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Symbolic Regression is the study of algorithms that automate the search foranalytic expressions that fit data. While recent advances in deep learning havegenerated renewed interest in such approaches, the development of symbolicregression methods has not been focused on physics, where we have importantadditional constraints due to the units associated with our data. Here wepresent $\Phi$-SO, a Physical Symbolic Optimization framework for recoveringanalytical symbolic expressions from physics data using deep reinforcementlearning techniques by learning units constraints. Our system is built, fromthe ground up, to propose solutions where the physical units are consistent byconstruction. This is useful not only in eliminating physically impossiblesolutions, but because the "grammatical" rules of dimensional analysis restrictenormously the freedom of the equation generator, thus vastly improvingperformance. The algorithm can be used to fit noiseless data, which can beuseful for instance when attempting to derive an analytical property of aphysical model, and it can also be used to obtain analytical approximations tonoisy data. We test our machinery on a standard benchmark of equations from theFeynman Lectures on Physics and other physics textbooks, achievingstate-of-the-art performance in the presence of noise (exceeding 0.1%) and showthat it is robust even in the presence of substantial (10%) noise. We showcaseits abilities on a panel of examples from astrophysics.

Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws