (RoPINN), is seamlessly derived from this new paradigm.
  arXiv  Detail & Related papers  (2024-05-23T09:45:57Z)
• Stochastic Unrolled Federated Learning [85.6993263983062]
  We introduce UnRolled Federated learning (SURF), a method that expands algorithm unrolling to federated learning. Our proposed method tackles two challenges of this expansion, namely the need to feed whole datasets to the unrolleds and the decentralized nature of federated learning.
  arXiv  Detail & Related papers  (2023-05-24T17:26:22Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• A Novel Adaptive Causal Sampling Method for Physics-Informed Neural Networks [35.25394937917774]
  Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs) We introduce temporal causality into adaptive sampling and propose a novel adaptive causal sampling method to improve the performance and efficiency of PINs. We demonstrate that by utilizing such a relatively simple sampling method, prediction performance can be improved up to two orders of magnitude compared with state-of-the-art results.
  arXiv  Detail & Related papers  (2022-10-24T01:51:08Z)
• Adaptive Self-supervision Algorithms for Physics-informed Neural Networks [59.822151945132525]
  Physics-informed neural networks (PINNs) incorporate physical knowledge from the problem domain as a soft constraint on the loss function. We study the impact of the location of the collocation points on the trainability of these models. We propose a novel adaptive collocation scheme which progressively allocates more collocation points to areas where the model is making higher errors.
  arXiv  Detail & Related papers  (2022-07-08T18:17:06Z)
• Deep Learning for the Benes Filter [91.3755431537592]
  We present a new numerical method based on the mesh-free neural network representation of the density of the solution of the Benes model. We discuss the role of nonlinearity in the filtering model equations for the choice of the domain of the neural network.
  arXiv  Detail & Related papers  (2022-03-09T14:08:38Z)
• Efficient training of physics-informed neural networks via importance sampling [2.9005223064604078]
  Physics-In Neural Networks (PINNs) are a class of deep neural networks that are trained to compute systems governed by partial differential equations (PDEs) We show that an importance sampling approach will improve the convergence behavior of PINNs training.
  arXiv  Detail & Related papers  (2021-04-26T02:45:10Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.