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.

Bounding the Number of Processors and Checkpoints Needed in Time-minimal Parallel Reversal Schedules

Abstract: For derivative calculations, debugging, and interactive control one may need to reverse the execution of a computer program for given inputs. If any increase of the time needed for the reversal is unacceptable, the availability of enough auxiliary processors provides the possibility to reverse the computer program with minimal temporal complexity and a surprisingly small spatial complexity using parallel reversal schedules. This paper describes the structure of such parallel reversal schedules that use the checkpointing technique on a multi-processor machine. They are shown to require the least number of processors and memory locations to store checkpoints given a certain number of time steps.

Optimization of triple-ring electrodes on piezoceramic transducers using algorithmic differentiation

Abstract: Data of material properties given by manufacturers of piezoelectric ceramics is often flawed due to, for example, slightly different manufacturing conditions for each production batch. Hence, the n...

On the efficient generation of taylor expansions for DAE solutions by automatic differentiation

Abstract: Under certain conditions the signature method suggested by Pantiledes and Pryce facilitates the local expansion of DAE solutions by Taylor polynomials of arbitrary order. The successive calculation of Taylor coefficients involves the solution of nonlinear algebraic equations by some variant of the Gauss-Newton method. Hence, one needs to evaluate certain Jacobians and several right hand sides. Without advocating a particular solver we discuss how this information can be efficiently obtained using ADOL-C or similar automatic differentiation packages.

Optimal r-order of an adjoint Broyden method without the assumption of linearly independent steps

Abstract: Quasi-Newton methods based on least change secant updating formulas that solve linear equations Ax=b in n=dim(x)=dim(b) steps can be expected to solve the smooth nonlinear systems n-step quadratically, i.e. with an r-order of ρ=21/n=1+1/n+O(1/n2). The best rate one can generally expect is ρn-k for some fixed k, where ρn is the positive root of ρn(ρ-1)=1. Irrespective of the shift k, the ratio [image omitted] tends to 1 for large n. To show that this asymptotically optimal rate is actually achieved, one usually has to impose a priori some kind of linear independence condition on the sequence of steps taken by the quasi-Newton iteration in question. Without any such assumptions, we establish in this paper the convergence order ρn for the adjoint Broyden formula proposed by Schlenkrich et al. [S. Schlenkrich, A. Griewank, and A. Walther, Local convergence analysis of TR1 updates for solving nonlinear equations, MATHEON Preprint 337 (2006)]. It requires the evaluation of adjoint vectors, is invariant with respect to linear transformations on the variable domain, and combines the properties of bounded deterioration and heredity.

Beyond the Oracle: Opportunities of Piecewise Differentiation

Abstract: For more than 30 years much of the research and development in nonsmooth optimization has been predicated on the assumption that the user provides an oracle that evaluates at any given \({\boldsymbol x} \in \mathbb {R}^n\) the objective function value φ(x) and a generalized gradient g ∈ ∂φ(x) in the sense of Clarke. We will argue here that, if there is a realistic possibility of computing a vector g that is guaranteed to be a generalized gradient, then one must know so much about the way \(\varphi : \mathbb {R}^n \to \mathbb {R}\) is calculated that more information about the behavior of φ in a neighborhood of the evaluation point can be extracted. Moreover, the latter can be achieved with reasonable effort and in a stable manner so that the derivative information provided varies Lipschitz continuously with respect to x. In particular we describe the calculation of directionally active generalized gradients, generalized e-gradients and the checking of first and second order optimality conditions. All this is based on the abs-linearization of a piecewise smooth objective in abs-normal form.

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.