Model-free machine learning of conservation laws from data

We present a machine learning based method for learning first integrals of systems of ordinary differential equations from given trajectory data. The method is model-free in that it does not require explicit knowledge of the underlying system of differential equations that generated the trajectories. As a by-product, once the first integrals have been learned, also the system of differential equations will be known. We illustrate our method by considering several classical problems from the mathematical sciences.