Development and application of methods for complexity reduction, metamodelling and optimal experimental design based on global sensitivity analysis

基于模型的复杂过程仿真是探索和研究实验分析昂贵或耗时的系统的一种有效方法。现代真实系统的数学模型往往具有很高的复杂性，有数百个变量。使用这类模型的直接建模可能在计算上代价高昂，甚至很难处理。良好的建模实践需要灵敏度分析(SA)，通过分析模型结构、选择最佳模型类型和有效识别重要的模型参数来确保模型质量。全局模拟退火算法优于其他模拟退火算法。它可以应用于任何类型的模型，在不牺牲精度的情况下量化和降低问题的复杂性，并且它不像局部SA方法那样依赖于标称点。我们提出了一些先进的模型分析和复杂性降低技术的发展，这些技术基于全局模拟算法和高效的高维蒙特卡罗(MC)和拟MC方法。特别是，我们将开发具有改进的一致性特性的高维Sobol序列产生器。一般而言，它将允许提高全局SA和准MC方法的效率。Sobol的全局灵敏度指数方法优于其他全局SA方法。然而，由于现有技术的计算限制，它仅应用于低尺度模式。我们提出了一些技术来提高Sobol方法的效率。我们还提出了一组新的全局SA度量，与基于方差的方法相比，它们的计算量要小得多。通过将基于Fisher信息矩阵和GSA的方法相结合，我们将开发一种新的参数估计和模型验证的最优实验设计技术，从而大大降低实验成本。模型分析的一个非常有前途的发展是取代复杂模型和需要用等价的操作元模型在线重复运行的模型。现有方法的采样努力随着输入变量的数量呈指数增长，这使得它们在高维情况下是不实用的。我们将开发一种新的基于准随机抽样的元建模方法-高维模型表示法(QRS-HDMR)，它将原来的指数难度转化为一个仅具有多项式复杂性的问题。我们提出通过为目标函数和约束集建立QRS-HDMR元模型来解决具有高维和计算代价的目标函数的优化问题。与原始模型相比，这种基于元模型的优化问题的求解成本要低一个数量级。将这些方法应用于生物处理将涉及为哺乳动物细胞培养开发高保真模型，这些模型可以生产高价值的生物药物，如克隆抗体。备受瞩目的例子包括乳腺癌药物赫赛汀和重磅炸弹抗癌药物阿瓦斯丁。然而，此类药物的生产往往依赖于人工控制和优化，这增加了成本和上市时间。另一方面，现代基于模型的优化和控制方法的实施需要预测性的、计算上容易处理的模型，这些模型通常涉及许多参数，并且需要大量昂贵的测量来验证它们。为了解决这些问题，并最大限度地减少实验的成本和时间，将使用GSA和最佳实验设计来制定最先进的哺乳动物细胞培养模型，用于计算机实验、系统分析和推导用于在线应用的元模型。这种方法的有效性将通过龙沙生物公司提供的产生抗体的CHO细胞的案例研究来证明。

Model based simulation of complex processes is an efficient approach to explore and study systems whose experimental analysis is costly or time-consuming. Modern mathematical models of real systems often have high complexity with hundreds of variables. Straightforward modelling using such models can be computationally costly or even intractable. Good modelling practice requires sensitivity analysis (SA) to ensure the model quality by analysing the model structure, selecting the best type of model and effectively identifying the important model parameters. Global SA is superior to other SA methods. It can be applied to any type of model for quantifying and reducing problem complexity without sacrificing accuracy and it is not dependent on a nominal point like local SA methods. We propose the development of a number of advanced model analysis and complexity reduction techniques based on global SA and efficient high dimensional Monte Carlo (MC) and Quasi MC methods. In particular, we will develop high dimensional Sobol' sequence generators with improved uniformity properties. It will allow increasing the efficiency of global SA and Quasi MC methods in general. The Sobol' method of global sensitivity indices is superior to other global SA methods. However, it has been applied only to low scale models because of the computational limitations of the existing technique. We propose a number of techniques which will improve the efficiency of the Sobol' method. We also propose a set of new global SA measures which are much less computationally demanding than variance based methods. By combining approaches based on the Fisher information matrix and GSA, we will develop a new technique for parameter estimation and optimal experimental design for model validation which would dramatically reduce experimental cost. One of the very promising developments of model analysis is the replacement of complex models and models which need to be run repeatedly on-line with equivalent operational meta models. Sampling efforts of the existing approaches grow exponentially with the number of input variables which makes them impractical in high dimensional cases. We will develop a novel approach to metamodelling using quasi random sampling - high dimensional model representation method (QRS-HDMR) which renders the original exponential difficulty to a problem of only polynomial complexity. We propose to solve optimization problems with high dimensional and computationally expensive objective functions by building QRS-HDMR meta models for the objective functions and set of constraints. Such meta models based optimization problems can be orders of magnitude cheaper to solve compared to the original models. The application of these methods to bioprocessing will involve the development of high-fidelity models for mammalian cell cultures, which produce high-value biological drugs, such as monoclonal antibodies. High-profile examples include the breast cancer drug Herceptin and blockbuster cancer drug Avastin. However, the production of such drugs often relies on manual control and optimisation, which increase cost and time-to-market. On the other hand, the implementation of modern model-based methodologies for optimisation and control necessitates predictive, computationally tractable models, which usually involve numerous parameters and require a high volume of expensive measurements for their validation. In order to address these issues and minimise the cost and time of experimentation, GSA and optimal experimental design will be used to formulate a state-of-the art model of mammalian cell cultures for in silico experimentation, system analysis and derivation of a metamodel for online applications. The validity of this approach will be demonstrated through a case study on antibody-producing CHO cells supplied by Lonza Biologics.