Obey validity limits of data-driven models through topological data analysis and one-class classification

Abstract

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).

Machine Learning in Chemical Engineering: A Perspective

“…Thus, the development of models describing the validity domain of data-driven models are desired [77,99,118]. However, when training datadriven models on industry data, defining and modeling the validity domain is a major issue [99]. Similar issues can arise when applying GNNs to molecular property prediction [119,120] or when applying RL to control processes [44,121].…”

“…Considering increasingly high-dimensional data sets, manifold learning has become ever more important. Among others, Aimin et al [99,100] use manifold learning as the basis for soft-sensor developments for a fermentation process and a debutanizer column. To tackle highly different data frequencies or data, which is erroneous or incomplete, [20] suggest using semi-supervised learning.…”

“…It is well-known that the extrapolation capacity of data-driven models over their initial training domain is limited [77,99,118]. Thus, the development of models describing the validity domain of data-driven models are desired [77,99,118]. However, when training datadriven models on industry data, defining and modeling the validity domain is a major issue [99].…”

Dynamic Ramping Constraints for Demand Response of Flat MIMO Processes

“…As, in the general case, the limit functions ρ (γ) min , ρ (γ) max are multivariate functions, multivariate regression methods, e.g., hinging hyperplanes (Breiman, 1993;Adeniran and Ferik, 2017;Kämper et al, 2021), convex region surrogates Schweidtmann et al, 2021), or artificial neural networks with ReLU activation functions (Grimstad and Andersson, 2019;Lueg et al, 2021), can be used to find piece-wise affine approximations.…”

Towards a Systematic Data Harmonization to Enable AI Application in the Process Industry

“…The QuantityTypes allow to compare different quantities and they are defined in the definition 3.2 of the ISO 80000-1 standard [36]. Furthermore, well-structured data lays the ground for better results in optimization of data, which can be also shown in the recent work of Schweidtmann et al [37].…”