peterparity/conservation-laws-manifold-learning

Discovering Conservation Laws using Optimal Transport and Manifold Learning

Discovering Conservation Laws using Optimal Transport and Manifold Learning

This is an implementation of our method for discovering conservation laws directly from trajectory samples. We reformulate this task as a manifold learning problem and propose a non-parametric approach, combining the Wasserstein metric from optimal transport with diffusion maps, to discover conserved quantities that vary across trajectories sampled from a dynamical system. The Wasserstein distances are efficiently computed using the Sinkhorn algorithm implemented by the OTT-JAX library, and the diffusion maps are implemented using NumPy/SciPy.

Please cite "Discovering Conservation Laws using Optimal Transport and Manifold Learning" (https://www.nature.com/articles/s41467-023-40325-7) and see the paper for more details. This is the official repository for the paper.