Learning heterogenous reaction rates from stochastic simulations

Ariana Torres-Knoop and Ivan Kryven
Phys. Rev. E 103, 052402 – Published 4 May 2021

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 nonhomogeneous 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 peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.

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  • Received 28 February 2021
  • Accepted 10 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.052402

©2021 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft MatterCondensed Matter, Materials & Applied PhysicsGeneral Physics

Authors & Affiliations

Ariana Torres-Knoop

  • SURF, Hoog Catharijne, Moreelsepark 48, 3511 EP Utrecht, the Netherlands

Ivan Kryven*

  • Mathematical Institute, Utrecht University, Budapestlaan 6, 3508 TA Utrecht, Netherlands and Centre for Complex Systems Studies, 3584 CE Utrecht, Netherlands

  • *i.kryven@uu.nl

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Vol. 103, Iss. 5 — May 2021

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