Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation
Brute force meets Bruno force in parameter optimisation: introduction of novel constraints for parameter accuracy improvement by symbolic computation
复制标题
蛮力与布鲁诺力在参数优化中的结合：通过符号计算引入新颖的约束来提高参数精度
DOI：
10.1049/iet-syb.2010.0051
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发表时间：
2011
影响因子：
2.3
通讯作者：
F.
中科院分区：
文献类型：
--
作者：
Nakatsui;M.;Horimoto;K.;Lemaire;F.;Urguplu;A.;Sedoglavic;A.;Boulier;F.
最近在计算机性能方面的显著进步使我们能够通过数值计算的巨大能力，即所谓的‘布鲁特力’来估计参数值，从而导致对大量参数值的高速同时估计。然而，这些进步并没有被充分利用来提高参数估计的精度。在这里，作者回顾了一种新的利用符号计算能力进行参数估计的方法--布鲁诺力，该方法是以布鲁诺·布赫伯格的名字命名的，他发现了Gröbner基。在该方法中，结合符号计算技术建立了目标函数。首先，作者利用了一种符号计算技术--微分消去法，它将一个等价的微分方程组象征性地归结为一个给定模型中的一个系统。其次，由于其等价系统往往由大的方程组成，因此通过另一种符号计算进一步简化了该系统。通过简单的级联模型和负反馈模型这两个具有代表性的生物学模型与以往的数值方法进行比较，说明了该方法提高参数精度的性能。最后，根据“Bruno力”对参数估计新视界发展的可能力量，讨论了作者方法的局限性和扩展。
Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called ‘Brute force’, resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, ‘Bruno force’, named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of ‘Bruno force’ for the development of a new horizon in parameter estimation.