Machine Learning Conservation Laws of Dynamical systems

TL;DR

This paper introduces a kernel-based machine learning method to identify conservation laws in dynamical systems from trajectory data, offering a computationally efficient alternative to neural networks.

Contribution

It presents the first kernel method for learning conservation laws, reducing computational costs and training data requirements compared to neural network approaches.

Findings

Kernel methods effectively discover conservation laws from data.

Lower computational costs than neural network approaches.

Requires less training data for accurate results.

Abstract

Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such 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 here a simple approach minimising the length of the coefficient vector to discover a single conservation law.