Claudia Schillings
Personal Data
Nationality German.
Date of Birth 15.03.1982.
Place of Birth Zell (Mosel).
Education
Apr 2011 Doctor of Natural Sciences (Dr. rer. nat.) in Mathematics, Universität Trier,
Optimal aerodynamic design under uncertainties, Grade: summa cum laude.
Mar 2007 - Apr 2011 PhD Student, Universität Trier.
Mar 2007 Diploma in Applied Mathematics and Computer Science, Universität Trier,
Grade: 0.87 (with distinction).
Oct 2006 Diploma Thesis, Collaboration with Daimler AG, Research Center Ulm, Modeling
of a fuel cell component in Matlab/Simulink using parameter estimation and
neuronal networks (in German).
Oct 2001 - Mar 2007 Studies of Applied Mathematics and Computer Science, Universität
Trier, Focus in Mathematics: Numerical Mathematics, Operations Research,
Focus in Computer Science: Algorithms and Data Structures.
Jun 2001 Abitur, Cusanus Gymnasium Wittlich, Award of the German Physical Society
(DPG), Grade: 1.6.
Oct 1999 - Sep 2000 Early Introduction in the Study of Physics FIPS (Distance Learning), TU
Kaiserslautern.
Workshops
Jan 2013 Numerical Methods for PDE Constrained Optimization with Uncertain Data,
Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach.
Oct 2011 TAU Short Courses: Scripting (Python) and Linear Solvers, Institute of
Aerodynamics and Flow Technology DLR, Braunschweig.
Jan 2009 Numerical Techniques for Optimization Problems with PDE Constraints,
Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach.
Apr 2007 Spring School Stochastic Programming: Theory and Application, Università
degli studi di Bergamo, Bergamo.
Sep 2007 HLRS Parallel Programming Workshop: Iterative Solver and Parallelization,
High Performance Computing Center (HLRS), Garching.
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Sep 2000 Summer School in Computer Science, Universität Passau.
Sep 1999 Summer School in Computer Science, Universität Passau.
Professional Experience
since Sep 2014 Research Associate at the Mathematics Institute - Prof. Dr. A. M. Stuart,
University of Warwick.
Mar 2012 - Aug 2014 Research Associate at the Seminar for Applied Mathematics - Prof. Dr. C.
Schwab, ETH Zürich.
Mar 2007 - Mar 2012 Research Assistant at the Department of Mathematics in the Research
Group Numerical Mathematics - Optimization, PDE of Prof. Dr. V. Schulz,
Universität Trier.
Summer Term 11 Lecturer, FOM Hochschule für Ökonomie & Management (University of Applied
Sciences), Luxemburg.
Winter Term 06/07
May 2006 - Oct 2006
Winter Term 05/06
Jul 2005 - Oct 2005
Student Assistant, Universität Trier, Prof. Dr. W. Luh.
Diploma thesis, Daimler AG, Research Center Ulm, Fuel cell modeling/simulation.
Student Assistant, Universität Trier, Prof. Dr. W. Luh.
Internship, Daimler AG, Research Center Ulm, Fuel cell modeling/simulation.
Research Summary
Overall goal
Mathematical research driven by real-world problems governed by partial
differential equations.
Proper treatment of uncertainties within a numerical context.
Maintain a theoretical sound base.
Keywords
Interests Numerical Mathematics, Inverse Problems, PDE Constrained Optimization, Uncertainty Quantification, Optimization under Uncertainty, Model
Reduction.
Methods (Adaptive) Sparse Grids, Monte-Carlo Methods, (Non-intrusive) Polynomial Chaos, Stochastic Collocation, POD, One-shot Approaches, Adjoint Methods, Discontinuous Galerkin.
Applications Bayesian Inverse Problems, Biological Systems Identification, Aerodynamic
Shape Optimization.
Research Projects
Since Sep 2014 EQUIP Enabling Quantification of Uncertainty for Large-Scale Inverse
Problems.
This project will develop the mathematical, statistical and computational tools required to
significantly advance understanding of large-scale inverse problems arising in engineering.
