Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structure

• URL: http://arxiv.org/abs/2401.04986v1
• Date: Wed, 10 Jan 2024 08:02:38 GMT
• Title: Structure-Preserving Physics-Informed Neural Networks With Energy or Lyapunov Structure
• Authors: Haoyu Chu, Yuto Miyatake, Wenjun Cui, Shikui Wei and Daisuke Furihata
• Abstract summary: We propose structure-preserving PINNs to improve their performance and broaden their applications for downstream tasks. A framework that utilizes structure-preserving PINN for robust image recognition is proposed. Experimental results demonstrate that the proposed method improves the numerical accuracy of PINNs for partial differential equations.
• Score: 9.571966961251347
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be established. This limitation could be a potential reason why the learning process for PINNs is not always efficient and the numerical results may suggest nonphysical behavior. Besides, there is little research on their applications on downstream tasks. To address these issues, we propose structure-preserving PINNs to improve their performance and broaden their applications for downstream tasks. Firstly, by leveraging prior knowledge about the physical system, a structure-preserving loss function is designed to assist the PINN in learning the underlying structure. Secondly, a framework that utilizes structure-preserving PINN for robust image recognition is proposed. Here, preserving the Lyapunov structure of the underlying system ensures the stability of the system. Experimental results demonstrate that the proposed method improves the numerical accuracy of PINNs for partial differential equations. Furthermore, the robustness of the model against adversarial perturbations in image data is enhanced.

Related papers

• Sidecar: A Structure-Preserving Framework for Solving Partial Differential Equations with Neural Networks [0.0]
  We propose Sidecar, a novel framework that enhances the accuracy and physical consistency of existing neural network solvers. Our experimental results on benchmark PDEs demonstrate the improvement of the existing neural network solvers.
  arXiv  Detail & Related papers  (2025-04-14T14:40:11Z)
• ProPINN: Demystifying Propagation Failures in Physics-Informed Neural Networks [71.02216400133858]
  Physics-informed neural networks (PINNs) have earned high expectations in solving partial differential equations (PDEs) Previous research observed the propagation failure phenomenon of PINNs. This paper provides the first formal and in-depth study of propagation failure and its root cause.
  arXiv  Detail & Related papers  (2025-02-02T13:56:38Z)
• SetPINNs: Set-based Physics-informed Neural Networks [31.193471532024407]
  We introduce SetPINNs, a framework that effectively captures local dependencies. We partition a domain into sets to model local dependencies while simultaneously enforcing physical laws.
  arXiv  Detail & Related papers  (2024-09-30T11:41:58Z)
• Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning [0.0]
  This paper introduces novel residual-based architectures, designed to enhance stability and accuracy in physics-informed neural networks (PINNs) The architectures augment traditional neural networks by incorporating residual connections, which facilitate smoother weight updates and improve backpropagation efficiency. The Squared Residual Network, in particular, exhibits robust performance, achieving enhanced stability and accuracy compared to conventional neural networks.
  arXiv  Detail & Related papers  (2024-07-10T05:20:43Z)
• Densely Multiplied Physics Informed Neural Networks [1.8554335256160261]
  physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs) This paper improves the neural network architecture to improve the performance of PINN. We propose a densely multiply PINN (DM-PINN) architecture, which multiplies the output of a hidden layer with the outputs of all the behind hidden layers.
  arXiv  Detail & Related papers  (2024-02-06T20:45:31Z)
• Enriched Physics-informed Neural Networks for Dynamic Poisson-Nernst-Planck Systems [0.8192907805418583]
  This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs) to solve dynamic Poisson-Nernst-Planck (PNP) equations. The EPINNs takes the traditional physics-informed neural networks as the foundation framework, and adds the adaptive loss weight to balance the loss functions. Numerical results indicate that the new method has better applicability than traditional numerical methods in solving such coupled nonlinear systems.
  arXiv  Detail & Related papers  (2024-02-01T02:57:07Z)
• Efficient and Flexible Neural Network Training through Layer-wise Feedback Propagation [49.44309457870649]
  Layer-wise Feedback feedback (LFP) is a novel training principle for neural network-like predictors.<n>LFP decomposes a reward to individual neurons based on their respective contributions.<n>Our method then implements a greedy reinforcing approach helpful parts of the network and weakening harmful ones.
  arXiv  Detail & Related papers  (2023-08-23T10:48:28Z)
• PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks [22.39904196850583]
  Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs) We introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs.
  arXiv  Detail & Related papers  (2023-07-21T18:06:27Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• On the Intrinsic Structures of Spiking Neural Networks [66.57589494713515]
  Recent years have emerged a surge of interest in SNNs owing to their remarkable potential to handle time-dependent and event-driven data. There has been a dearth of comprehensive studies examining the impact of intrinsic structures within spiking computations. This work delves deep into the intrinsic structures of SNNs, by elucidating their influence on the expressivity of SNNs.
  arXiv  Detail & Related papers  (2022-06-21T09:42:30Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• 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)
• 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)
• Rectified Linear Postsynaptic Potential Function for Backpropagation in Deep Spiking Neural Networks [55.0627904986664]
  Spiking Neural Networks (SNNs) usetemporal spike patterns to represent and transmit information, which is not only biologically realistic but also suitable for ultra-low-power event-driven neuromorphic implementation. This paper investigates the contribution of spike timing dynamics to information encoding, synaptic plasticity and decision making, providing a new perspective to design of future DeepSNNs and neuromorphic hardware systems.
  arXiv  Detail & Related papers  (2020-03-26T11:13:07Z)

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.