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

Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz simulate out-of-equilibrium dynamics in two-dimensional systems using time-dependent Monte Carlo (t-VMC). In particular, stable and accurate time propagation over long scales has observed the square-lattice Heisenberg model Restricted Boltzmann machine architecture. However, achieving similar performance other proven more challenging. this article, we focus on two-leg ladder driven out of equilibrium by pulsed excitation as benchmark system. We demonstrate that unmitigated noise is strongly amplified nonlinear equations motion for network parameters, which causes numerical instabilities evolution. As consequence, achievable accuracy simulated result interplay between expressiveness measures required remedy these instabilities. show stability can greatly improved appropriate choice regularization. This particularly useful tuning regularization typically imposes no additional computational cost. Inspired learning practice, propose validation-set based diagnostic tool help determining optimal hyperparameters t-VMC schemes. For our benchmark, achieved regimes sufficiently regularized dynamics.