  Despite very promising results, capturing the dynamics of complex quantum
systems with neural-network ans\"atze has been plagued by several problems, one
of which being stochastic noise that makes the dynamics unstable and highly
dependent on some regularization hyperparameters. We present an alternative
general scheme that enables one to capture long-time dynamics of quantum
systems in a stable fashion, provided the neural-network ansatz is normalized,
which can be ensured by the autoregressive property of the chosen ansatz. We
then apply the scheme to time-dependent quench dynamics by investigating the
Kibble-Zurek mechanism in the two-dimensional quantum Ising model. We find an
excellent agreement with exact dynamics for small systems and are able to
recover scaling laws in agreement with other variational methods.
