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.

Differentiation methods for industrial strength problems

Abstract: The importance of simulation has been growing in industrial production for many years. Because of reduced product cycles, new and more complicated computer models have to be developed more quickly. The correct description and implementation of the interaction between different components of the entire simulation model as well as the nonlinear behaviour of these components lead in many cases to the need for derivative information. In this chapter, we use software packages for automatic differentiation (AD) in three real world simulation systems typical for a wide range of tasks that have to be solved in numerous industrial applications. We consider difficulties arising from particular aspects of the modelling such as the integration of ordinary differential equations or fixed-point iterations for the solution of equations. Furthermore, we discuss challenges caused by technical software issues such as inhomogeneous source codes written in different languages or table lookups. Several results concerning the use of tools such as ADIFOR, Odyssee, and ADOL-C are presented. We discuss the benefits and the difficulties of current AD techniques applied to real industrial codes. Finally, we outline possible future developments.

Efficient calculation of sensitivities for optimization problems

Abstract: Sensitivity information is required by numerous applications such as, for example, optimization algorithms, parameter estimations or real time control. Sensitivities can be computed with working accuracy using the forward mode of automatic differentiation (AD). ADOL-C is an AD-tool for programs written in C or C++. Originally, when applying ADOL-C, tapes for values, operations and locations are written during the function evaluation to generate an internal function representation. Subsequently, these tapes are evaluated to compute the derivatives, sparsity patterns etc., using the forward or reverse mode of AD. The generation of the tapes can be completely avoided by applying the recently implemented tapeless variant of the forward mode for scalar and vector calculations. The tapeless forward mode enables the joint computation of function and derivative values directly from main memory within one sweep. Compared to the original approach shorter runtimes are achieved due to the avoidance of tape handling and a more effective, joint optimization for function and derivative code. Advantages and disadvantages of the tapeless forward mode provided by ADOL-C will be discussed. Furthermore, runtime comparisons for two implemented variants of the tapeless forward mode are presented. The results are based on two numerical examples that require the computation of sensitivity information.

Structure-Exploiting Automatic Differentiation of Finite Element Discretizations

Abstract: A common way to solve PDE constrained optimal control problems by automatic differentiation (AD) is the full black box approach. This technique may fail because of the large memory requirement. In this paper we present two alternative approaches. First, we exploit the structure in time yielding a reduced memory requirement. Second, we additionally exploit the structure in space by providing derivatives on a reference finite element. This approach reduces the memory requirement once again compared to the exploitation in time. We present numerical results for both approaches, where the derivatives are determined by the AD-enabled NAGWare Fortran compiler.

Tailoring the high-harmonic emission in two-level systems and semiconductors by pulse shaping

Abstract: The generation of specific high harmonics for an optical two-level system is elucidated. The desired emitted radiation can be induced by a carefully designed excitation pulse, which is found by a multiparameter optimization procedure. The presented mechanism can also be applied to semiconductor structures for which the calculations result in much higher emission frequencies. The optimization procedure is either performed using a genetic algorithm or a rigorous mathematical optimization technique.

Adjoint calculation using time­ minimal program reversals for multi-processor machines

Abstract: For computational purposes such as debugging, derivative computations using the reverse mode of automatic differentiation, or optimal control by Newton’s method, one may need to reverse the execution of a program The simplest option is to record a complete execution log and then to read it backwards As a result, massive amounts of storage are normally required This paper proposes a new approach to reversing program executions The presented technique runs the forward simulation and the reversal process at the same speed For that purpose, one only employs a fixed and usually small amount of memory pads called checkpoints to store intermediate states and a certain number of processors The execution log is generated piecewise by restarting the evaluation repeatedly and concurrently from suitably placed checkpoints The paper illustrates the principle structure of time-minimal parallel reversal schedules and quotes the required resources Furthermore, some specific aspects of adjoint calculations are discussed Initial results for the steering of a Formula 1 car are shown

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.