  Master equations are of fundamental importance in modeling stochastic
dynamical systems.However, solving master equations is challenging due to the
exponential increase in the number of possible states or trajectories with the
dimension of the state space. In this study, we propose repurposing language
models as a machine learning approach to solve master equations. We design a
prompt-based neural network to map rate parameters, initial conditions, and
time values directly to the state joint probability distribution that exactly
matches the input contexts. In this way, we approximate the solution of the
master equation in its most general form. We train the network using the policy
gradient algorithm within the reinforcement learning framework, with feedback
rewards provided by a set of variational autoregressive models. By applying
this approach to representative examples, we observe high accuracy for both
multi-module and high-dimensional systems. The trained network also exhibits
extrapolating ability, extending its predictability to unseen data. Our
findings establish the connection between language models and master equations,
highlighting the possibility of using a single pretrained large model to solve
any master equation.
