Mean-field optimal control for biological pattern formation

Author:

Burger Martin,Kreusser Lisa MariaORCID,Totzeck Claudia

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.

Funder

H2020 Marie Skłodowska-Curie Actions

Studienstiftung des Deutschen Volkes

Magdalene College, University of Cambridge

Engineering and Physical Sciences Research Council

Cantab Capital Institute for the Mathematics of Information

European Social Fund

Ministerium für Wissenschaft, Forschung und Kunst Baden-Württemberg

Baden-Württemberg bwHPC

Deutsche Forschungsgemeinschaft

Publisher

EDP Sciences

Subject

Computational Mathematics,Control and Optimization,Control and Systems Engineering

Reference29 articles.

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3. Mean-Field Pontryagin Maximum Principle

4. Pattern formation of a nonlocal, anisotropic interaction model

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