PINNfluence: Influence Functions for Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2409.08958v1
• Date: Fri, 13 Sep 2024 16:23:17 GMT
• Title: PINNfluence: Influence Functions for Physics-Informed Neural Networks
• Authors: Jonas R. Naujoks, Aleksander Krasowski, Moritz Weckbecker, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, René P. Klausen,
• Abstract summary: Physics-informed neural networks (PINNs) have emerged as a flexible and promising application of deep learning to partial differential equations in the physical sciences. We explore the application of influence functions (IFs) to validate and debug PINNs post-hoc.
• Score: 47.27512105490682
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Recently, physics-informed neural networks (PINNs) have emerged as a flexible and promising application of deep learning to partial differential equations in the physical sciences. While offering strong performance and competitive inference speeds on forward and inverse problems, their black-box nature limits interpretability, particularly regarding alignment with expected physical behavior. In the present work, we explore the application of influence functions (IFs) to validate and debug PINNs post-hoc. Specifically, we apply variations of IF-based indicators to gauge the influence of different types of collocation points on the prediction of PINNs applied to a 2D Navier-Stokes fluid flow problem. Our results demonstrate how IFs can be adapted to PINNs to reveal the potential for further studies.

Related papers

• Learnable Activation Functions in Physics-Informed Neural Networks for Solving Partial Differential Equations [0.0]
  We investigate the use of learnable activation functions in Physics-Informed Networks (PINNs) for solving Partial Differential Equations (PDEs) We compare the efficacy of traditional Multilayer Perceptrons (MLPs) with fixed and learnable activations against Kolmogorov-Arnold Neural Networks (KANs) The findings offer insights into the design of neural network architectures that balance training efficiency, convergence speed, and test accuracy for PDE solvers.
  arXiv  Detail & Related papers  (2024-11-22T18:25:13Z)
• Element-wise Multiplication Based Deeper Physics-Informed Neural Networks [1.8554335256160261]
  PINNs are a promising framework for resolving partial differential equations (PDEs) Lack of expressive ability and pathology issues are found to prevent the application of PINNs in complex PDEs. We propose Deeper Physics-Informed Neural Network (Deeper-PINN) to resolve these issues.
  arXiv  Detail & Related papers  (2024-06-06T15:27:52Z)
• RBF-PINN: Non-Fourier Positional Embedding in Physics-Informed Neural Networks [1.9819034119774483]
  We highlight the limitations of widely used Fourier-based feature mapping in certain situations. We suggest the use of the conditionally positive definite Radial Basis Function. Our method can be seamlessly integrated into coordinate-based input neural networks.
  arXiv  Detail & Related papers  (2024-02-13T10:54:43Z)
• On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it [1.3927943269211593]
  PINNs are Neural Network architectures trained to emulate solutions of differential equations without the necessity of solution data. We perform an empirical analysis of the behavior of PINN predictions outside their training domain. We assess whether the algorithmic setup of PINNs can influence their potential for generalization and showcase the respective effect on the prediction.
  arXiv  Detail & Related papers  (2023-02-15T09:51:56Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method [70.19159220248805]
  Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs) We propose the generative adversarial neural network (GA-PINN), which integrates the generative adversarial (GA) mechanism with the structure of PINNs. Inspired from the weighting strategy of the Adaboost method, we then introduce a point-weighting (PW) method to improve the training efficiency of PINNs.
  arXiv  Detail & Related papers  (2022-05-18T06:50:44Z)
• Robust Learning of Physics Informed Neural Networks [2.86989372262348]
  Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE.
  arXiv  Detail & Related papers  (2021-10-26T00:10:57Z)
• Characterizing possible failure modes in physics-informed neural networks [55.83255669840384]
  Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena even for simple PDEs. We show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize.
  arXiv  Detail & Related papers  (2021-09-02T16:06:45Z)
• Influence Functions in Deep Learning Are Fragile [52.31375893260445]
  influence functions approximate the effect of samples in test-time predictions. influence estimates are fairly accurate for shallow networks. Hessian regularization is important to get highquality influence estimates.
  arXiv  Detail & Related papers  (2020-06-25T18:25:59Z)
• Phase Detection with Neural Networks: Interpreting the Black Box [58.720142291102135]
  Neural networks (NNs) usually hinder any insight into the reasoning behind their predictions. We demonstrate how influence functions can unravel the black box of NN when trained to predict the phases of the one-dimensional extended spinless Fermi-Hubbard model at half-filling.
  arXiv  Detail & Related papers  (2020-04-09T17:45:45Z)

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.