In particular it will be aimed at the quantification of uncertainty in predictions based on
imperfect physical models and noisy data. The work will be guided by applications arising
in subsurface geophysics, including carbon sequestration, compressed air storage, ground
and water engineering, and nuclear waste burial, as well as fossil fuel extraction.
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Apr 2012 - Aug 2014 STAHDPDE Sparse Tensor Approximations of High-Dimensional and stochastic Partial Differential Equations (Sparse techniques for parametric differential equations).
The focus of the project is on the efficient numerical approximation of parametric differential
equations, in particular on methods which are dimensionally robust, i.e. whose efficiency
(meaning accuracy versus computational cost measured in terms of the total number of
floating point operations to achieve this accuracy) is provably robust with respect to the
number of parameters. In order to allow for efficient approximations of the parametric
solutions on the entire, possibly infinite dimensional parameter space, some form of sparsity
in the parametric dependence of the solution is necessary. Based on the theoretical results,
a major goal of the project is to develop numerical algorithms which allow to exploit
computationally the sparse parameter dependence of the solutions and, hence, to achieve
the optimal complexity by the sparse approximations.
Jun 2010 - Mar 2012 DGHPOPT Discontinuous Galerkin Methods for Robust Aerodynamic
Design on High Performance Computer Architectures.
The DGHPOPT project is focused on developing new computational techniques for enhancing the capability of computational fluid dynamics simulations by exploiting the full
potential of high-order discontinuous Galerkin methods, efficient optimization methods for
robust aerodynamic design and the use of novel hardware architectures.
Nov 2010 - Mar 2012 MUNAplus.
On the basis of the project MUNA, the follow-up project MUNAplus focuses on further
improvements and the increase in efficiency of the developed methods and approaches
in order to reduce the additional computational effort arising from the treatment of
uncertainties and the resulting robust shape optimization problems.
Mar 2007 - May 2010 MUNA Management and Minimization of Uncertainties in Numerical
Aerodynamics.
The project MUNA was initiated to introduce uncertainties within the computational fluid
dynamics simulation process. The main objectives of the project are identification and
quantification of uncertainty sources, analysis of sensitivities and computation of confidence
intervals, development of methods and strategies to minimize the main uncertainties and
errors and verification of the developed methods and demonstration of their reliability. The
University of Trier contributes to the proper treatment of irreducible uncertainties arising in
the formulation of aerodynamic design tasks. Existing simulation and optimization methods
will be improved, so that numerical uncertainties are identified, quantized and included in
the overall optimization procedure, thus making robust design in this sense possible.
Selected Talks
Mar 2015 Analysis of the Ensemble Kalman Filter for Inverse Problems, B(A)MC, Cambridge
(invited talk).
Mar 2015 Analysis of the Ensemble Kalman Filter for Inverse Problems, SIAM CSE, Salt Lake
City.
Mar 2015 On the Efficient Treatment of Uncertainties in Optimization Problems, Workshop
Women in Optimization, Heidelberg (invited talk).
Feb 2015 Scaling Limits in Computational Bayesian Inversion, University of Birmingham
(invited talk).
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Dec 2014 Scaling Limits in Computational Bayesian Inversion, University of Reading (invited
talk).
Jun 2014 Exploiting Sparsity in Bayesian Inverse Problems of Parametric Operator Equations,
TUM, München (invited talk).
May 2014 Optimal Aerodynamic Design under Uncertainty, EPFL, Lausanne (invited talk).
Apr 2014 Exploiting Sparsity in Bayesian Inverse Problems of Parametric Operator Equations,
Mascot Num, ETH, Zürich (invited opening lecture).
Apr 2014 Sparse, Adaptive Methods for Bayesian Inverse Problems of Parametric Operator
Equations, Workshop Numerical Methods for High-Dimensional Problems, Paris.
Apr 2014 Sparsity in Bayesian Inversion, SIAM UQ, Savannah.
Mar 2014 Sparse Approximation Algorithms for High Dimensional Parametric Initial Value
Problems, GAMM, Erlangen.
Aug 2013 Sparsity in Bayesian Inverse Problems, ENUMATH, Lausanne.
