Identification of Chemotaxis Models with Volume-Filling

Abstract

Chemotaxis refers to the directed movement of cells in response to a chemical signal called chemoattractant. A crucial point in the mathematical modeling of chemotactic processes is the correct description of the chemotactic sensitivity and of the production rate of the chemoattractant. In this paper, we investigate the identification of these nonlinear parameter functions in a chemotaxis model with volume-filling. We also discuss the numerical realization of Tikhonov regularization for the stable solution of the inverse problem. Our theoretical findings are supported by numerical tests.

On Learned Operator Correction in Inverse Problems

“…Further, related work that considers learned corrections by utilising explicit knowledge of the operator range are [7,9,36]. Another line of research examines the incorporation of imperfectly known forward operators in a fully variational model [10,29] as well as perturbations in [13,31]. We note also the connection to the concept of calibration in a Bayesian setting [26].…”

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“…The function a(u) depends on the system at hand and is usually unknown. The same is in principle true also for the coefficients b and h, which may however be at least partially determined, provided that a is known and that the measurements are sufficiently rich; see [14] and Section 7. To complete the description of the problem, we further require the boundary conditions…”

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