Clemens Elster’s research while affiliated with German National Metrology Institute and other places

Adversarial attacks pose a significant threat to the robustness of neural networks. Recent studies have shown that an imperceptible altering of the input can fool trained models to yield false predictions. However, the perturbations that underlie adversarial attacks are usually hard to interpret. This paper proposes a novel interpretable adversarial attack based on a recently introduced explainability technique known as oriented, modified integrated gradients. We will demonstrate the effectiveness of the proposed method on popular image classification datasets and compare it with state-of-the-art adversarial attacks. In addition, we will analyze the visual similarity between original images and the corresponding adversarial perturbations, both qualitatively and quantitatively, and demonstrate that the proposed approach generates adversarial perturbations with significantly improved interpretability.

In the data analysis of measurements, the simplified assumption of homoscedastic Gaussian noise is often made to account for the random fluctuations between observations. This may be an inadequate assumption which can deteriorate the results of a data analysis. Repeated measurements, which can be used to infer the true distribution of the data, may be inaccessible, making the true distribution hard to find. In such circumstances, thoroughly designed virtual experiments (VEs) can mimic real and possibly complex measurement processes to infer the true data distribution, which can subsequently be accounted for in an improved analysis of real observations. We explore the potential benefit of such an approach in terms of a metrological application, the tilted-wave interferometer (TWI). Our VE for the TWI yields not just the mean of the data, but also their physically modelled, random fluctuations arising in repeated observations. We use the virtual data to derive a statistical data model that includes correlations and heteroscedasticity. In applying a Bayesian data analysis procedure utilising said statistical model in conjunction with a vague prior for the quantity of interest, virtual data with a known ground truth are analysed and the quality of the resulting estimates are assessed. In addition, a comparison is carried out to the often-employed, simplified approach assuming homoscedastic, independent noise. We observe a significant improvement in the results when a more adequate statistical model for the data is utilised, along with a reliable uncertainty quantification. The work proposes the idea to extend the utilisation of a VE to inferring the noise characteristics of real observations, in turn leading to significantly improved data analysis procedures. The potential benefit is demonstrated to be substantial in terms of the considered metrological case study. Future research is discussed, including other ways that VEs could be used to further improve data analysis.

The applications of virtual metrology and the concept of using virtual experiments (VEs) or digital twins in measurement tasks have gained significant interest in recent years. When real measurements are costly or scarce, a VE can replicate complex mathematical and physical models. As a digital representation of a measurement process, a VE can, among other use-cases, be used in an uncertainty evaluation. Here, simulated and real observations can be combined without explicit knowledge of a model for the measurand – a usual requirement for uncertainty evaluation according to the GUM and its supplement JCGM 101. Including the variability of repeated measurements in a VE can be a challenging task. However, metrologists are aware of the potential impact of repeatability conditions and usually have significant knowledge about the precision of their measurement instrument. In this work, we develop a Monte Carlo sampling approach and software to perform an uncertainty evaluation that includes such prior knowledge about the precision of the measurement device, requiring only evaluations of the VE. Using an example of a calibrated measurement application, we demonstrate that there is a notable benefit to using available prior knowledge during an uncertainty evaluation, particularly in the case of limited observations.

Errors-in-Variables is the statistical concept used to explicitly model input variable errors caused, for example, by noise. While it has long been known in statistics that not accounting for such errors can produce a substantial bias, the vast majority of deep learning models have thus far neglected Errors-in-Variables approaches. Reasons for this include a significant increase of the numerical burden and the challenge in assigning an appropriate prior in a Bayesian treatment. To date, the attempts made to use Errors-in-Variables for neural networks do not scale to deep networks or are too simplistic to enhance the prediction performance. This work shows for the first time how Bayesian deep Errors-in-Variables models can increase the prediction performance. We present a scalable variational inference scheme for Bayesian Errors-in-Variables and demonstrate a significant increase in prediction performance for the case of image classification. Concretely, we use a diffusion model as input posterior to obtain a distribution over the denoised image data. We also observe that training the diffusion model on an unnoisy surrogate dataset can suffice to achieve an improved prediction performance on noisy data.

