Learning finite symmetry groups of dynamical systems via equivariance detection
This provides a tool for researchers in dynamical systems and physics to automatically detect symmetries, which is incremental as it builds on existing equivariance detection methods.
The paper tackles the problem of discovering finite symmetry groups in dynamical systems by introducing the Equivariance Seeker Model (ESM), a data-driven method that identifies all symmetry transformations from trajectory data, achieving accurate results in both known and unknown equation scenarios.
In this work, we introduce the Equivariance Seeker Model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances equivariance preservation with the penalization of redundant solutions, ensuring the complete and accurate identification of all symmetry transformations. We apply this framework specifically to dynamical systems, identifying their symmetry groups directly from observed trajectory data. To demonstrate its versatility, we test ESM on multiple systems in two distinct scenarios: (i) when the governing equations are known theoretically and (ii) when they are unknown, and the equivariance finding relies solely on observed data. The latter case highlights ESM's fully data-driven capability, as it requires no prior knowledge of the system's equations to operate.