Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method

• URL: http://arxiv.org/abs/2205.08754v1
• Date: Wed, 18 May 2022 06:50:44 GMT
• Title: Revisiting PINNs: Generative Adversarial Physics-informed Neural Networks and Point-weighting Method
• Authors: Wensheng Li, Chao Zhang, Chuncheng Wang, Hanting Guan, Dacheng Tao
• Abstract summary: 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.
• Score: 70.19159220248805
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physics-informed neural networks (PINNs) provide a deep learning framework for numerically solving partial differential equations (PDEs), and have been widely used in a variety of PDE problems. However, there still remain some challenges in the application of PINNs: 1) the mechanism of PINNs is unsuitable (at least cannot be directly applied) to exploiting a small size of (usually very few) extra informative samples to refine the networks; and 2) the efficiency of training PINNs often becomes low for some complicated PDEs. In this paper, we propose the generative adversarial physics-informed neural network (GA-PINN), which integrates the generative adversarial (GA) mechanism with the structure of PINNs, to improve the performance of PINNs by exploiting only a small size of exact solutions to the PDEs. Inspired from the weighting strategy of the Adaboost method, we then introduce a point-weighting (PW) method to improve the training efficiency of PINNs, where the weight of each sample point is adaptively updated at each training iteration. The numerical experiments show that GA-PINNs outperform PINNs in many well-known PDEs and the PW method also improves the efficiency of training PINNs and GA-PINNs.

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