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Obey validity limits of data-driven models through topological data analysis and one-class classification
Optimization and Engineering ( IF 2.0 ) Pub Date : 2021-05-12 , DOI: 10.1007/s11081-021-09608-0
Artur M. Schweidtmann , Jana M. Weber , Christian Wende , Linus Netze , Alexander Mitsos

Data-driven models are becoming increasingly popular in engineering, on their own or in combination with mechanistic models. Commonly, the trained models are subsequently used in model-based optimization of design and/or operation of processes. Thus, it is critical to ensure that data-driven models are not evaluated outside their validity domain during process optimization. We propose a method to learn this validity domain and encode it as constraints in process optimization. We first perform a topological data analysis using persistent homology identifying potential holes or separated clusters in the training data. In case clusters or holes are identified, we train a one-class classifier, i.e., a one-class support vector machine, on the training data domain and encode it as constraints in the subsequent process optimization. Otherwise, we construct the convex hull of the data and encode it as constraints. We finally perform deterministic global process optimization with the data-driven models subject to their respective validity constraints. To ensure computational tractability, we develop a reduced-space formulation for trained one-class support vector machines and show that our formulation outperforms common full-space formulations by a factor of over 3000, making it a viable tool for engineering applications. The method is ready-to-use and available open-source as part of our MeLOn toolbox (https://git.rwth-aachen.de/avt.svt/public/MeLOn).



中文翻译:

通过拓扑数据分析和一类分类遵守数据驱动模型的有效性限制

数据驱动的模型,无论是单独使用还是与机械模型结合使用,在工程上都变得越来越流行。通常,训练后的模型随后用于基于模型的过程设​​计和/或操作的优化。因此,至关重要的是要确保在过程优化过程中不会在数据有效性模型之外评估数据驱动的模型。我们提出了一种学习此有效性域并将其编码为过程优化约束的方法。我们首先使用持久性同源性执行拓扑数据分析,以识别训练数据中的潜在空洞或分离的簇。如果识别出簇或孔,我们将在训练数据域上训练一类分类器(即一类支持向量机),并将其编码为约束,以进行后续流程优化。除此以外,我们构造数据的凸包并将其编码为约束。最终,我们将根据数据驱动模型的有效性约束执行确定性的全局过程优化。为确保计算的可处理性,我们为受过训练的一类支持向量机开发了一种缩减空间的公式,并表明我们的公式比普通的全空间公式要好3000倍,这使其成为工程应用的可行工具。该方法是现成的,并且是我们的MeLOn工具箱(https://git.rwth-aachen.de/avt.svt/public/MeLOn)的一部分,可作为开放源代码使用。我们为受过训练的一类支持向量机开发了一种缩减空间的公式,并表明我们的公式比普通的全空间公式的性能高出3000倍,使其成为工程应用的可行工具。该方法是现成的,并且是我们的MeLOn工具箱(https://git.rwth-aachen.de/avt.svt/public/MeLOn)的一部分,可作为开放源代码使用。我们为受过训练的一类支持向量机开发了一种缩减空间的公式,并表明我们的公式比普通的全空间公式的性能高出3000倍,使其成为工程应用的可行工具。该方法是现成的,并且是我们的MeLOn工具箱(https://git.rwth-aachen.de/avt.svt/public/MeLOn)的一部分,可作为开放源代码使用。

更新日期:2021-05-13
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