  We present an approach for using machine learning to automatically discover
the governing equations and hidden properties of real physical systems from
observations. We train a "graph neural network" to simulate the dynamics of our
solar system's Sun, planets, and large moons from 30 years of trajectory data.
We then use symbolic regression to discover an analytical expression for the
force law implicitly learned by the neural network, which our results showed is
equivalent to Newton's law of gravitation. The key assumptions that were
required were translational and rotational equivariance, and Newton's second
and third laws of motion. Our approach correctly discovered the form of the
symbolic force law. Furthermore, our approach did not require any assumptions
about the masses of planets and moons or physical constants. They, too, were
accurately inferred through our methods. Though, of course, the classical law
of gravitation has been known since Isaac Newton, our result serves as a
validation that our method can discover unknown laws and hidden properties from
observed data. More broadly this work represents a key step toward realizing
the potential of machine learning for accelerating scientific discovery.
