Machine Learning Dynamic Correlation in Chemical Kinetics

06 August 2021, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


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.


lattice Lotka-Volterra model
moment closure
machine learning
kinetic Monte Carlo
pair approximation
chemical kinetics
surface reactions

Supplementary materials

Supporting Information: Machine Learning Dynamic Correlations in Chemical Kinetics
Coarse-graining of NO + CO / Pt(100)-(1×1) on to LLVM; 2D and 3D plots of three-site probabilities as functions of one-site and two-site probabilities; table of rate constants and initial conditions that were represented in the training data; scatter plots of the ML and PA estimates of the three-site probabilities in the log scale; additional examples of time-dependent coverages according to PA, ML, and KMC; and contour plots of nonlinear oscillation frequencies and amplitude ratios.


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