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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.


Uncertainty quantification can help to understand the behavior of a trained neural network and, in particular, foster confidence in its predictions. This is especially true for deep regression, where a single-point estimate of a sought function without any information regarding its accuracy can be largely meaningless. We propose a novel framework for benchmarking uncertainty quantification in deep...

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Bacteria organize in a variety of collective states, from swarming—rapid surface exploration, to biofilms—highly dense immobile communities attributed to stress resistance. It has been suggested that biofilm and swarming are oppositely controlled, making this transition  particularly  interesting  for  understanding  the  ability  of  bacterial  colonies to adapt to challenging environments....

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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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