  Despite the advancements in learning governing differential equations from
observations of dynamical systems, data-driven methods are often unaware of
fundamental physical laws, such as frame invariance. As a result, these
algorithms may search an unnecessarily large space and discover equations that
are less accurate or overly complex. In this paper, we propose to leverage
symmetry in automated equation discovery to compress the equation search space
and improve the accuracy and simplicity of the learned equations. Specifically,
we derive equivariance constraints from the time-independent symmetries of
ODEs. Depending on the types of symmetries, we develop a pipeline for
incorporating symmetry constraints into various equation discovery algorithms,
including sparse regression and genetic programming. In experiments across a
diverse range of dynamical systems, our approach demonstrates better robustness
against noise and recovers governing equations with significantly higher
probability than baselines without symmetry.
