Improving physics-informed neural networks with meta-learned optimization

We show that the error achievable using physics-informed neural networks for solving differential equations can be substantially reduced when these networks are trained using meta-learned optimization methods rather than using fixed, hand-crafted optimizers as traditionally done. We choose a learnable optimization method based on a shallow multi-layer perceptron that is meta-trained for specific classes of differential equations. We illustrate meta-trained optimizers for several equations of practical relevance in mathematical physics, including the linear advection equation, Poisson's equation, the Korteweg-de Vries …

differential error layer meta networks neural networks optimization perceptron physics physics-informed show