Data-driven Modeling in Metrology -- A Short Introduction, Current Developments and Future Perspectives

TL;DR

The paper surveys data-driven modeling in metrology, contrasting white-box analytical, black-box data-driven, and grey-box hybrid approaches, and discusses how intelligent adaptive systems and digital twins can transform measurement science. It explains forward/inverse modeling, uncertainty evaluation, and the role of EDMD/Koopman, Bayesian methods, and physics-informed learning in uncertainty quantification. It introduces emergent paradigms such as Artificial Neural Twins and reservoir computing and outlines construction/uses of digital twins in metrology. The work highlights challenges, including transferability, interpretability, and standardization, and argues for integrated, end-to-end differentiable pipelines to enable accurate, adaptive measurement in networked sensor environments.

Abstract

Mathematical models are vital to the field of metrology, playing a key role in the derivation of measurement results and the calculation of uncertainties from measurement data, informed by an understanding of the measurement process. These models generally represent the correlation between the quantity being measured and all other pertinent quantities. Such relationships are used to construct measurement systems that can interpret measurement data to generate conclusions and predictions about the measurement system itself. Classic models are typically analytical, built on fundamental physical principles. However, the rise of digital technology, expansive sensor networks, and high-performance computing hardware have led to a growing shift towards data-driven methodologies. This trend is especially prominent when dealing with large, intricate networked sensor systems in situations where there is limited expert understanding of the frequently changing real-world contexts. Here, we demonstrate the variety of opportunities that data-driven modeling presents, and how they have been already implemented in various real-world applications.

Figures (9)

• Figure 1: White, grey and black box models with their basic properties paper.
• Figure 2: Diagram illustrating the conventional pattern recognition system used for automated decision making. The sensor data is pre-processed and "hand-crafted" features are extracted during both the training and testing phases. In the training phase, a classifier is developed, which is then used in the testing phase to automatically determine the classes (Figure reprinted under CC BY 4.0 niemann2013pattern).
• Figure 3: Today, several methods are commonly used to introduce an inductive bias into machine learning models. They range from "graduate student descent" in Deep Learning to Meta Learning and regularisation methods. The image is reprinted under CC BY 4.0 maier2022known.
• Figure 4: Illustration of the bioprocess control using soft sensors based on sequential filtering of metabolic heat signals Paulsson2014.
• Figure 5: Results of the vessel segmentation before and after training. The colors red, green, and yellow represent the manual annotations, the segmentation results, and the overlaps between them, respectively Fu2017.