The Mathematical Institute, University of Oxford, Eprints Archive

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

Garvie, M R and Maini, P. K. and Trenchea, C (2010) An efficient and robust numerical algorithm for estimating parameters in turing systems. Journal of Computational Physics, 229 (19). 7058-7071.

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Optimal control theory; Parameter identification; Reaction–diffusion equations; Diffusion-driven instability; Finite element method
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:941
Deposited By:Philip Maini
Deposited On:16 Sep 2010 07:51
Last Modified:16 Sep 2010 07:51

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