Mean-field optimal control for biological pattern formation

Burger M, Kreusser LM, Totzeck C (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Esaim-Control Optimisation and Calculus of Variations EDP Sciences

Book Volume: 27

Article Number: 40

DOI: 10.1051/cocv/2021034

Abstract

We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The first-order optimality conditions corresponding to the optimal control problem are derived using a Lagrangian approach on the mean-field level. Based on these conditions we propose a gradient descent method to identify relevant parameters such as angle of rotation and force scaling which may be spatially inhomogeneous. We discretize the first-order optimality conditions in order to employ the algorithm on the particle level. Moreover, we prove a rate for the convergence of the controls as the number of particles used for the discretization tends to infinity. Numerical results for the spatially homogeneous case demonstrate the feasibility of the approach.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Universität Mannheim DE Germany (DE)

How to cite

APA:

Burger, M., Kreusser, L.M., & Totzeck, C. (2021). Mean-field optimal control for biological pattern formation. Esaim-Control Optimisation and Calculus of Variations, 27. https://doi.org/10.1051/cocv/2021034

MLA:

Burger, Martin, Lisa Maria Kreusser, and Claudia Totzeck. "Mean-field optimal control for biological pattern formation." Esaim-Control Optimisation and Calculus of Variations 27 (2021).

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