Research Group Andreas Griewank

Publications

Find our recent publications on the preprint server of the DFG Research Center MATHEON.

Research Projects

Nonlinear Programming Algorithms
Automated Extension of Fixed Point PDE Solvers
Optimization in Aerodynamics
Automatic Differentiation with Compiler Integration
Storage Reduced Optimal Control
Analysis and Treatment of DAEs using Automatic Differentiation
Sensitivity Analysis and Parameter Estimation for Virus Diseases of Animals
Structural and Topological Optimisation for Mass Production Automobiles
Nonlinear Optimum Experimental Design

General Purpose, Linearly Invariant
Algorithms for Large Scale Nonlinear Problems

People: Andreas Griewank, Kshitij Kulshreshta, Torsten Bosse
Project C12 in DFG Research Center: Mathematics for key technologies (MATHEON): → Project description, →Project website
Description: Development of NLP algorithms that avoid the formation and factorization of Jacobian and (full) Hessian matrices.

Publications: Recent Publications at DFG Research Center MATHEON

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Automated extension of fixed point PDE solvers for optimal design with bounded retardation

People: Andreas Griewank, Nicolas Gauger, N.N.
Description: Development of mathematical methods, algorithmic techniques and software tools for the transition from simulation to optimization.
Further Information
Cooperation: Dr. Thomas Slawig, TU Berlin
Funding: DFG Schwerpunktprogramm 1253

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Optimization in Aerodynamics

People: Andreas Griewank, Nicolas Gauger
Description: Optimization of aircraft shapes and structures on the basis of first and second order adjoint evaluations.
Cooperation

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Algorithmic/Automatic Differentiation with Compiler Integration

People: Andreas Griewank, Jan Riehme
Description: Development of AD tools that exploit sparsity and other structure.
Cooperation

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Storage Reduced Optimal Control

People: Andreas Griewank, Julia Sternberg
Description: Reduction of storage requirement by checkpointing for time-dependent optimal control problems in ODEs and PDEs.
Cooperation

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Analysis and Treatment of DAEs using Automatic Differentiation

People: Andreas Griewank, Caren Tischendorf, René Lamour, Dagmar Monett Díaz
Website
Description: The analysis and treatment of systems of differential algebraic equations (DAEs) may involve high order derivatives, as it is the case in much practical problems. Solving such DAEs, for example, may be very difficult numerically but also of high complexity. Most solving methods for ordinary differential equations (ODEs) are not practicable anymore for such systems; new techniques should be considered indeed.

Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs” [2]. AD (see also [1]) is quite useful for analyzing and numerically solving DAEs. This is why it is to become an important component of general-purpose analysis and integration schemes in the future.

Our main research goal is to contribute to the use of AD in the theoretical analysis and numerical solution of DAEs. For example, we want to develop and implement an algorithm for the determination of the index in DAEs. Similarly to [3], we consider DAEs as presented in [4, 5, 6]: DAEs with properly stated leading terms. The calculation of the index of these systems is based on a matrix sequence with suitable chosen projectors [3]. We expect to permorm all needed differentiations by using AD.
Funding: Max-Planck Research Prize of A.Griewank

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Sensitivity Analysis and Parameter Estimation for Virus Diseases of Animals

People: Andreas Griewank, Stefan Körkel, Jana Vesely
Description: Zur Bekämpfung epidemisch verlaufender Tierkrankheiten werden in der Praxis verschiedene Bekämpfungsstrategien angewendet. Dazu gehören intensive Beprobung und Überwachung, Behandlung, Impfung, Quarantäne, Selektion, Handelseinschränkung u.a. Diese Maßnahmen sind abhängig von der konkreten Erkrankung und vom Ausmaß der Epidemie. In dieser Kooperation sollen Methoden für die mathematische Analyse geeigneter dynamischer Modelle entwickelt werden, mit deren Hilfe adäquate Bekämpfungsstrategien abgeleitet und mögliche Einflußfaktoren optimiert werden können.
Cooperation: Bundesforschungsanstalt für Viruskrankheitem der Tiere

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Structural and Topological Optimisation for Mass Production Automobiles

People

Andreas Griewank, Kshitij Kulshreshtha

Description

Das Projekt "Karosseriestruktur-Optimierung - Design to Cost" umfasst eine Untersuchung zur Optimierung der Karosserie durch Veränderung der Struktur bei wirtschaftlichem Einsatz von Materialien unter Erhaltung der erwünschten statischen und dynamischen Eigenschaften der Karosserie.

Es erfolgt eine Untersuchung der Rahmenstruktur für Massenfahrzeuge mit Verschiebungs- und Spannungsbedingungen unter verschiedenen, mehrfachen Belastungsszenarien, um die Spitzenspannung in Verbindungsstücken und Fugen zu reduzieren.

Das Optimierungsverfahren wird als Mehrzieloptimierung mit Abgleich zwischen verschiedenen Zielfunktionen (z.B. Kosten und Gewicht) in Abhängigkeit von ihrer Priorität durchgeführt. Soweit wie möglich sollen dabei absolute, d.h. globale Optima bestimmt werden.

Um Simulation und Optimierungsläufe in wenigen Minuten und damit interaktiv durchführen zu können, wird die Gesamtzahl sowohl der Entwurfs- wie auch der Zustandsvariablen im Bereich von einigen Hunderten oder maximal wenigen Tausenden gehalten werden. Zu diesem Zweck wird der Fahrzeugrahmen zunächst als ein Stabwerk aus biegsamen Balken modelliert.

Phase stability for mixed fluids by Global Optimization using symplectic trajectories: presentation by Andreas Griewank, October 27, 2005.

Cooperation

Volkswagen AG

Funding

Volkswagen AG

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Nonlinear Optimum Experimental Design

People: Stefan Körkel
Description: Adequate models for dynamic processes are nonlinear differential algebraic equation (DAE) systems. Usually they contain unknown parameters which have to be estimated from experimental data. Layout and mode of processing of the experiments determine the statistical quality of the parameter estimation. The task of experimental design consists in minimizing the uncertainty of the estimates under given experimental costs and further restrictions. The arising nonlinear constrained optimization problems possess an intricate objective function which is defined on the variance-covariance matrix of the parameter estimation and hence depends implicitly on sensitivities of the solution of the underlying DAE system.
We are developing the software package VPLAN which provides a general purpose tool for modeling, simulation, parameter estimation and optimum experimental design for processes which can be described by nonlinear DAE systems. VPLAN has been and is being applied successfully for processes especially in chemistry and molecular biology. Our partner company BASF has been using VPLAN in industrial practice for several years.
Cooperation