  The machine learning approaches are applied in the dynamical simulation of
open quantum systems. The long short-term memory recurrent neural network
(LSTM-RNN) models are used to simulate the long-time quantum dynamics, which
are built based on the key information of the short-time evolution. We employ
various hyperparameter optimization methods, including the simulated annealing,
Bayesian optimization with tree-structured parzen estimator and random search,
to achieve the automatic construction and adjustment of the LSTM-RNN models.
The implementation details of three hyperparameter optimization methods are
examined, and among them the simulated annealing approach is strongly
recommended due to its excellent performance. The uncertainties of the machine
learning models are comprehensively analyzed by the combination of bootstrap
sampling and Monte-Carlo dropout approaches, which give the prediction
confidence of the LSTM-RNN models in the simulation of the open quantum
dynamics. This work builds an effective machine learning approach to simulate
the dynamics evolution of open quantum systems. In addition, the current study
provides an efficient protocol to build the optimal neural networks and to
estimate the trustiness of the machine learning models.
