Discover Physical Concepts and Equations with Machine Learning

Machine learning can uncover physical concepts or physical equations when prior knowledge from another one is available. However, in many cases, these two aspects are coupled and cannot be discovered independently. We extend SciNet, which is a neural network architecture that simulates the human physical reasoning process for physics discovery, by proposing a model that combines Variational Autoencoders (VAEs) with Neural Ordinary Differential Equations (Neural ODEs). This allows us to simultaneously discover physical concepts and governing equations from simulated experimental data across diverse physical systems. We apply the model to several key examples inspired by the history of physics, including Copernicus' heliocentric solar system, Newton's law of universal gravitation, the wave function together with the Schr\"odinger equation, and spin-1/2 along with the Pauli equation. The results demonstrate that the neural network successfully reconstructs the corresponding theories.