Learning heterogenous reaction rates from stochastic simulations

TL;DR

This paper introduces a data assimilation method to infer non-homogeneous reaction rates from stochastic molecular simulations, enabling the derivation of effective macroscopic reaction equations that account for microscopic phenomena.

Contribution

It presents a novel procedure for learning microscopic kinetic parameters from molecular simulations to improve macroscopic reaction rate models.

Findings

Learned parameters reveal complex time and temperature dependencies.

Effective differential equations accurately predict long-term system behavior.

Universal distribution observed for network strand cycling probability.

Abstract

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning non-homogenous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature a peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.