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

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. Particularly, the bootstrap resampling method is applied in the LSTM-NN construction and prediction, which provides a Monte-Carlo approach in the estimation of forecasting confidence interval. In this bootstrap-based LSTM-NN approach, a large number of LSTM-NNs are constructed under the resampling of time-series data sequences that were obtained from the early-stage quantum evolution given by numerically-exact multilayer multiconfigurational time-dependent Hartree method. The built LSTM-NN ensemble is used for the reliable propagation of the long-time quantum dynamics, and the forecasting uncertainty that partially reflects the reliability of the LSTM-NN prediction is given at the same time. The long-time quantum dissipative dynamics simulated by the current bootstrap-based LSTM-NN approach is highly consistent with the exact quantum dynamics results. This demonstrates that the LSTM-NN prediction combined with the bootstrap approach is a practical and powerful tool to propagate the long-time quantum dynamics of open systems with high accuracy and low computational cost.