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

Abstract

We investigated how neural networks(NNs) understand physics using one-dimensional 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 a different potential than the one learned, focus on minima and maxima of a potential, predict the probability distribution of the existence of particles not used during training, and reproduce untrained physical phenomena. These results show that NNs can learn the laws of physics from only a limited set of data, predict the results of experiments under conditions different from those used for training, and predict physical quantities of types not provided during training. Since NNs understand physics through a different path than humans take, and by complementing the human way of understanding, they will be a powerful tool for advancing physics.