We present an approach for using machine learning to automatically discover a physical law and associated properties of the system from real observations. We trained a neural network-based architecture, whose structure corresponds to classical mechanics, to simulate the dynamics of our Solar System from 30 years of observed trajectory data. We then used symbolic regression to extract a symbolic formula for the force law, which our results show matches Newtonian gravity. We find that by scaling the model's predicted acceleration by a trainable scalar variable, we could infer bodies' (relative) masses despite that they were not observable in the data itself. Though ``Newtonian'' gravity has of course been known since Newton, our approach did not require knowledge of this physical law, and so our results serve as a proof of principle that our method can extract unknown laws from observed data. This work takes a step towards using modern machine learning tools beyond data processing and analysis, but automated scientific theory formation and development.

Slides: in Keynote

Video: https://youtu.be/y05V_q69ryg