  We develop a spacetime neural network method with second order optimization
for solving quantum dynamics from the high dimensional Schr\"{o}dinger
equation. In contrast to the standard iterative first order optimization and
the time-dependent variational principle, our approach utilizes the implicit
mid-point method and generates the solution for all spatial and temporal values
simultaneously after optimization. We demonstrate the method in the
Schr\"{o}dinger equation with a self-normalized autoregressive spacetime neural
network construction. Future explorations for solving different high
dimensional differential equations are discussed.
