An efficient and robust numerical algorithm for estimating parameters in Turing systems
An efficient and robust numerical algorithm for estimating parameters in Turing systems
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DOI：
10.1016/j.jcp.2010.05.040
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发表时间：
2010-09-20
影响因子：
4.1
通讯作者：
Trenchea, Catalin
中科院分区：
文献类型：
--
作者：
Garvie, Marcus R.;Maini, Philip K.;Trenchea, Catalin
我们提出了一种新的算法来估计反应扩散系统中的参数，该系统通过扩散驱动的不稳定性机制显示图案形成。利用偏微分方程约束优化技术，以Schnakenberg和Giererer-Meinhardt反应扩散系统为例，给出了一种改进的离散最优控制算法。MDOCA算法是标准变步长梯度算法的一种改进，大大节省了计算成本。数值实验结果表明，该算法能够准确地估计与模型本身产生的平稳目标函数相关的关键参数。此外，该算法的鲁棒性进行了验证，通过与目标函数与不同水平的加性噪声扰动的实验。当实验数据可用时，MDOCA算法可以在现实图灵系统的数学建模中具有重要的应用。(C)2010年由Elsevier Inc.出版
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.