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Discovering conservation laws for a given dynamical system is important butchallenging. In a theorist setup (differential equations and basis functionsare both known), we propose the Sparse Invariant Detector (SID), an algorithmthat auto-discovers conservation laws from differential equations. Itsalgorithmic simplicity allows robustness and interpretability of the discoveredconserved quantities. We show that SID is able to rediscover known and evendiscover new conservation laws in a variety of systems. For two examples influid mechanics and atmospheric chemistry, SID discovers 14 and 3 conservedquantities, respectively, where only 12 and 2 were previously known to domainexperts.

Discovering New Interpretable Conservation Laws as Sparse Invariants