Jun 2013 Sparsity in Bayesian Inversion of Parametric Operator Equations, Application talk,
Junior Professorship for Uncertainty Quantification, TU Darmstadt (invited talk).
Jun 2013 Adaptive, Sparse Quadratures for Bayesian Inverse Problems, MAFELAP, London.
Apr 2013 Sparse, Adaptive Quadratures for Bayesian Inverse Problems (in German), Application talk, Junior Professorship in Nonsmooth Optimization and Variational Analysis,
HU Berlin (invited talk).
Apr 2013 Sparse, Adaptive Quadratures for Bayesian Inverse Problems (in German), Application talk, Junior Professorship in Numerical Mathematics and Scientific Computing,
FU Berlin (invited talk).
Mar 2013 Sparse, Adaptive Quadratures for Bayesian Inverse Problems, TU Bergakademie
Freiberg (invited talk).
Feb 2013 Sparse Quadrature Approach to Bayesian Inverse Problems, SIAM CSE, Boston.
Jan 2013 Sparse, Adaptive Smolyak Quadratures for Bayesian Inverse Problems, Numerical
Methods for PDE Constrained Optimization with Uncertain Data, Oberwolfach.
Aug 2012 On the Influence of Robustness Measures on Shape Optimization with Stochastic
Uncertainties, ISMP, Berlin.
Mar 2012 On the Treatment of Uncertainties in Aerodynamic Design, HPSC Conference,
Hanoi.
Nov 2011 On the Treatment of Uncertainties in Aerodynamic Design, SAM, ETH, Zürich
(invited talk).
Nov 2011 Optimal Aerodynamic Design under Shape Uncertainty, WIAS, Berlin (invited talk).
Jul 2011 Aerodynamic Shape Optimization under Uncertainty - A general framework in
order to handle uncertainties in aerodynamic shape optimization problems, ICIAM,
Vancouver.
May 2011 Optimal Aerodynamic Design under Uncertainties - Identification, quantification
and minimization of uncertainties arising in the formulation of aerodynamic design
tasks, ECCOMAS CFD & Optimization, Antalya.
May 2011 Numerical Treatment of Uncertainties in Aerodynamic Shape Optimization Combination of one-shot methods and uncertainty quantification techniques, SIAM
Optimization, Darmstadt.
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Mar 2011 On the Treatment of Uncertainties in Aerodynamic Shape Optimization Generalization of one-shot approaches to robust optimization problems, SIAM
CSE, Reno.
Jul 2009 Aerodynamic Shape Optimization under Uncertainty - Adaptive sparse grid
techniques to reduce the computational effort in robust optimization, ISMP, Chicago.
Mar 2009 Robust Optimization in CFD - Model reduction using a goal-oriented KarhunenLoève basis representing the random field of uncertainties, SIAM CSE, Miami.
Jan 2009 Robust Optimization in CFD - Sparse grids in robust optimization in order to
overcome the curse of dimensionality, Numerical Techniques for Optimization
Problems with PDE Constraints, Oberwolfach.
Service Activities
Co-organization of the MIR@W (Mathematical Interdisciplinary Research at Warwick) Workshop on Reduced Order Models in Uncertainty Quantification, November
2014.
Co-organization of focus session on Optimization under Uncertainties at the 3rd
European Conference on Computational Optimization, Chemnitz, July 2013.
Co-organization of minisymposium on Stochastic partial differential equations
(SPDEs) and applications at the 83rd Annual Meeting of the International
Association of Applied Mathematics and Mechanics, Darmstadt, March 2012.
Co-organization of minisymposium on the Treatment of Uncertainties in PDE
Constrained Problems at the 7th International Congress on Industrial and Applied
Mathematics, Vancouver, July 2011.
Reviewer for SIAM Journal on Scientific Computing (SISC), Optimization and Engineering (OPTE), Inverse Problems (IOP), SIAM Journal on Uncertainty Quantification (JUQ), Journal of Computational Physics (JCP) and Applied and Computational
Harmonic Analysis (ACHA).
Awards
GAMM Junior Fellow, 2014.
