Variational Learning of Physical Intuition from a Few Observations

Humans often predict physical outcomes from only a few observations, a capability known as physical intuition. The mechanisms underlying this efficient learning remain elusive. Here, we introduce a variational learning framework in which small neural networks learn the mapping from observational parameters to optimal physical states from merely two or three similar examples. Demonstrating across classical and quantum regimes including strongly correlated molecules, networks trained this way generalize far beyond the training data. 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. The theory predicts the existence of a critical network size below which robust generalization fails to emerge. Our work establishes variational learning as a principled route to acquiring artificial physical intuition and offers a theoretical perspective for understanding similar capabilities in biological intelligence.