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

A non-Markovian neural quantum propagator and its application in the simulation of ultrafast nonlinear spectra

The accurate solution of dissipative quantum dynamics plays an important role in the simulation of open quantum systems. Here, we propose a machine learning-based universal solver for the hierarchical equations of motion, one of the most widely used approaches which takes into account non-Markovian effects and nonperturbative system-environment interactions in a numerically exact manner. We develop a neural quantum propagator model by utilizing the neural network architecture, which avoids time-consuming iterations and can be used to evolve any initial quantum state for arbitrarily long times. To demonstrate the efficacy of our model, we apply it to the simulation of population dynamics and linear and two-dimensional spectra of the Fenna-Matthews-Olson complex.

How Sophisticated Are Neural Networks Needed to Predict Long-Term Nonadiabatic Dynamics?

Nonadiabatic dynamics is key for understanding solar energy conversion and photochemical processes in condensed phases. This often involves the non-Markovian dynamics of the reduced density matrix in open quantum systems, where knowledge of the system's prior states is necessary to predict its future behavior. In this study, we explore time-series machine learning methods for predicting long-time nonadiabatic dynamics based on short-time input data, comparing these methods with the physics-based transfer tensor method (TTM). To understand the impact of memory time on these approaches, we demonstrate that non-Markovian dynamics can be represented as a linear map within the Nakajima-Zwanzig generalized quantum master equation framework. We further propose a practical method to estimate the effective memory time, within a given tolerance, for reduced density matrix propagation. Our predictive models are applied to various physical systems, including spin-boson models, multistate harmonic (MSH) models with Ohmic spectral densities and for a realistic organic photovoltaic system composed of a carotenoid-porphyrin-fullerene triad dissolved in tetrahydrofuran. Results indicate that the simple linear-mapping fully connected neural network (FCN) outperforms the more complicated nonlinear-mapping networks including the gated recurrent unit (GRU) and the convolutional neural network/long short-term memory (CNN-LSTM) in systems with short memory times, such as spin-boson and MSH models. Conversely, the nonlinear CNN-LSTM and GRU models yield higher accuracy in the triad MSH systems characterized by long memory times. These findings offer valuable insights into the role of effective memory time in non-Markovian quantum dynamics, providing practical guidance for the application of time-series machine learning models to complex chemical systems.

A short trajectory is all you need: A transformer-based model for long-time dissipative quantum dynamics

In this Communication, we demonstrate that a deep artificial neural network based on a transformer architecture with self-attention layers can predict the long-time population dynamics of a quantum system coupled to a dissipative environment provided that the short-time population dynamics of the system is known. The transformer neural network model developed in this work predicts the long-time dynamics of spin-boson model efficiently and very accurately across different regimes, from weak system-bath coupling to strong coupling non-Markovian regimes. Our model is more accurate than classical forecasting models, such as recurrent neural networks, and is comparable to the state-of-the-art models for simulating the dynamics of quantum dissipative systems based on kernel ridge regression.

Unsupervised Machine Learning in the Analysis of Nonadiabatic Molecular Dynamics Simulation

The all-atomic full-dimensional-level simulations of nonadiabatic molecular dynamics (NAMD) in large realistic systems has received high research interest in recent years. However, such NAMD simulations normally generate an enormous amount of time-dependent high-dimensional data, leading to a significant challenge in result analyses. Based on unsupervised machine learning (ML) methods, considerable efforts were devoted to developing novel and easy-to-use analysis tools for the identification of photoinduced reaction channels and the comprehensive understanding of complicated molecular motions in NAMD simulations. Here, we tried to survey recent advances in this field, particularly to focus on how to use unsupervised ML methods to analyze the trajectory-based NAMD simulation results. Our purpose is to offer a comprehensive discussion on several essential components of this analysis protocol, including the selection of ML methods, the construction of molecular descriptors, the establishment of analytical frameworks, their advantages and limitations, and persistent challenges.

Fusing 2D and 3D molecular graphs as unambiguous molecular descriptors for conformational and chiral stereoisomers

The rapid progress of machine learning (ML) in predicting molecular properties enables high-precision predictions being routinely achieved. However, many ML models, such as conventional molecular graph, cannot differentiate stereoisomers of certain types, particularly conformational and chiral ones that share the same bonding connectivity but differ in spatial arrangement. Here, we designed a hybrid molecular graph network, Chemical Feature Fusion Network (CFFN), to address the issue by integrating planar and stereo information of molecules in an interweaved fashion. The three-dimensional (3D, i.e., stereo) modality guarantees precision and completeness by providing unabridged information, while the two-dimensional (2D, i.e., planar) modality brings in chemical intuitions as prior knowledge for guidance. The zipper-like arrangement of 2D and 3D information processing promotes cooperativity between them, and their synergy is the key to our model's success. Experiments on various molecules or conformational datasets including a special newly created chiral molecule dataset comprised of various configurations and conformations demonstrate the superior performance of CFFN. The advantage of CFFN is even more significant in datasets made of small samples. Ablation experiments confirm that fusing 2D and 3D molecular graphs as unambiguous molecular descriptors can not only effectively distinguish molecules and their conformations, but also achieve more accurate and robust prediction of quantum chemical properties.

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.

All-Atom Nonadiabatic Semiclassical Mapping Dynamics for Photoinduced Charge Transfer of Organic Photovoltaic Molecules in Explicit Solvents

Direct all-atom simulation of nonadiabatic dynamics in disordered condensed phases like liquid solutions and amorphous solids has been challenging. The first all-atom simulation of the photoinduced charge-transfer dynamics of a prototypical organic photovoltaic carotenoid-porphyrin-C₆₀ molecular triad in explicit tetrahydrofuran is presented. Based on the Meyer-Miller mapping Hamiltonian, various semiclassical and mixed quantum-classical dynamics are employed, including the linearized semiclassical, symmetrical quasiclassical, mean-field Ehrenfest, classical mapping model, and spin-mapping model approaches. The all-atom nonadiabatic dynamics were compared to multi-state harmonic models with a globally shared bath, and the models built using the ensemble averages on the initial electronic state could reproduce the all-atom results. The solvent effect was found to be critical for the photoinduced charge transfer, and the time-dependent solute-solvent radial distribution functions revealed that only the nonadiabatic dynamics started with the effective forces on the initial electronic state could capture the correct nuclear dynamics. The proposed strategy for modeling condensed-phase nonadiabatic dynamics with atomistic details is readily applied to complex condensed-phase systems.

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.