Competitive Physics Informed Networks

• URL: http://arxiv.org/abs/2204.11144v1
• Date: Sat, 23 Apr 2022 22:01:37 GMT
• Title: Competitive Physics Informed Networks
• Authors: Qi Zeng, Spencer H. Bryngelson, Florian Sch\"afer
• Abstract summary: PINNs solve partial differential equations (PDEs) by representing them as neural networks. We formulate and test an adversarial approach called competitive PINNs (CPINNs) to overcome this limitation. CPINNs train a discriminator that is rewarded for predicting PINN mistakes. Numerical experiments show that a CPINN trained with competitive gradient descent can achieve two orders of magnitude smaller than that of a PINN trained with Adam or gradient descent.
• Score: 8.724433470897763
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physics Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by representing them as neural networks. The original PINN implementation does not provide high accuracy, typically attaining about $0.1\%$ relative error. We formulate and test an adversarial approach called competitive PINNs (CPINNs) to overcome this limitation. CPINNs train a discriminator that is rewarded for predicting PINN mistakes. The discriminator and PINN participate in a zero-sum game with the exact PDE solution as an optimal strategy. This approach avoids the issue of squaring the large condition numbers of PDE discretizations. Numerical experiments show that a CPINN trained with competitive gradient descent can achieve errors two orders of magnitude smaller than that of a PINN trained with Adam or stochastic gradient descent.

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