Speeding up quantum dissipative dynamics of open systems with kernel methods

Abstract

The future forecasting ability of machine learning (ML) makes ML a promising tool for predicting long-time quantum dissipative dynamics of open systems. In this Article, we employ nonparametric machine learning algorithm (kernel ridge regression as a representative of the kernel methods) to study the quantum dissipative dynamics of the widely-used spin-boson model. Our ML model takes short-time dynamics as an input and is used for fast propagation of the long-time dynamics, greatly reducing the computational effort in comparison with the traditional approaches. Presented results show that the ML model performs well in both symmetric and asymmetric spin-boson models. Our approach is not limited to spin-boson model and can be extended to complex systems.

MLQD: A package for machine learning-based quantum dissipative dynamics

“…MLQD package is written in Python language and provides the implementation of our recently proposed ML-based approaches for quantum dissipative dynamics. 91,98,99 This section lays out the concise documentation of theory, code design, use and implementation. Coming to the code design, we provide a simplified flowchart of MLQD architecture in Fig.…”

“…where σ is a hyperparameter defining the length scale. It is worth emphasising that many other kernel functions K(r, r i ) such as Matérn and exponential kernels 117,118 can also be used, however, based on our previous studies, 91,92 these kernels do not outperform the Gaussian kernel, thus in MLQD, we only use the Gaussian kernel.…”

“…For KRR, a short-time trajectory of t m ∆ = 4.0 is used as an input and following the algorithm described in Fig. 2, 91 we transform the trajectories beyond t m ∆ = 4.0 into target values. We train separate KRR models for each diagonal element of the RDM.…”

“…81 Without discussing the broad use of ML, in recent years, ML has seen a surge in the field of quantum dynamics in general and, in particular, quantum dissipative dynamics. To be specific, ML has been used to predict molecular configurations in the four-dimensional space, 90 the relaxation dynamics of a two-state system [91][92][93][94][95][96][97] the excitation energy transfer in Fenna-Matthews-Olson light-harvesting complex, [98][99][100][101] average exciton transfer times and transfer efficiencies, 102 parameters of Hamiltonian, 103 evolution of the proton density in a potential well 104 and vibronic Hamiltonians as a direct function of time. 105 Machine learning has also been extended to Meyer-Miller mapping based symmetrical quasi-classical 106 and fewest-switches surface hopping dynamics.…”

“…MLQD is incorporated with kernel ridge regression (KRR) and convolutional neural networks (CNN) models and a user can train and predict dynamics following both recursive and non-recursive approaches. We follow our recently published recursive KRR-based approach on the relaxation dynamics of the spin-boson model 91,92 and non-recursive CNN-based AIQD and OSTL approaches. 98,99 MLQD also supports hyperparameter optimization using MLATOM's grid search functionality [108][109][110] for KRR and Bayesian methods with Tree-structured Parzen Estimator (TPE) 111 for CNN models via the HYPEROPT package.…”