Miles Cranmer

Miles Cranmer

07-03-2022

19:37

Could machine learning rediscover the law of gravitation simply by observing our solar system? With our new approach, the answer is *YES*. Led by: @PabloLemosP With: @Niall_Jeffrey @cosmo_shirley @PeterWBattaglia Paper: Blog:

Here are two classes of problems which we can already solve: 1. Known law, unknown parameters => parameter inference. 2. Unknown law, known parameters => model discovery (eg, / Here we look at unknown law AND unknown parameters!

Summary of the algorithm: 1. Declare unknown physical properties of a system as trainable parameters in a machine learning model. 2. Update these parameters simultaneously with the model weights. 3. Finally, distill the learned model to a set of symbolic rules.

After training, we use PySR (to find the following symbolic forms as approximations of our graph neural network's edge function. The symbolic rule which best balances accuracy and simplicity is the same as the law of universal gravitation (in teal):

Let's look at the per-node parameters learned in our model. These are actually strongly correlated with the true masses! Note that the model's scale is arbitrary, so these are shown normalized to the mass of the sun. We also have to fix F=ma to eliminate a functional degeneracy.

This approach allows us to do model discovery even when missing crucial information about our system! I anticipate this being very useful for model discovery in real-world datasets. For more details check out the paper



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