A comparative study of different machine learning methods for dissipative quantum dynamics

Recently, Machine Learning (ML) is increasingly used for fast and accurate propagation of quantum dissipative dynamics including our works for the two-state system and seven-site FMO complex. The studies carried out so far demonstrated the use of different ML models and given the plethora of available ML models, it is challenging to assess their performance on an equal footing. In the study published in the journal Machine learning: Science and Technology, we have performed a comparative study of 22 different ML models including 8 kernel-based and 14 neural networks (NN) models.

The comparative study is performed for a general two-state spin-boson model where the performance of the models was assessed by the mean absolute error (MAE) and computational times for training and prediction. In NN models, each model has been tuned to have approximately the same number of trainable parameters. In kernel-based models, as the number of parameters is equal to the number of training points, all models have the same number of parameters. Our comparative study shows that kernel methods with non-linear kernel functions outperform the NN models in both accuracy and computational time. Among NN models, the Convolutional Gated Recurrent Unit model is the most efficient ANN model. For the performance of other models, readers are referred to the main text.

To conclude, in the existing plethora of ML models, the kernel methods should be preferred at least for problems similar to those we studied, i.e., for relatively simple two-state spin-boson models. However, for more complex systems, additional investigations are desirable. As usual, the article has links to the open-source code and data, and, for kernel-based calculations, we used our package MLatom.

• Luis E. Herrera Rodríguez, Arif Ullah, Kennet J. Rueda Espinosa, Pavlo O. Dral*, Alexei A. Kananenka*. A comparative study of different machine learning methods for dissipative quantum dynamics. Mach. Learn. Sci. Technol. 2022, accepted. DOI: 10.1088/2632-2153/ac9a9d.