Discovering New Interpretable Conservation Laws as Sparse Invariants
This work addresses the challenge of discovering conservation laws for dynamical systems, which is important for fields like fluid mechanics and atmospheric chemistry, but it appears incremental as it builds on existing theoretical setups.
The authors tackled the problem of discovering conservation laws from differential equations by proposing the Sparse Invariant Detector (SID) algorithm, which automatically identifies such laws and demonstrated its ability to rediscover known and discover new ones, finding 14 and 3 conserved quantities in fluid mechanics and atmospheric chemistry systems where only 12 and 2 were previously known.
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.