Discover physical concepts and equations with machine learning

TL;DR

This paper introduces a novel neural network model combining Variational Autoencoders and Neural ODEs to simultaneously discover physical concepts and equations from data, advancing automated physics discovery.

Contribution

It extends SciNet by integrating VAE and Neural ODEs, enabling independent discovery of physical concepts and governing equations from experimental data.

Findings

Successfully discovered physical theories like heliocentrism, gravity, wave mechanics, and spin-magnetic formulations.

The model accurately uncovers underlying physical laws from simulated data.

Demonstrates the potential of neural networks in automated scientific discovery.

Abstract

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, Schr\"odinger's wave mechanics, and Pauli's spin-magnetic formulation. The results demonstrate that the correct physical theories can emerge in the neural network.