Automatic Evolution of Machine-Learning-Based Quantum Dynamics with Uncertainty Analysis

Abstract

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 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 optimal neural networks and estimate the trustiness of the machine learning models.

Trajectory Propagation of Symmetrical Quasi-classical Dynamics with Meyer-Miller Mapping Hamiltonian Using Machine Learning

“…Such an idea was also realized to propagate the reduced quantum dynamics for a given systemplus-bath model by using different ML models. 9,11,12,14,15,23 These works showed the possibilities of applying the ML methods to deal with the nonadiabatic dynamics propagation. In addition, it is also possible to build a unified ML model for a group of system-plus-bath Hamiltonians with different parameters.…”

“…With the rapid development of computer facilities and artificial intelligence sciences in recent years, machine learning (ML) methods are extensively used as the important auxiliary tools in theoretical simulations of chemical dynamics, such as the construction of the potential energy surfaces, − the automatic analysis of molecular dynamics evolution, − and the numerical solution of the dynamical equation. − Among these works, considerable efforts were made to employ the various ML approaches as the supplement but powerful computational tools to propagate the nonadiabatic dynamics evolutions, ,− ,,, in which the strong electronic-nuclear couplings exist.…”

“…Nonadiabatic dynamics plays an essential role in the photoinduced molecular processes. − Therefore, many dynamical approaches were developed to describe nonadiabatic transitions. ,,− In recent years, many efforts were made to combine the ML approaches and the nonadiabatic dynamics simulations, including the employment of the ML potential energy surfaces ,, and the identification of the major molecular motion. ,, In addition, several works tried to introduce ML approaches to realize the long-time nonadiabatic dynamics propagation by learning the short-time evolution. ,,,,, Some of these works are relevant to the interesting idea of the transfer tensor method (TTM) . The TTM formalism is built on the central concept of time-translational invariance and the organization of information content of dynamical trajectories.…”

“…For practical implementation, the TTM also reveals the crucial role of the initial condition, such that the correlated and product system-bath initial states lead to different dynamic evolution. Such an idea was also realized to propagate the reduced quantum dynamics for a given system-plus-bath model by using different ML models. ,,,,, These works showed the possibilities of applying the ML methods to deal with the nonadiabatic dynamics propagation. In addition, it is also possible to build a unified ML model for a group of system-plus-bath Hamiltonians with different parameters. , Many of these works more-or-less require the early short-time dynamics data in the ML model construction in order to make the long-time dynamics prediction.…”

“…8,44,45 In addition, several works tried to introduce ML approaches to realize the long-time nonadiabatic dynamics propagation by learning the short-time evolution. 9,11,12,14,15,23 Some of these works are relevant to the interesting idea of the transfer tensor method (TTM). 46 The TTM formalism is built on the central concept of timetranslational invariance and the organization of information content of dynamical trajectories.…”