Class Symbolic Regression: Gotta Fit 'Em All

We introduce "Class Symbolic Regression" a first framework for automatically finding a single analytical functional form that accurately fits multiple datasets - each governed by its own (possibly) unique set of fitting parameters. This hierarchical framework leverages the common constraint that all the members of a single class of physical phenomena follow a common governing law. Our approach extends the capabilities of our earlier Physical Symbolic Optimization ($\Phi$-SO) framework for Symbolic Regression, which integrates dimensional analysis constraints and deep reinforcement learning for symbolic analytical function discovery from data. We demonstrate the efficacy of this novel approach by applying it to a panel of synthetic toy case datasets and showcase its practical utility for astrophysics by successfully extracting an analytic galaxy potential from a set of simulated orbits approximating stellar streams.