Observing how deep neural networks understand physics through the energy spectrum of one-dimensional quantum mechanics

TL;DR

This paper demonstrates that neural networks trained on 1D quantum mechanics data can generalize to unseen potentials, predict untrained physical phenomena, and understand underlying physical laws, highlighting their potential as tools for physics discovery.

Contribution

The study shows neural networks can learn and generalize physical laws from data, extending their capabilities beyond training conditions in quantum mechanics.

Findings

NNs accurately predict energy eigenvalues for unseen potentials.

NNs can predict probability distributions of particles not used in training.

NNs reproduce untrained physical phenomena and predict unknown matter effects.

Abstract

We investigate how neural networks (NNs) understand physics using 1D quantum mechanics. After training an NN to accurately predict energy eigenvalues from potentials, we used it to confirm the NN's understanding of physics from four different aspects. The trained NN could predict energy eigenvalues of different kinds of potentials than the ones learned, predict the probability distribution of the existence of particles not used during training, reproduce untrained physical phenomena, and predict the energy eigenvalues of potentials with an unknown matter effect. These results show that NNs can learn physical laws from experimental data, predict the results of experiments under conditions different from those used for training, and predict physical quantities of types not provided during training. Because NNs understand physics in a different way than humans, they will be a powerful tool for advancing physics by complementing the human way of understanding.