Competitive Physics Informed Neural Network
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Zeng, Qi
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Abstract
Physics Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by representing their solutions as neural networks. The original PINN implementation does not provide high accuracy, typically attaining about 0.1% relative error. To overcome this limitation, we formulate an adversarial approach called competitive PINNs (CPINNs). 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 on a Poisson problem show that a CPINN trained with competitive gradient descent can achieve errors four orders of magnitude smaller than that of a PINN trained with Adam, achieving nearly single-precision relative accuracy and consistently decreasing errors with each iteration. Numerical experiments on nonlinear Schrödinger and Burgers’ equations show that these improvements are not limited to linear problems.
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Undergraduate Research Option Thesis