Mean-field optimal control for biological pattern formation
Burger M, Kreusser LM, Totzeck C (2021)
Publication Type: Journal article
Publication year: 2021
Journal
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.
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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://dx.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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