  One of the approaches used to solve for the dynamics of open quantum systems
is the hierarchical equations of motion (HEOM). Although it is numerically
exact, this method requires immense computational resources to solve. The
objective here is to demonstrate whether models such as SARIMA, CatBoost,
Prophet, convolutional and recurrent neural networks are able to bypass this
requirement. We are able to show this successfully by first solving the HEOM to
generate a data set of time series that depict the dissipative dynamics of
excitation energy transfer in photosynthetic systems then, we use this data to
test the models ability to predict the long-time dynamics when only the initial
short-time dynamics is given. Our results suggest that the SARIMA model can
serve as a computationally inexpensive yet accurate way to predict long-time
dynamics.
