Hybrid solver methods for ODEs: Machine-Learning combined with standard methods

TL;DR

This paper explores hybrid approaches combining machine learning and traditional numerical methods to solve ODEs and PDEs, aiming to accelerate the solving process through integrated algorithms.

Contribution

It introduces a novel framework that integrates ML algorithms with standard discretization methods for more efficient ODE and PDE solving.

Findings

ML methods can accelerate traditional ODE solvers

Hybrid methods effectively minimize combined optimization problems

The approach improves computational efficiency of solving differential equations

Abstract

In this article, we consider combined standard and machine learning methods to solve ODEs and PDEs. We deal with the minimisation problems for the machine learning algorithms and standard discretization methods, which are related to Runge-Kutta methods and finite difference methods. We show, that we could solve the ODEs with additional ML methods, e.g., feedforward network, such that it will accelerate the solver process.