  Recurrent neural networks have seen widespread use in modeling dynamical
systems in varied domains such as weather prediction, text prediction and
several others. Often one wishes to supplement the experimentally observed
dynamics with prior knowledge or intuition about the system. While the
recurrent nature of these networks allows them to model arbitrarily long
memories in the time series used in training, it makes it harder to impose
prior knowledge or intuition through generic constraints. In this work, we
present a path sampling approach based on principle of Maximum Caliber that
allows us to include generic thermodynamic or kinetic constraints into
recurrent neural networks. We show the method here for a widely used type of
recurrent neural network known as long short-term memory network in the context
of supplementing time series collected from different application domains.
These include classical Molecular Dynamics of a protein and Monte Carlo
simulations of an open quantum system continuously losing photons to the
environment and displaying Rabi oscillations. Our method can be easily
generalized to other generative artificial intelligence models and to generic
time series in different areas of physical and social sciences, where one
wishes to supplement limited data with intuition or theory based corrections.
