Solving Partial Differential Equations for Physical and Chemical Problems Using Physics-Informed Neural Networks

Abstract

Numerous physical and chemical problems at a high school level can be described by ordinary differential equations (ODEs) and partial differential equations (PDEs). However, the underlying equations troubled high school students because they often lack advanced mathematical skills, such as discrete calculus. Our goal is not to elaborate on those skills, but to offer a shortcut to the solution. In this paper, we demonstrated the use of Physics-Informed Neural Networks (PINNs), a neural network which solves the PDEs by incorporating the PDEs into the loss functions. The heat transfer equation and second order chemical kinetics are the two chosen model problems for high school seniors. Using PINNs, we were able to solve these two problems without recurring to university math. Hence, we strongly recommend peers to employ this method for physical or chemical problems for high school students and beyond.