Machine learning dynamic correlation in chemical kinetics

Lattice models are a useful tool to simulate the kinetics of surface reactions. Since it is expensive to propagate the probabilities of the entire lattice configurations, it is practical to consider the occupation probabilities of a typical site or a cluster of sites instead. This amounts to a moment closure approximation of the chemical master equation. Unfortunately, simple closures, such as the mean-field and the pair approximation (PA), exhibit weaknesses in systems with significant long-range correlation. In this paper, we show that machine learning (ML) can be used to construct accurate moment closures in chemical kinetics using the lattice Lotka-Volterra model as a model system. We trained feedforward neural networks on kinetic Monte Carlo (KMC) results at select values of rate constants and initial conditions. Given the same level of input as PA, the ML moment closure (MLMC) gave accurate predictions of the instantaneous three-site occupation probabilities. Solving the kinetic equations in conjunction with MLMC gave drastic improvements in the simulated dynamics and descriptions of the dynamical regimes throughout the parameter space. In this way, MLMC is a promising tool to interpolate KMC simulations or construct pretrained closures that would enable researchers to extract useful insight at a fraction of the computational cost