Approximating solutions of the Chemical Master equation using neural networks

The Chemical Master Equation (CME) provides an accurate description of stochastic biochemical reaction networks in well-mixed conditions, but it cannot be solved analytically for most systems of practical interest. Although Monte Carlo methods provide a principled means to probe system dynamics, the large number of simulations typically required can render the estimation of molecule number distributions and other quantities infeasible. In this article, we aim to leverage the representational power of neural networks to approximate the solutions of the CME and propose a framework for the Neural Estimation of Stochastic Simulations for Inference and Exploration (Nessie). Our approach is based on training neural networks to learn the distributions predicted by the CME from relatively few stochastic simulations. We show on biologically relevant examples that simple neural networks with one hidden layer can capture highly complex distributions across parameter space, thereby accelerating computationally intensive tasks such as parameter exploration and inference.