Reconstructing the kinetic chemotaxis kernel using macroscopic data: well-posedness and ill-posedness

Abstract

Bacterial motion is steered by external stimuli (chemotaxis), and the motion described on the mesoscopic scale is uniquely determined by a parameter $K$ that models velocity change response from the bacteria. This parameter is called chemotaxis kernel. In a practical setting, it is inferred by experimental data. We deploy a PDE-constrained optimization framework to perform this reconstruction using velocity-averaged, localized data taken in the interior of the domain. The problem can be well-posed or ill-posed depending on the data preparation and the experimental setup. In particular, we propose one specific design that guarantees numerical reconstructability and local convergence. This design is adapted to the discretization of $K$ in space and decouples the reconstruction of local values of $K$ into smaller cell problems, opening up parallelization opportunities. Numerical evidences support the theoretical findings.

References in corpus (9)

• Data-driven quantitative modeling of bacterial active nematics
• Characterization and Control of the Run-and-Tumble Dynamics of {\it Escherichia Coli}
• Traveling Pulses for a Two-Species Chemotaxis Model
• Quantitative characterization of run-and-tumble statistics in bulk bacterial suspensions
• Online learning in optical tomography: a stochastic approach
• An efficient Quasi-Newton method for nonlinear inverse problems via learned singular values
• Statistical parameter inference of bacterial swimming strategies
• Applications of Kinetic Tools to Inverse Transport Problems
• Kinetic chemotaxis tumbling kernel determined from macroscopic quantities