Virtual experiments are a digital representation of a real measurement and play a crucial role in modern measurement sciences and metrology. Beyond their common usage as a modeling and validation tool, a virtual experiment may also be employed to perform a parameter sensitivity analysis or to carry out a measurement uncertainty evaluation. For the latter to be compliant with statistical principles and metrological guidelines, the procedure to obtain an estimate and a corresponding measurement uncertainty requires careful consideration. We employ a Monte Carlo sampling procedure using a virtual experiment that allows one to perform a measurement uncertainty evaluation according to the Monte Carlo approach of JCGM-101 and JCGM-102, two widely applied guidelines for uncertainty evaluation in metrology. We extend and formalize a previously published approach for simple additive models to account for a large class of non-linear virtual experiments and measurement models for multidimensionality of the data and output quantities, and for the case of unknown variance of repeated measurements. With the algorithm developed here, a simple procedure for the evaluation of measurement uncertainty is provided that may be applied in various applications that admit a certain structure for their virtual experiment. Moreover, the measurement model commonly employed for uncertainty evaluation according to JCGM-101 and JCGM-102 is not required for this algorithm, and only evaluations of the virtual experiment are performed to obtain an estimate and an associated uncertainty of the measurand. We demonstrate the efficacy of the developed approach and the effect of the underlying assumptions for a generic polynomial regression example and an example of a simplified coordinate measuring machine and its virtual representation. The results of this work highlight that considerable effort, diligence, and statistical considerations need to be invested to make use of a virtual experiment for uncertainty evaluation in a way that ensures equivalence with the accepted guidelines.

Type A uncertainty evaluation can significantly benefit from incorporating prior knowledge about the precision of an employed measurement device, which allows for reliable uncertainty assessments with limited observations. The Bayesian framework, employing Bayes theorem and Markov Chain Monte Carlo (MCMC), is recommended to incorporate such prior knowledge in a statistically rigorous way. While MCMC is recommended, metrologists are usually well-familiar with plain Monte Carlo sampling and previous work demonstrated the integration of similar prior knowledge into an uncertainty evaluation framework following the plain Monte Carlo sampling of JCGM 101–the Supplement 1 to the GUM. In this work, we explore the potential and limitations of such an approach, presenting classes of data distributions for informative Type A uncertainty evaluations. Our work justifies an informative extension of the JCGM 101 Type A uncertainty evaluation from a statistical perspective, providing theoretical insight and practical guidance. Explicit distributions are proposed for input quantities in Type A scenarios, aligning with Bayesian uncertainty evaluations. In addition, inherent limitations of the JCGM 101 Monte Carlo approach are discussed concerning general Bayesian inference. Metrological examples support the theoretical findings, significantly expanding the applicability of the JCGM 101 Monte Carlo technique from a Bayesian perspective.

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements, acquired with a special setup, and sophisticated mathematical evaluation procedures. To determine the form of the surface under test, a computational model is required that closely mimics the measurement process of the physical measurement instruments. The parameters of the computational model, comprising the surface under test sought, are then tuned by solving an inverse problem. Due to this embedded structure of the real experiment and computational model and the overall complexity, a thorough uncertainty evaluation is challenging. In this work, a Bayesian approach is proposed to tackle the inverse problem, based on a statistical model derived from the computational model of the tilted-wave interferometer. Such a procedure naturally allows for uncertainty quantification to be made. We present an approximate inference scheme to efficiently sample quantities of the posterior using Monte Carlo sampling involving the statistical model. In particular, the methodology derived is applied to the tilted-wave interferometer to obtain an estimate and corresponding uncertainty of the pixel-by-pixel form of the surface under test for two typical surfaces taking into account a number of key influencing factors. A statistical analysis using experimental design is employed to identify main influencing factors and a subsequent analysis confirms the efficacy of the method derived.

The aim is to demonstrate the reliability of a population at consecutive points in time, where a sample at each current point must prove that at least 100% of the devices function until the next point with a probability of at least . To test the reliability of the population, we flexibilise standard lifetime models by allowing the unknown parameter(s) of the corresponding counting process to vary in time. At the same time, we assign a prior distribution that assumes the parameters to be constant within a certain interval. This flexibilisation has several advantages: it can be applied for all parametric lifetimes; its Markov property allows the efficient derivation of the number of defective devices, even for a large number of testing times; and the inference is less certain and hence more realistic and leads to less frequent acceptance of poor quality populations. On the other hand, the inference is stabilised by the informative prior. Based on the flexibilisation of the homogeneous Poisson process (HPP), we derive acceptance sampling plans to test the future reliability of a population. Applying the zero failure sampling plans on simulations of Weibull processes shows their good frequentist properties and their robustness. In the case of utility meters subject to German regulations (Mess‐ und Eichverordnung (MessEV). 2014: 2010–2073.), application of the derived sequential sampling plans when the conditions of these plans are met can lead to an extension of the verification validity period. These sampling plans protect the consumer better than those from an HPP and are still cost efficient.