Competitive Physics Informed Networks - Overcoming Limitations in PDE Solutions

Explore an innovative approach to solving partial differential equations using neural networks in this hour-long lecture on Competitive Physics Informed Networks. Delve into the limitations of traditional physics-informed neural networks (PINNs) and discover how the new competitive PINNs (CPINNs) method achieves unprecedented accuracy. Learn about the adversarial training process, where a discriminator and PINN engage in a zero-sum game, leading to solutions with relative errors on par with single-precision accuracy. Examine numerical experiments on a Poisson problem demonstrating CPINNs' superior performance, achieving errors four orders of magnitude smaller than conventional PINNs. Gain insights into the theoretical foundations, implementation challenges, and potential applications of this groundbreaking technique in computational physics and engineering.

Introduction
History of Neural Networks
Physics Informed Neural Networks
The Problem
Simultaneous Gradient Descent
Linearization
Gradient Descent
Cross Derivatives
Nash Equilibrium
Ablation Study
Stokes Training
Summary
Questions
Forward Pass Computation
Discussion Question