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.

翻译：本文开发了一个框架，用于发现一阶常微分方程组初值问题解的分量间关系。该框架通过对当前初值问题数值解所表示的数据应用稀疏识别技术来实现。其唯一假设是连接各分量的项数量有限，因此待发现的数学关系在可能函数集合中表现为稀疏性。我们通过应用实例阐述了该方法。