Investigating the density evolution of charged particles inside a square domain

Abstract: In this work, I propose a hybrid particle simulator for charged particles. The simulator consists of a physics-informed neural network, which can handle arbitrary external electric fields with continuous coordinates by solving the Poisson equation, and a graph-based algorithm that computes the interacting forces between the particles. The simulator is then applied to a set of particles inside a square domain under the influence of some external electric field. As the system evolves in time, particles will gradually leave the domain causing the particle density of the domain to change. This work aims to find a model which describes the particle density evolution of the system.