Competitive Physics Informed Networks

Qi Zeng, Spencer H Bryngelson, Florian Tobias Schaefer

Keywords: Physics informed learning, multi-agent games, Lagrange multipliers, partial differential equations

TL;DR: We introduce competitive physics informed networks where two neural networks solve a partial differential equation by playing a zero-sum game.

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 $10^{-3}$ $L_2$ 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.

Community Implementations: [ 4 code implementations](https://www.catalyzex.com/paper/competitive-physics-informed-networks/code)