Competitive Physics Informed Networks
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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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