English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

MPS-Authors
/persons/resource/persons241274

Hofmann,  D.
Theoretical Description of Pump-Probe Spectroscopies in Solids, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science (CFEL);

/persons/resource/persons182604

Sentef,  M. A.
Theoretical Description of Pump-Probe Spectroscopies in Solids, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;
Center for Free-Electron Laser Science (CFEL);

External Resource
Fulltext (public)

SciPostPhys_12_5_165.pdf
(Publisher version), 3MB

Supplementary Material (public)
There is no public supplementary material available
Citation

Hofmann, D., Fabiani, G., Mentink, J. H., Carleo, G., & Sentef, M. A. (2022). Role of stochastic noise and generalization error in the time propagation of neural-network quantum states. SciPost Physics, 12(5): 165. doi:10.21468/SciPostPhys.12.5.165.


Cite as: http://hdl.handle.net/21.11116/0000-0008-72F9-F
Abstract
Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics in two-dimensional systems using time-dependent variational Monte Carlo (t-VMC). In particular, stable and accurate time propagation over long time scales has been observed in the square-lattice Heisenberg model using the Restricted Boltzmann machine architecture. However, achieving similar performance in other systems has proven to be more challenging. In this article, we focus on the two-leg Heisenberg ladder driven out of equilibrium by a pulsed excitation as a benchmark system. We demonstrate that unmitigated noise is strongly amplified by the nonlinear equations of motion for the network parameters, which causes numerical instabilities in the time evolution. As a consequence, the achievable accuracy of the simulated dynamics is a result of the interplay between network expressiveness and measures required to remedy these instabilities. We show that stability can be greatly improved by appropriate choice of regularization. This is particularly useful as tuning of the regularization typically imposes no additional computational cost. Inspired by machine learning practice, we propose a validation-set based diagnostic tool to help determining optimal regularization hyperparameters for t-VMC based propagation schemes. For our benchmark, we show that stable and accurate time propagation can be achieved in regimes of sufficiently regularized variational dynamics.