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.

翻译：物理信息神经网络(PINNs)代表他们作为神经网络,解决部分差异方程式(PDEs),最初的PINN实施并不提供高精度,通常达到约0.1美元相对差错。我们制定并测试了一种称为竞争性PINNs(CPINNs)的对抗性办法,以克服这一限制。CPINNs培训了一名因预测PINN错误而得到奖励的歧视问题人。歧视者和PINN参加零和游戏,将精确的PDE解决方案作为最佳战略。这种方法避免了划分PDE离散性大号的问题。数字实验表明,受过竞争性梯度下行训练的CPINN可能会出现两个小于以亚当或随机梯度梯度下位为训练的PINN的错误。