Discovering New Interpretable Conservation Laws as Sparse Invariants

TL;DR

The paper introduces SID, a simple and robust algorithm that automatically discovers interpretable conservation laws in dynamical systems, including previously unknown invariants in fluid mechanics and atmospheric chemistry.

Contribution

The paper presents SID, a novel sparse invariant detector that auto-discovers conservation laws from differential equations with high interpretability and robustness.

Findings

SID rediscovered known conservation laws in tested systems.

SID discovered new conservation laws in fluid mechanics and atmospheric chemistry.

SID identified 14 and 3 conserved quantities where fewer were previously known.

Abstract

Discovering conservation laws for a given dynamical system is important but challenging. In a theorist setup (differential equations and basis functions are both known), we propose the Sparse Invariant Detector (SID), an algorithm that auto-discovers conservation laws from differential equations. Its algorithmic simplicity allows robustness and interpretability of the discovered conserved quantities. We show that SID is able to rediscover known and even discover new conservation laws in a variety of systems. For two examples in fluid mechanics and atmospheric chemistry, SID discovers 14 and 3 conserved quantities, respectively, where only 12 and 2 were previously known to domain experts.