Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data

Publication Date

7-1-2023

Document Type

Article

Publication Title

Journal of Mathematical Biology

Volume

87

Issue

1

DOI

10.1007/s00285-023-01946-0

Abstract

We propose a machine learning framework for the data-driven discovery of macroscopic chemotactic Partial Differential Equations (PDEs)—and the closures that lead to them- from high-fidelity, individual-based stochastic simulations of Escherichia coli bacterial motility. The fine scale, chemomechanical, hybrid (continuum—Monte Carlo) simulation model embodies the underlying biophysics, and its parameters are informed from experimental observations of individual cells. Using a parsimonious set of collective observables, we learn effective, coarse-grained “Keller–Segel class” chemotactic PDEs using machine learning regressors: (a) (shallow) feedforward neural networks and (b) Gaussian Processes. The learned laws can be black-box (when no prior knowledge about the PDE law structure is assumed) or gray-box when parts of the equation (e.g. the pure diffusion part) is known and “hardwired” in the regression process. More importantly, we discuss data-driven corrections (both additive and functional), to analytically known, approximate closures.

Funding Number

FISR2020IP - 02893

Funding Sponsor

U.S. Department of Energy

Keywords

Chemotaxis, Inverse problems, Machine learning, Multiscale methods, Numerical analysis, Partial differential equations, Stochastic simulations

Department

Applied Data Science

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