Discovering Symbolic Models from Deep Learning with Inductive Biases (Paper Explained)

Neural networks are very good at predicting systems’ numerical outputs, but not very good at deriving the discrete symbolic equations that govern many physical systems. This paper combines Graph Networks with symbolic regression and shows that the strong inductive biases of these models can be used to derive accurate symbolic equations from observation data. OUTLINE: 0:00 - Intro & Outline 1:10 - Problem Statement 4:25 - Symbolic Regression 6:40 - Graph Neural Networks 12:05 - Inductive Biases for Physics 15:15 - How Graph Networks compute outputs 23:10 - Loss Backpropagation 24:30 - Graph Network Recap 26:10 - Analogies of GN to Newtonian Mechanics 28:40 - From Graph Network to Equation 33:50 - L1 Regularization of Edge Messages 40:10 - Newtonian Dynamics Example 43:10 - Cosmology Example 44:45 - Conclusions & Appendix Paper: Code: Abstract: We develop a general approach to distill symbolic representations of a learned