Universal Generalization Theory for Physical Intuitions from Small Artificial Neural Networks

Physical intuitions are native functions from human brains, yet the understanding of how physical intuitions are formulated has remained elusive. In this Letter, we propose a mechanism that simulates how human brain can quickly develop intuitional understandings from limited observations. Conceiving a training algorithm adapted from the well-known variational principle in physics, small artificial neural networks can possess strong physical intuitions that master the problems of brachistochrone and quantum harmonic oscillators, by learning from a few highly similar samples. Our simulations suggest that the variational principle is the governing mechanism for artificial physical intuitions. This generalization is explained by a unified theory: it arises when the network approximates a solution manifold where the Euler-Lagrange operator is stationary with respect to observation features. Our theory also rationalizes that there is a threshold of artificial neural network size below which satisfactory physical intuitions are not possible. Our work offers insights into how strong physical intuition can be formulated as humans or as artificial intelligences.