A physics informed neural network architecture for moving boundary problems in science and engineering.

Abstract

The study of moving boundary problems requires determining the moving interface which is a-priori unknown, significantly affecting the problem's physics. Traditional methods for tracking the moving interface struggle with the coupling of the moving interface with the dependent variables. Recent advances in Deep Learning have led to new numerical methods and improvements to existing algorithms. Physics-Informed Neural Networks offer a mesh-free approach to solving Partial Differential Equations by converting the problem into an optimization problem for the cost function defined based on the residual of the governing equations. Physics-Informed Neural Networks represent a significant advancement for solving complex problems in classical scenarios where the spatial domain of interest is well-defined and does not change over time. Here, a novel and general Physics-Informed Neural Network architecture is designed specifically for the class of moving boundary problems where the spatial domain of interest evolves with time. The Physics-Informed Neural Network architecture we suggest uses two separate neural networks to predict the free boundary and the dependent (system) variables. It is effectively used to solve various moving boundary problems, promising greater ease and feasibility, where applying traditional methods to handle complex moving boundary dynamics is challenging. The comparison of solutions obtained through Physics-Informed Neural Networks demonstrates their potential as a robust simulation platform for moving boundary problems in science and engineering.