An efficient and robust numerical algorithm for estimating parameters in Turing systems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Garvie, Marcus R.¹  Maini, Philip K.^2,3  Trenchea, Catalin⁴ 

[1] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

[2] Univ Oxford, Inst Math, Ctr Math Biol, Oxford OX1 3LB, England

[3] Oxford Ctr Integrat Syst Biol, Dept Biochem, Oxford OX1 3QU, England

[4] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

关键词: Optimal control theory;    Parameter identification;    Reaction-diffusion equations;    Diffusion-driven instability;    Finite element method;   

DOI  :  10.1016/j.jcp.2010.05.040

来源: Elsevier

【 摘 要 】

We present a new algorithm for estimating parameters in reaction-diffusion systems that display pattern formation via the mechanism of diffusion-driven instability. A Modified Discrete Optimal Control Algorithm (MDOCA) is illustrated with the Schnakenberg and Gierer-Meinhardt reaction-diffusion systems using PDE constrained optimization techniques. The MDOCA algorithm is a modification of a standard variable step gradient algorithm that yields a huge saving in computational cost. The results of numerical experiments demonstrate that the algorithm accurately estimated key parameters associated with stationary target functions generated from the models themselves. Furthermore, the robustness of the algorithm was verified by performing experiments with target functions perturbed with various levels of additive noise. The MDOCA algorithm could have important applications in the mathematical modeling of realistic Turing systems when experimental data are available. (C) 2010 Published by Elsevier Inc.

【 授权许可】

Free