PinnDE: Physics-Informed Neural Networks for Solving Differential Equations

• URL: http://arxiv.org/abs/2408.10011v1
• Date: Mon, 19 Aug 2024 14:05:28 GMT
• Title: PinnDE: Physics-Informed Neural Networks for Solving Differential Equations
• Authors: Jason Matthews, Alex Bihlo,
• Abstract summary: We propose PinnDE, an open-source python library for solving differential equations with both PINNs and DeepONets. We give a brief review of both PINNs and DeepONets, introduce PinnDE along with the structure and usage of the package, and present worked examples to show its effectiveness.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful approaches in approximating differential equation solutions using machine learning. Here, we propose PinnDE, an open-source python library for solving differential equations with both PINNs and DeepONets. We give a brief review of both PINNs and DeepONets, introduce PinnDE along with the structure and usage of the package, and present worked examples to show PinnDE's effectiveness in approximating solutions with both PINNs and DeepONets.

Related papers

• A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks [1.0055663066199056]
  Ordinary and partial differential equations (DE) are used extensively in scientific and mathematical domains to model physical systems. Current literature has focused primarily on deep neural network (DNN) based methods for solving a specific DE or a family of DEs. This paper surveys and classifies previous works and provides an educational tutorial for senior practitioners, professionals, and graduate students in engineering and computer science.
  arXiv  Detail & Related papers  (2023-04-26T20:14:25Z)
• iPINNs: Incremental learning for Physics-informed neural networks [66.4795381419701]
  Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs) We propose incremental PINNs that can learn multiple tasks sequentially without additional parameters for new tasks and improve performance for every equation in the sequence. Our approach learns multiple PDEs starting from the simplest one by creating its own subnetwork for each PDE and allowing each subnetwork to overlap with previously learnedworks.
  arXiv  Detail & Related papers  (2023-04-10T20:19:20Z)
• A physics-informed neural network framework for modeling obstacle-related equations [3.687313790402688]
  Physics-informed neural networks (PINNs) are an attractive tool for solving partial differential equations based on sparse and noisy data. Here we extend PINNs to solve obstacle-related PDEs which present a great computational challenge. The performance of the proposed PINNs is demonstrated in multiple scenarios for linear and nonlinear PDEs subject to regular and irregular obstacles.
  arXiv  Detail & Related papers  (2023-04-07T09:22:28Z)
• SVD-PINNs: Transfer Learning of Physics-Informed Neural Networks via Singular Value Decomposition [24.422082821785487]
  One neural network corresponds to one partial differential equations. In practice, we usually need to solve a class of PDEs, not just one. We propose a transfer learning method of PINNs via keeping singular vectors and optimizing singular values.
  arXiv  Detail & Related papers  (2022-11-16T08:46:10Z)
• PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network [12.385926494640932]
  We propose PhyGNNet for solving partial differential equations on the basics of a graph neural network. In particular, we divide the computing area into regular grids, define partial differential operators on the grids, then construct pde loss for the network to optimize to build PhyGNNet model.
  arXiv  Detail & Related papers  (2022-08-07T13:33:34Z)
• 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)
• Improved Training of Physics-Informed Neural Networks with Model Ensembles [81.38804205212425]
  We propose to expand the solution interval gradually to make the PINN converge to the correct solution. All ensemble members converge to the same solution in the vicinity of observed data. We show experimentally that the proposed method can improve the accuracy of the found solution.
  arXiv  Detail & Related papers  (2022-04-11T14:05:34Z)
• Learning Physics-Informed Neural Networks without Stacked Back-propagation [82.26566759276105]
  We develop a novel approach that can significantly accelerate the training of Physics-Informed Neural Networks. In particular, we parameterize the PDE solution by the Gaussian smoothed model and show that, derived from Stein's Identity, the second-order derivatives can be efficiently calculated without back-propagation. Experimental results show that our proposed method can achieve competitive error compared to standard PINN training but is two orders of magnitude faster.
  arXiv  Detail & Related papers  (2022-02-18T18:07:54Z)
• IDRLnet: A Physics-Informed Neural Network Library [9.877979064734802]
  Physics Informed Neural Network (PINN) is a scientific computing framework used to solve both forward and inverse problems. This paper introduces IDRLnet, a Python toolbox for modeling and solving problems through PINN systematically.
  arXiv  Detail & Related papers  (2021-07-09T09:18:35Z)
• dNNsolve: an efficient NN-based PDE solver [62.997667081978825]
  We introduce dNNsolve, that makes use of dual Neural Networks to solve ODEs/PDEs. We show that dNNsolve is capable of solving a broad range of ODEs/PDEs in 1, 2 and 3 spacetime dimensions.
  arXiv  Detail & Related papers  (2021-03-15T19:14:41Z)

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.