  Can physical concepts and laws emerge in a neural network as it learns to
predict the observation data of physical systems? As a benchmark and a
proof-of-principle study of this possibility, here we show an introspective
learning architecture that can automatically develop the concept of the quantum
wave function and discover the Schr\"odinger equation from simulated
experimental data of the potential-to-density mappings of a quantum particle.
This introspective learning architecture contains a machine translator to
perform the potential to density mapping, and a knowledge distiller
auto-encoder to extract the essential information and its update law from the
hidden states of the translator, which turns out to be the quantum wave
function and the Schr\"odinger equation. We envision that our introspective
learning architecture can enable machine learning to discover new physics in
the future.
