Easy to Learn Hard to Master - How to Solve an Arbitrary Equation with PINN

Abstract

Physics-informed neural networks (PINNs) offer predictive capabilities for processes defined by known equations and limited data. While custom architectures and loss computations are often designed for each equation, the untapped potential of classical architectures remains unclear. To make a comprehensive study, it is required to compare performance of a given neural network architecture and loss formulation for different types of equations. This paper introduces an open-source framework for unified handling of ordinary differential equations (ODEs), partial differential equations (PDEs), and their systems. We explore PINN applicability and convergence comprehensively, demonstrating its performance across ODEs, PDEs, ODE systems, and PDE systems.