Machine Learning Dynamic Correlation in Chemical Kinetics

The kinetics of surface reactions are often described using a lattice model. Since it is expensive to propagate the configuration probabilities of the entire lattice, 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 (CME). Unfortunately, simple closures, such as the mean-field (MF) 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 (LLVM) as a model system. We trained feed-forward neural networks (FFNNs) on kinetic Monte Carlo (KMC) results at select values of rate constants and initial conditions. Given the same level of input as PA, the machine learning 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 pre-trained closures that would enable researchers to extract useful insight at a fraction of the computational cost.