Model-agnostic machine learning of conservation laws from data
This addresses the challenge of discovering conservation laws from data in fields like physics and engineering, but it appears incremental as it builds on existing machine learning approaches for dynamical systems.
The authors tackled the problem of learning conservation laws (first integrals) from trajectory data without requiring explicit knowledge of the underlying differential equations, achieving a model-agnostic method that can also recover the system of differential equations as a by-product.
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-agnostic 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.