AI Poincar\'{e} 2.0: Machine Learning Conservation Laws from Differential Equations
Machine Learning
2022-11-01 v2 Earth and Planetary Astrophysics
Exactly Solvable and Integrable Systems
Classical Physics
Fluid Dynamics
Abstract
We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schr\"odinger equation.
Cite
@article{arxiv.2203.12610,
title = {AI Poincar\'{e} 2.0: Machine Learning Conservation Laws from Differential Equations},
author = {Ziming Liu and Varun Madhavan and Max Tegmark},
journal= {arXiv preprint arXiv:2203.12610},
year = {2022}
}
Comments
15 pages, 12 figures