Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data. (arXiv:2205.13545v1 [q-bio.QM])

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.

Source: https://arxiv.org/abs/2205.13545

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