Observing how deep neural networks understand physics through the energy spectrum of one-dimensional quantum mechanics
This work shows that neural networks can complement human understanding in physics by learning and predicting physical laws from data, potentially advancing the field through novel insights.
The researchers trained a neural network to predict energy eigenvalues from potentials in 1D quantum mechanics, and it successfully generalized to predict energy eigenvalues for different potentials, probability distributions for untrained particles, reproduce untrained phenomena, and handle unknown matter effects, demonstrating that NNs can learn physical laws from data and make predictions beyond training conditions.
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.