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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.


Artificial intelligence and machine learning tools hold promise to assist or drive high-stakes decisions in areas such as finance, medicine, or autonomous driving. The upcoming AI Act will require that the principles by which such algorithms arrive at their predictions should be transparent. However, the field of XAI is lacking formal problem specifications and theoretical results. In a new study,...

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When a real measurement procedure is reproduced by simulations, it may be referred to as a “virtual measurement”. From a metrological point of view, the question is how to ensure confidence in such virtual measurements. While methods to estimate diverse sources of error in simulations have been developed over the past decades, there has to date been no accepted strategy for meeting the...

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Hydrogen plays an important role for the decarbonization of the energy sector. In its gaseous form, it is stored at pressures of up to 1000 bar at which real gas effects become relevant. To capture these effects in numerical simulations, accurate real gas models are required. We propose new correlation equations for relevant hydrogen properties …


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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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