Year: 2025
Type: article
Abstract: 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.
Source: Physical review. E
Authors: Meskerem Abebaw Mebratie, Rüdiger Nather, Guido Falk von Rudorff, Werner M. Seiler
Institution: University of Kassel
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Funder: Deutsche Forschungsgemeinschaft
Award: G7065877029
OpenAlex ID: W4407520212