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Mathematical Modelling and Data Analysis

Department 8.4


We focus on the areas of applied mathematics which have fundamental importance for metrology. Our work addresses analytical and numerical modelling of physics applications, data analysis and methods for the evaluation of measurement uncertainty. The department is newly founded and exists since January 2004. Main tasks are support in the application of suitable tools and methods within PTB as well as external collaborations with applied math and related institutes in the Berlin area and beyond. Our goal is to provide expertise in the fields of partial differential equations, stochastic processes, signal processing and data analysis. The spectrum ranges from applied mathematics research to development and application of software.


Image quality assessment is of particular relevance in image processing applications. This is especially true in mammography, where it helps to achieve a high detection quality at the lowest possible radiation dose. The assessment of image quality in mammography is carried out in accordance with the recommendation of a European Guideline. Recent research has shown that the use of deep neural...

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Artificial intelligence (AI, e.g., deep learning) is increasingly used to assist high-stakes decisions in areas such as finance, medicine, or autonomous driving. Upcoming regulations will require that the principles by which such algorithms arrive at their predictions should be transparent. However, while numerous “explainable” AI (XAI) methods have been proposed, the field is lacking formal...

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Virtual experiments simulating real measurement processes by means of numerical models have become increasingly important in modern metrology and industrial applications. Combined with Monte Carlo methods, virtual experiments have also been proposed for the evaluation of measurement uncertainties for a corresponding real experiment. However, such a proceeding is not always in line with the current...

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Originally developed for fast global sensitivity analysis and efficient parameter reconstruction for applications in nano-optical metrology, PyThia provides an all purpose non-intrusive Python package to approximate high dimensional functions. Based on general polynomial chaos approximation obtained via linear regression, PyThia generates functional surrogates by relying purely on training data...

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