  High-fidelity quantum dynamics emulators can be used to predict the time
evolution of complex physical systems. Here, we introduce an efficient training
framework for constructing machine learning-based emulators. Our approach is
based on the idea of knowledge distillation and uses elements of curriculum
learning. It works by constructing a set of simple, but rich-in-physics
training examples (a curriculum). These examples are used by the emulator to
learn the general rules describing the time evolution of a quantum system
(knowledge distillation). The goal is not only to obtain high-quality
predictions, but also to examine the process of how the emulator learns the
physics of the underlying problem. This allows us to discover new facts about
the physical system, detect symmetries, and measure relative importance of the
contributing physical processes. We illustrate this approach by training an
artificial neural network to predict the time evolution of quantum wave
packages propagating through a potential landscape. We focus on the question of
how the emulator learns the rules of quantum dynamics from the curriculum of
simple training examples and to which extent it can generalize the acquired
knowledge to solve more challenging cases.
