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New large observational surveys such as Gaia are leading us into an era ofdata abundance, offering unprecedented opportunities to discover new physicallaws through the power of machine learning. Here we present an end-to-endstrategy for recovering a free-form analytical potential from a mere snapshotof stellar positions and velocities. First we show how auto-differentiation canbe used to capture an agnostic map of the gravitational potential and itsunderlying dark matter distribution in the form of a neural network. However,in the context of physics, neural networks are both a plague and a blessing asthey are extremely flexible for modeling physical systems but largely consistin non-interpretable black boxes. Therefore, in addition, we show how acomplementary symbolic regression approach can be used to open up this neuralnetwork into a physically meaningful expression. We demonstrate our strategy byrecovering the potential of a toy isochrone system.

An end-to-end strategy for recovering a free-form potential from a snapshot of stellar coordinates