Identifying Solution Constraints for ODE Systems

TL;DR

This paper introduces a sparse identification framework to discover solution component relations in first-order ODE systems using numerical data, assuming sparsity in the connecting functions.

Contribution

It presents a novel method for identifying sparse relations between ODE solution components from numerical data, expanding the tools for analyzing differential systems.

Findings

Successfully identified relations in example systems

Demonstrated effectiveness with numerical solutions

Applicable to various first-order ODE systems

Abstract

This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques on the data represented by the numerical solution of the initial-value problem at hand. The only assumption is that there are only a few terms that connects the components, so that the mathematical relations to be discovered are sparse in the set of possible functions. We illustrate the method through examples of applications.