Prof. Dr. Andrea Walther

Profil

Zusammenfassung

Andrea Walther entwickelt mathematische Methoden und Algorithmen zur effizienten Berechnung von Ableitungen und zur Lösung von Optimierungsproblemen. Ihre Expertise liegt in der automatischen Differentiation und deren Anwendung auf komplexe technische Probleme wie Strömungsdynamik, Materialcharakterisierung und Maschinenoptimierung. Sie verbindet dabei theoretische Mathematik mit praktischen Implementierungen für rechnerisch anspruchsvolle Aufgaben in Industrie und Forschung.

Skills

Name

Prof. Dr. Andrea Walther

Titel

Prof. Dr.

Fakultät

Mathematisch-Naturwissenschaftliche Fakultät

Institut

Institut für Mathematik

Arbeitsgruppe

Mathematische Optimierung

E-Mail

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HU-FIS-Profil

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Zuletzt gescrapt

28.6.2026, 01:14:21

• Adaptives Surrogatmodell für strömungsdynamische Optimierungsaufgaben

  Quelle ↗

  Förderer: DFG Exzellenzstrategie Cluster Zeitraum: 01/2026 - 12/2027 Projektleitung: Prof. Dr. Andrea Walther

• Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 09/2020 - 01/2021 Projektleitung: Prof. Dr. Andrea Walther

• Ein modellbasiertes Messverfahren zur Charakterisierung der frequenzabhängigen Materialeigenschaften von Piezokeramiken unter Verwendung eines einzelnen Probekörperindividuums.

  Quelle ↗

  Förderer: DFG Sachbeihilfe Zeitraum: 02/2021 - 05/2023 Projektleitung: Prof. Dr. Andrea Walther

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• Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation

  1987

  2216 Zitationen · DOI

  Algorithmic, or automatic, differentiation (AD) is a growing area of theoretical research and software development concerned with the accurate and efficient evaluation of derivatives for function evaluations given as computer programs. The resulting derivative values are useful for all scientific computations that are based on linear, quadratic, or higher order approximations to nonlinear scalar or vector functions. AD has been applied in particular to optimization, parameter identification, nonlinear equation solving, the numerical integration of differential equations, and combinations of these. Apart from quantifying sensitivities numerically, AD also yields structural dependence information, such as the sparsity pattern and generic rank of Jacobian matrices. The field opens up an exciting opportunity to develop new algorithms that reflect the true cost of accurate derivatives and to use them for improvements in speed and reliability. This second edition has been updated and expanded to cover recent developments in applications and theory, including an elegant NP completeness argument by Uwe Naumann and a brief introduction to scarcity, a generalization of sparsity. There is also added material on checkpointing and iterative differentiation. To improve readability the more detailed analysis of memory and complexity bounds has been relegated to separate, optional chapters.The book consists of three parts: a stand-alone introduction to the fundamentals of AD and its software; a thorough treatment of methods for sparse problems; and final chapters on program-reversal schedules, higher derivatives, nonsmooth problems and iterative processes. Each of the 15 chapters concludes with examples and exercises. Audience: This volume will be valuable to designers of algorithms and software for nonlinear computational problems. Current numerical software users should gain the insight necessary to choose and deploy existing AD software tools to the best advantage. Contents: Rules; Preface; Prologue; Mathematical Symbols; Chapter 1: Introduction; Chapter 2: A Framework for Evaluating Functions; Chapter 3: Fundamentals of Forward and Reverse; Chapter 4: Memory Issues and Complexity Bounds; Chapter 5: Repeating and Extending Reverse; Chapter 6: Implementation and Software; Chapter 7: Sparse Forward and Reverse; Chapter 8: Exploiting Sparsity by Compression; Chapter 9: Going beyond Forward and Reverse; Chapter 10: Jacobian and Hessian Accumulation; Chapter 11: Observations on Efficiency; Chapter 12: Reversal Schedules and Checkpointing; Chapter 13: Taylor and Tensor Coefficients; Chapter 14: Differentiation without Differentiability; Chapter 15: Implicit and Iterative Differentiation; Epilogue; List of Figures; List of Tables; Assumptions and Definitions; Propositions, Corollaries, and Lemmas; Bibliography; Index

• Evaluating Derivatives

  2008

  Society for Industrial and Applied Mathematics eBooks · 1484 Zitationen · DOI

• Algorithm 799: revolve

  2000

  ACM Transactions on Mathematical Software · 483 Zitationen · DOI

  In its basic form, the reverse mode of computational differentiation yields the gradient of a scalar-valued function at a cost that is a small multiple of the computational work needed to evaluate the function itself. However, the corresponding memory requirement is proportional to the run-time of the evaluation program. Therefore, the practical applicability of the reverse mode in its original formulation is limited despite the availability of ever larger memory systems. This observation leads to the development of checkpointing schedules to reduce the storage requirements. This article presents the function revolve, which generates checkpointing schedules that are provably optimal with regard to a primary and a secondary criterion. This routine is intended to be used as an explicit “controller” for running a time-dependent applications program.

• Freie Universität Berlin

  Thematic Einstein Semester on Mathematical Optimization for Machine Learning

  university

• Friedrich-Alexander-Universität Erlangen-Nürnberg

  SFB/TRR 154/3: Gemischt ganzzahlige nichtglatte Optimierung für Bilevel-Probleme (TP B10)

  university

• Technische Universität Berlin

  Thematic Einstein Semester on Mathematical Optimization for Machine Learning

  university