🤖 AI Summary
This study addresses the challenge of jointly discovering physically meaningful concepts and their governing equations—where physical principles and differential equations are tightly coupled and cannot be identified independently. We propose a unified end-to-end discovery framework that integrates variational autoencoders (VAEs) with neural ordinary differential equations (Neural ODEs), embedding differentiable physics-informed priors and emulating human-like physical reasoning inspired by the SciNet architecture. The framework simultaneously learns interpretable latent physical concepts and their exact mathematical formulations from simulation data. Crucially, it enables joint differentiable optimization of both concept representations and equation structures—overcoming limitations of conventional symbolic regression and black-box fitting. Evaluated on canonical problems—including heliocentrism, Newtonian gravitation, the Schrödinger equation, and the Pauli magnetic moment—the model recovers theoretically correct functional forms; learned concepts carry clear physical interpretations; and predictive errors remain below 1%.
📝 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.