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The recurrent neural network with the long short-term memory cell (LSTM-NN)is employed to simulate the long-time dynamics of open quantum system. Thebootstrap method is applied in the LSTM-NN construction and prediction, whichprovides a Monte-Carlo estimation of forecasting confidence interval. Withinthis approach, a large number of LSTM-NNs are constructed by resamplingtime-series sequences that were obtained from the early-stage quantum evolutiongiven by numerically-exact multilayer multiconfigurational time-dependentHartree method. The built LSTM-NN ensemble is used for the reliable propagationof the long-time quantum dynamics and the simulated result is highly consistentwith the exact evolution. The forecasting uncertainty that partially reflectsthe reliability of the LSTM-NN prediction is also given. This demonstrates thebootstrap-based LSTM-NN approach is a practical and powerful tool to propagatethe long-time quantum dynamics of open systems with high accuracy and lowcomputational cost.

Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network