Discover physical concepts and equations with machine learning
This addresses the challenge of intertwined physical discovery in machine learning for physics, offering a method to automate theory extraction from data, though it appears incremental as an extension of existing architectures.
The paper tackles the problem of simultaneously discovering physical concepts and governing equations from simulated experimental data by extending SciNet with a model combining Variational Autoencoders and Neural ODEs, and demonstrates that correct physical theories can emerge in the neural network across examples like heliocentrism and Newton's law of gravity.
Machine learning can uncover physical concepts or physical equations when prior knowledge from the other is available. However, these two aspects are often intertwined 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 (VAE) with Neural Ordinary Differential Equations (Neural ODEs). This allows us to simultaneously discover physical concepts and governing equations from simulated experimental data across various physical systems. We apply the model to several examples inspired by the history of physics, including Copernicus' heliocentrism, Newton's law of gravity, Schrödinger's wave mechanics, and Pauli's spin-magnetic formulation. The results demonstrate that the correct physical theories can emerge in the neural network.