Physics informed neural network for charged particles surrounded by conductive boundaries

Abstract

Molecular dynamics of charged particles in porous conductive media have received considerable attention in recent years due to their application in cutting-edge technologies such as batteries and supercapacitors. Due to the presence of long-range electrical interactions, induced charges present at the boundary, and the influence of boundary conditions, the simulation of these systems is more challenging than the simulation of typical molecular dynamic systems. Simulating these kinds of systems typically involves using a numerical solver to solve the Poisson equation, which is a very time-consuming procedure. Recently, Physics-Informed Neural Networks (PINNs) have been introduced as an alternative to numerical solutions of PDEs. In this paper, we present a new PINN-based model for predicting the potential of point-charged particles surrounded by conductive walls. As a result of the proposed PINN model, the mean square error is less than 7% and R^{2} score is more than 90% for the corresponding example simulation. Results have been compared with typical neural networks and random forest as standard machine learning algorithms. The R^{2} score of the random forest model was 70%, and a standard neural network could not be trained well.