On a Structure of an Automated Differential Equation Solver Based on Machine Learning Methods

Differential equation solvers are usually well-established software. On the one hand, conventional solvers are designed in a high-performance computation paradigm. On the other hand, it is hard to make changes to the conventional solver structures. In some applications, as an example equation discovery, it is viable to move from high-performance solutions for a given class of equations to a universal machine learning tool that could handle wide classes of equations. In this paper, we describe the current state of automated differential equation solvers and propose the architecture of such software. We highlight the difference between conventional and automated solvers. We also propose the architecture of the differential equation solver based on a machine learning paradigm.