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

• URL: http://arxiv.org/abs/2205.13545v1
• Date: Thu, 26 May 2022 03:02:49 GMT
• Title: Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data
• Authors: Seungjoon Lee, Yorgos M. Psarellis, Constantinos I. Siettos, Ioannis G. Kevrekidis
• Abstract summary: We propose a machine learning framework for the data-driven discovery of macroscopic chemotactic Partial Differential Equations (PDEs) The fine scale, detailed, hybrid (continuum - Monte Carlo) simulation model embodies the underlying biophysics. We learn effective, coarse-grained "Keller-Segel class" chemotactic PDEs using machine learning regressors.
• Score: 0.6882042556551611
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 E.coli bacterial motility. The fine scale, detailed, hybrid (continuum - Monte Carlo) simulation model embodies the underlying biophysics, and its parameters are informed from experimental observations of individual cells. We exploit Automatic Relevance Determination (ARD) within a Gaussian Process framework for the identification of a parsimonious set of collective observables that parametrize the law of the effective PDEs. Using these observables, in a second step 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. We also discuss data-driven corrections (both additive and functional) of analytically known, approximate closures.

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