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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.


Feature importance methods promise to provide a ranking of features according to importance for a given classification task. A wide range of methods exist but their rankings often disagree and they are inherently difficult to evaluate due to a lack of ground truth beyond synthetic datasets. In a recent paper, PTB  together with colleagues from NPL, IMBIH, King´s College, KIT, Fraunhofer HHI and...

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The Bayesian approach to solving inverse problems strongly depends on the choice of a prior. Usually, a prior is constructed from expert knowledge or known physical constraints in a probabilistic fashion. A modern alternative to formulate such expert knowledge are generative models, a popular tool in machine learning to generate data whose properties closely resemble a given database by an...

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Scanning probe based spectroscopy using broadband infrared radiation emerged as a promising imaging technique at nanometer spatial resolution. However, the pixel-by-pixel data acquisition leads to prohibitive imaging times and enhanced radiation damage. To overcome this issue, a novel hyperspectral imaging scheme was developed in this project using Bayesian compressed sensing (BCS).

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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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