Machine learning conservation laws of dynamical systems

Conservation laws are of great theoretical and practical interest. We describe an alternative approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is a unique approach based on kernel methods instead of neural networks which leads to lower computational costs and requires a lower amount of training data. We propose the use of an “indeterminate” form of kernel ridge regression where the labels still have to be found by additional conditions.We use a simple approach minimizing the length of the coefficient vector to discover a single conservation law.