Solving the chemical master equation for stochastic biochemical systems: A variational autoencoder approach with effective reactions

• An Efficient chemical master equation solver is devised for stochastic biochemical dynamics based on variational autoencoder. • The solver finds an effective reaction for a set of intermediate reactions to circumvent the curse of dimensionality. • The trained solver can extrapolate to another reaction system of different reaction topologies and reaction parameters. The stochasticity of biochemical reactions at mesoscopic scale presents significant challenges to our understanding of the underpinnings. The Chemical Master Equation (CME) serves as a crucial tool for describing the dynamics of biochemical reactions, but solving the CME is notoriously difficult and often faces the curse of dimensionality. In this paper, we propose an efficient CME solver for stochastic biochemical dynamics leveraging the power of Variational Autoencoder (VAE). VAE is employed to find effective reactions from a group of elementary reactions, reducing the complexity of the system. By using VAE to find equivalent propensity for a set of complex reactions, we simplify the intermediate reactions, reducing the sample size and time for training. The trained VAE can predict the distributions of unseen time points, different reaction structures and unobserved species. We show a robust method that simplifies the resolution of CME, providing a powerful tool for analyzing stochastic biochemical systems.