Applications of neural networks to dynamics simulation of Landau-Zener transitions

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

The long short-term memory recurrent neural network (LSTM-RNN) approach is applied to realize the trajectory-based nonadiabatic dynamics within the framework of the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC). After construction, the LSTM-RNN model allows us to propagate the entire trajectory evolutions of all involved degrees of freedoms (DOFs) from initial conditions. The proposed idea is proven to be reliable and accurate in the simulations of the dynamics of several site-exciton electron-phonon coupling models and three Tully's scattering models. It indicates that the LSTM-RNN model perfectly captures the dynamical information on the trajectory evolution in the MM-SQC dynamics. Our work proposes a novel machine learning approach in the simulation of trajectory-based nonadiabatic dynamic of complex systems with a large number of DOFs.

Fewest-Switches Surface Hopping with Long Short-Term Memory Networks

The mixed quantum-classical dynamical simulation is essential for studying nonadiabatic phenomena in photophysics and photochemistry. In recent years, many machine learning models have been developed to accelerate the time evolution of the nuclear subsystem. Herein, we implement long short-term memory (LSTM) networks as a propagator to accelerate the time evolution of the electronic subsystem during the fewest-switches surface hopping (FSSH) simulations. A small number of reference trajectories are generated using the original FSSH method, and then the LSTM networks can be built, accompanied by careful examination of typical LSTM-FSSH trajectories that employ the same initial condition and random numbers as the corresponding reference. The constructed network is applied to FSSH to further produce a trajectory ensemble to reveal the mechanism of nonadiabatic processes. Taking Tully's three models as test systems, we qualitatively reproduced the collective results. This work demonstrates that LSTM can be applied to the most popular surface hopping simulations.

One-Shot Trajectory Learning of Open Quantum Systems Dynamics

Nonadiabatic quantum dynamics is important for understanding light-harvesting processes, but its propagation with traditional methods can be rather expensive. Here we present a one-shot trajectory learning approach that allows us to directly make an ultrafast prediction of the entire trajectory of the reduced density matrix for a new set of such simulation parameters as temperature and reorganization energy. The whole 10-ps-long propagation takes 70 ms as we demonstrate on the comparatively large quantum system, the Fenna-Matthews-Olsen (FMO) complex. Our approach also significantly reduces time and memory requirements for training.

Forecasting nonadiabatic dynamics using hybrid convolutional neural network/long short-term memory network

Modeling nonadiabatic dynamics in complex molecular or condensed-phase systems has been challenging, especially for the long-time dynamics. In this work, we propose a time series machine learning scheme based on the hybrid convolutional neural network/long short-term memory (CNN-LSTM) framework for predicting the long-time quantum behavior, given only the short-time dynamics. This scheme takes advantage of both the powerful local feature extraction ability of CNN and the long-term global sequential pattern recognition ability of LSTM. With feature fusion of individually trained CNN-LSTM models for the quantum population and coherence dynamics, the proposed scheme is shown to have high accuracy and robustness in predicting the linearized semiclassical and symmetrical quasiclassical mapping dynamics as well as the mixed quantum-classical Liouville dynamics of various spin-boson models with learning time up to 0.3 ps. Furthermore, if the hybrid network has learned the dynamics of a system, this knowledge is transferable that could significantly enhance the accuracy in predicting the dynamics of a similar system. The hybrid CNN-LSTM network is thus believed to have high predictive power in forecasting the nonadiabatic dynamics in realistic charge and energy transfer processes in photoinduced energy conversion.

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 systems. The bootstrap method is applied in the LSTM-NN construction and prediction, which provides a Monte Carlo estimation of a forecasting confidence interval. Within this approach, a large number of LSTM-NNs are constructed by resampling time-series 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 simulated result is highly consistent with the exact evolution. The forecasting uncertainty that partially reflects the reliability of the LSTM-NN prediction is also given. This demonstrates the bootstrap-based LSTM-NN approach is a practical and powerful tool to propagate the long-time quantum dynamics of open systems with high accuracy and low computational cost.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.

Convolutional Neural Networks for Long Time Dissipative Quantum Dynamics

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network composed of convolutional layers is a powerful tool for predicting long-time dynamics of open quantum systems provided the preceding short-time evolution of a system is known. The neural network model developed in this work simulates long-time dynamics efficiently and accurately across different dynamical regimes from weakly damped coherent motion to incoherent relaxation. The model was trained on a data set relevant to photosynthetic excitation energy transfer and can be deployed to study long-lasting quantum coherence phenomena observed in light-harvesting complexes. Furthermore, our model performs well for the initial conditions different than those used in the training. Our approach reduces the required computational resources for long-time simulations and holds the promise for becoming a valuable tool in the study of open quantum systems.