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arXiv:2409.11320 · The Journal of Chemical Physics

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

Luis E. Herrera Rodríguez, Alexei A. Kananenka

Published Nov 1, 2024• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/5.0232871

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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.
Abstract It has been recently shown that supervised machine learning (ML) algorithms can accurately and efficiently predict long-time population dynamics of dissipative quantum systems given only short-time population dynamics. In the present article we benchmarked 22 ML models on their ability to predict long-time dynamics of a two-level quantum system linearly coupled to harmonic bath. The models include uni- and bidirectional recurrent, convolutional, and fully-connected feedforward artificial neural networks (ANNs) and kernel ridge regression (KRR) with linear and most commonly used nonlinear kernels. Our results suggest that KRR with nonlinear kernels can serve as inexpensive yet accurate way to simulate long-time dynamics in cases where the constant length of input trajectories is appropriate. Convolutional gated recurrent unit model is found to be the most efficient ANN model.
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.
Simulating non-Markovian quantum dissipative dynamics remains a major challenge in theoretical and computational chemistry. While traditional numerical methods such as hierarchical equations of motion are numerically exact, they suffer from prohibitive computational costs when modeling systems with complex environmental couplings or strong non-Markovian effects. To address this limitation, we propose a deep learning framework based on two-dimensional convolutional neural networks (2D-CNN) for efficiently predicting long-time quantum dissipative dynamics using only short-time trajectory data. Our approach incorporates a 1D-to-2D feature reconstruction strategy, which transforms 1D time-series data into 2D images, and a multi-timescale fusion network to resolve complex dynamical features. We validate the framework on two paradigmatic cases — dissipative relaxation in a two-level system and Rabi oscillations in a dissipative spin system — achieving prediction mean absolute errors of 10−310^{-3}10−3 and 10−2,10^{-2},10−2, respectively. The results highlight the effectiveness of our 2D-CNN approach in capturing long-time temporal correlations, providing a computationally efficient pathway for simulating quantum dynamics in realistic open systems.
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.
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 ML algorithm (kernel ridge regression as a representative of the kernel methods) to study the quantum dissipative dynamics of the widely-used spin-boson (SB) 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 SB models.Our approach is not limited to SB model and can be extended to complex systems.