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一种有效的方法来探索和研究系统的实验分析是昂贵的或耗时的。真实的系统的现代数学模型通常具有数百个变量的高复杂性。使用这种模型的直接建模可能是计算成本很高甚至是棘手的。良好的建模实践需要敏感性分析，通过分析模型结构、选择最佳模型类型和有效识别重要模型参数来确保模型质量。全局SA比其他SA方法具有上级优势。它可以应用于任何类型的模型，用于量化和降低问题的复杂性，而不牺牲精度，它不依赖于一个名义点，如局部SA方法。我们提出了一些先进的模型分析和复杂性降低技术的基础上，全球SA和高效的高维蒙特卡罗（MC）和准MC方法的发展。特别是，我们将开发具有改进的均匀性的高维Sobol'序列发生器。它将允许提高全局SA和准MC方法的效率。全局灵敏度指标的Sobol方法上级其它全局SA方法。然而，由于现有技术的计算限制，它仅适用于低比例尺模型。我们提出了一些技术，这将提高效率的Sobol'方法。我们还提出了一组新的全球SA措施，这是计算量小得多的要求比方差为基础的方法。通过结合基于Fisher信息矩阵和GSA的方法，我们将开发一种新的技术，用于参数估计和模型验证的最优实验设计，这将大大降低实验成本。模型分析的一个非常有前途的发展是用等效的操作Meta模型代替复杂的模型和需要反复在线运行的模型。现有方法的采样工作量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不切实际。我们将开发一种新的方法，元建模使用准随机抽样-高维模型表示方法（QRS-HDMR），使原来的指数困难的问题，只有多项式的复杂性。我们建议通过为目标函数和约束集建立QRS-HDMR Meta模型来解决高维和计算昂贵的目标函数的优化问题。与原始模型相比，这种基于Meta模型的优化问题的求解成本可以低几个数量级。这些方法在生物加工中的应用将涉及开发用于哺乳动物细胞培养的高保真模型，该模型产生高价值的生物药物，例如单克隆抗体。引人注目的例子包括乳腺癌药物赫赛汀和重磅炸弹癌症药物阿瓦斯丁。然而，这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进行验证。为了解决这些问题并最大限度地减少实验的成本和时间，GSA和最佳实验设计将用于制定最先进的哺乳动物细胞培养模型，用于计算机实验，系统分析和在线应用元模型的推导。将通过Lonza Biologics提供的产抗体CHO细胞的案例研究证明该方法的有效性。

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.