In this talk I will argue two points. 1) Symbolic regression, a machine learning technique that fits data by iteratively searching the space of all possible analytic equations, should be a standard machine learning algorithm in astrophysics. 2) Symbolic regression can be extended to high-dimensional spaces, such as to models for N-body simulations, using the method we have developed. To begin the talk, I will introduce symbolic regression (SR), which is a relatively old but underdeveloped technique. I will demonstrate our new high-performance open-source SR software "PySR" (https://github.com/MilesCranmer/pysr). I will then discuss our research contribution: a technique for extending SR, which scales with O(n^n), n=number of variables(=features=dimensions), to high-dimensional spaces by the use of a neural network to break the problem down into small sub-problems. I will focus on Graph Neural Networks (GNNs), which are a physically motivated neural network architecture, and very relevant to many astrophysical problems. As a validation, I will demonstrate that we can use this technique of a GNN->SR to extract the correct force laws and Hamiltonians from simple particle simulations. I will then show work applying our method to the Quijote dark matter simulations---where it finds a simple analytic formula to estimate the overdensity of dark matter in a halo using learned metrics which summarize the nearby halos, giving a functional form that is more accurate than hand-derived formulas. Our approach simultaneously offers an interpretable ML technique for high-dimensional astrophysical data, and also a way of interpreting neural networks. (Demo code is available here: https://github.com/MilesCranmer/symbolic_deep_learning).
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