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Neural-network quantum states (NQS) have been shown to be a suitablevariational ansatz to simulate out-of-equilibrium dynamics in two-dimensionalsystems using time-dependent variational Monte Carlo (t-VMC). In particular,stable and accurate time propagation over long time scales has been observed inthe square-lattice Heisenberg model using the Restricted Boltzmann machinearchitecture. However, achieving similar performance in other systems hasproven to be more challenging. In this article, we focus on the two-legHeisenberg ladder driven out of equilibrium by a pulsed excitation as abenchmark system. We demonstrate that unmitigated noise is strongly amplifiedby the nonlinear equations of motion for the network parameters, which causesnumerical instabilities in the time evolution. As a consequence, the achievableaccuracy of the simulated dynamics is a result of the interplay between networkexpressiveness and measures required to remedy these instabilities. We showthat stability can be greatly improved by appropriate choice of regularization.This is particularly useful as tuning of the regularization typically imposesno additional computational cost. Inspired by machine learning practice, wepropose a validation-set based diagnostic tool to help determining optimalregularization hyperparameters for t-VMC based propagation schemes. For ourbenchmark, we show that stable and accurate time propagation can be achieved inregimes of sufficiently regularized variational dynamics.

Role of stochastic noise and generalization error in the time propagation of neural-network quantum states