  The core objective of machine-assisted scientific discovery is to learn
physical laws from experimental data without prior knowledge of the systems in
question. In the area of quantum physics, making progress towards these goals
is significantly more challenging due to the curse of dimensionality as well as
the counter-intuitive nature of quantum mechanics. Here, we present the QNODE,
a latent neural ODE trained on expectation values of closed and open quantum
systems dynamics. It can learn to generate such measurement data and
extrapolate outside of its training region that satisfies the von Neumann and
time-local Lindblad master equations for closed and open quantum systems
respectively in an unsupervised means. Furthermore, the QNODE rediscovers
quantum mechanical laws such as the Heisenberg's uncertainty principle in a
data-driven way, without any constraint or guidance. Additionally, we show that
trajectories that are generated from the QNODE that are close in its latent
space have similar quantum dynamics while preserving the physics of the
training system.
