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, multi-state 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.