Performance evaluation of predictive models for Poisson’s equations by PINN using low-discrepancy sequences

Abstract

This research focuses on Physics-Informed Neural Network (PINN), which is a neural network that approximates the solution function of the initial-boundary value problem of partial differential equations. In particular, numerical experiments are conducted to evaluate the effect of point set features on the computational accuracy of predictive models by PINN. As point sets, in addition to general pseudo-random number sequences, low-discrepancy sequences such as Halton sequences and Sobol sequences, which have been shown to be useful in quasi-Monte Carlo methods, are also used. Furthermore, this research proposes the use of a finite element mesh smoothed by centroidal Voronoi tessellation as a technique to make it easier to apply PINN to regions with arbitrary boundary shapes.