It has been recently shown that supervised machine learning (ML) algorithms can accurately and efficiently predict the long-time populations dynamics of dissipative quantum systems given only short-time population dynamics. In the present article, we benchmaked 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 feed-forward 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.
More Explanation on the training process and comparison between kernel and neural network methods is given.