Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations

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.