Andrea Walther

Bio: Andrea Walther is an academic researcher from University of Paderborn. The author has contributed to research in topics: Automatic differentiation & Jacobian matrix and determinant. The author has an hindex of 23, co-authored 109 publications receiving 5497 citations. Previous affiliations of Andrea Walther include Dresden University of Technology & Humboldt University of Berlin.

Computing roots for the modelling of waves in acoustic waveguides

Abstract: Computer aided simulation of guided acoustic waves in single- or multilayered waveguides is an essential tool for several applications of acoustics and ultrasonics (i.e. pipe inspection, noise reduction). To simulate wave propagation in geometrically simple waveguides (plates or rods), one may employ the analytical Global Matrix Method [3]. This requires the computation of all roots of the determinate of a certain submatrix. The evaluation of all real or even complex roots is actually the methods most concerning restriction. Previous approaches based on so called mode-tracers which use the physical phenomenon that solutions (roots) appear in a certain pattern (waveguide modes) and thus use known solutions to limit the root finding algorithms search space with respect to consecutive solutions. As the limitation of the search space might be unstable in some cases, we propose to replace the mode-tracer with a suitable version of an interval Newton method based on INTLAB [4]. To apply this interval based method, we extended the interval and derivative computation provided by INTLAB such that corresponding information is also available for Bessel functions used in the circular model (rods) of acoustic waveguides. We present numerical results of a simple acoustic waveguide and discuss extensions required for more realistic scenarios. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimal program execution reversal

Abstract: For adjoint calculations, debugging, and similar purposes one may need to reverse the execution of a computer program. The simplest option of recording a complete execution log and then reading it backwards requires massive amounts of storage. Instead one may generate the execution log piecewise by restarting the ``forward'' calculation repeatedly from suitably placed checkpoints. Our goal is to minimize the temporal and spatial complexity as measured by the number of evaluation repeats and the number of checkpoints, respectively. We present optimal checkpointing schedules for one-step and multi-step evolutions. These might arise for example as discretizations of ODEs by Euler's methods or multi-step schemes, respectively. Furthermore, we present parallel extensions, where auxiliary processors perform the repeated forward evaluations such that one processor can run backward without any interruption. For either case the length of the evolution that can be reversed is shown to grow exponentially with the number of checkpoints and either the number of repetitions or the number of processors.

Engineering high harmonic generation in semiconductors via pulse shaping

Abstract: High harmonic generation is investigated for a two-band model of a semiconductor nanostructure. Similar to an atomic two-level system, the semiconductor emits high harmonic radiation. We show how one can specifically enhance the emission for a given frequency by applying a non-trivially shaped laser pulse. Therefore, the semiconductor Bloch equations including the interband and additionally the intraband dynamics are solved numerically and the spectral shape of the input pulse is computed via an optimization algorithm. It is demonstrated that desired emission frequencies can be favored even though the overall input power is kept constant. We also suggest special metallic nano geometries to achieve enhanced localized optical fields. They are found by geometric optimization.

Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity

Abstract: A complete characterisation of piezo ceramic materials typically requires several differently processed specimen. Since the results of all these measurements are combined to form one single set of material parameters, inconsistencies occur naturally. The problem when considering only one specimen is the lack of sensitivity for several material parameters. Therefore, a triple-ring-electrode set-up is presented that is optimised to balance the sensitivity of the frequency dependent impedance for the full set of material parameters. This specific set-up is designed to characterise the material properties using only one specimen, hence reaching consistent material parameters while still aiming to be sufficiently sensitive to each parameter. This more complex set-up calls for a FEM-based inverse problem, that makes it possible to find parameters that fit the measured impedance. The whole optimisation procedure is described exemplarily for one specimen of PIC255 (PI ceramic, Lederhose, Germany) leading to feasi...

Automatic differentiation in PyTorch

Abstract: In this article, we describe an automatic differentiation module of PyTorch — a library designed to enable rapid research on machine learning models. It builds upon a few projects, most notably Lua Torch, Chainer, and HIPS Autograd [4], and provides a high performance environment with easy access to automatic differentiation of models executed on different devices (CPU and GPU). To make prototyping easier, PyTorch does not follow the symbolic approach used in many other deep learning frameworks, but focuses on differentiation of purely imperative programs, with a focus on extensibility and low overhead. Note that this preprint is a draft of certain sections from an upcoming paper covering all PyTorch features.

Phd by thesis

Abstract: Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

brms: An R Package for Bayesian Multilevel Models Using Stan

Abstract: The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan. A wide range of distributions and link functions are supported, allowing users to fit - among others - linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multilevel context. Further modeling options include autocorrelation of the response variable, user defined covariance structures, censored data, as well as meta-analytic standard errors. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with the Watanabe-Akaike information criterion and leave-one-out cross-validation.

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Abstract: Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

Bayesian Calibration of computer models

Abstract: We consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models. Such models, implemented as computer codes, are often generic in the sense that by a suitable choice of some of the model's input parameters the code can be used to predict the behaviour of the system in a variety of specific applications. However, in any specific application the values of necessary parameters may be unknown. In this case, physical observations of the system in the specific context are used to learn about the unknown parameters. The process of fitting the model to the observed data by adjusting the parameters is known as calibration. Calibration is typically effected by ad hoc fitting, and after calibration the model is used, with the fitted input values, to predict the future behaviour of the system. We present a Bayesian calibration technique which improves on this traditional approach in two respects. First, the predictions allow for all sources of uncertainty, including the remaining uncertainty over the fitted parameters. Second, they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best-fitting parameter values. The method is illustrated by using data from a nuclear radiation release at Tomsk, and from a more complex simulated nuclear accident exercise.