Machine Learning Conservation Laws of Dynamical Systems

Co-author(s): Meskerem Abebaw Mebratie, Rüdiger Nather and Guido Falk von Rudorff

Reference: Physical Review E, 111 (2025) 025305

Description: We show how an indeterminate form of kernel ridge regression can be used to discover conservation laws of continuous dynamical systems. The main emphasis is on discovering a single polynomial conserved quantity from numerical trajectory data. But we also discuss the extension to more general type of conservation laws and the learning of more than one conservation law. Finally, we demonstrate that our method can also be applied to discrete dynamical systems, to the discovery of integral manifolds and to implicitisation problems.

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