Mary-Kingsley Travel Award recipient, funding towards travel and expenses related
to the 5th International Conference on High Performance Scientific Computing
(HPSC), Hanoi, 2012.
SIAM Student Travel Award recipient, funding towards travel and expenses related
to the SIAM Conference on Computational Science and Engineering, Reno, 2011.
Mary-Kingsley Travel Award recipient, funding towards travel and expenses related
to the 12th International Conference on Stochastic Programming, Halifax, 2010.
Publications
Articles in Journals and Refereed Proceedings Volumes
C. Schillings and C. Schwab. Sparsity in Bayesian inversion of parametric operator
equations, Inverse Problems 30(6) (2014) 065007.
R. Gantner, C. Schillings and C. Schwab. Binned multilevel Monte Carlo for Bayesian
inverse problems with large data, (accepted for publication in DD22 Proceedings
Volume in LNCSE 2013).
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C. Schillings and V. Schulz. On the influence of robustness measures on shape
optimization, Optimization and Engineering, pp. 1-40, 2014.
C. Schillings and C. Schwab. Sparse, adaptive Smolyak quadratures for Bayesian
inverse problems, Inverse Problems 29 (2013) 065011.
M. Hansen, C. Schillings, and C. Schwab. Sparse approximation algorithms for high
dimensional parametric initial value problems, Report 2013-10 (Zürich, Switzerland:
Seminar for Applied Mathematics, ETH), (accepted for publication in Proceedings
of the 5th International Conference on High Performance Scientific Computing
2012).
C. Schillings, S. Schmidt and V. Schulz. Efficient shape optimization for certain and
uncertain aerodynamic design, Computers and Fluids, Vol. 46, No. 1, pp. 78-87,
2011.
A. Borzi, V. Schulz, C. Schillings and G. von Winckel. On the treatment of distributed
uncertainties in PDE-constrained optimization, GAMM-Mitteilungen, Vol. 33, No. 2,
pp. 230-246, 2010.
V. Schulz and C. Schillings. On the nature and treatment of uncertainties in
aerodynamic design, AIAA Journal, Vol. 47, No. 3, pp. 646-654, 2009.
Miscellaneous Publications
C. Schillings, M. Sunnaker, J. Stelling, C. Schwab. Efficient characterization of
parametric uncertainty of complex (bio)chemical networks, 2015 (submitted).
C. Schillings and C. Schwab. Scaling limits in computational Bayesian inversion,
Report 2014-26 (Zürich, Switzerland: Seminar for Applied Mathematics, ETH),
2014 (submitted).
C. Schwab and C. Schillings. Sparse quadrature approach to Bayesian inverse
problems, Oberwolfach Report, 39(1):2237–2240, 2013.
A. Litvinenko, D. Liu, C. Schillings and V. Schulz, Uncertainty quantification and
treatment in aircraft design - comparison of approaches, 2013 (submitted).
C. Schillings. A note on sparse, adaptive Smolyak quadratures for Bayesian inverse
problems, Oberwolfach Report, 10(1):239–293, 2013.
V. Schulz and C. Schillings, Optimal aerodynamic design under uncertainty, Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics,
B. Eisfeld, H. Barnewitz, W. Fritz, and F. Thiele, eds., Vol. 122 of Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Springer Berlin Heidelberg,
2013, pp. 297-338.
C. Schillings and V. Schulz. Optimal aerodynamic design under uncertainties, ECCOMAS CFD & Optimization, I.H. Tuncer, ed., ISBN 978-605-61427-4-1, No. 2011049, 2011.
V. Schulz and C. Schillings. Optimal aerodynamic design under shape uncertainties,
Trierer Forschungsbericht, 09-5, 2009 (submitted).
C. Dülk and C. Schillings. Patent application on the topic of optimal control of a
fuel cell component, 2006.
Work in Progress
C. Schillings, A. M. Stuart. Analysis of the ensemble Kalman filter for inverse
problems, 2015.
67A Albert Street – London NW1 7LX - England
T +44 (0)24 765 73495 • B c.schillings@warwick.ac.uk
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R. Hiptmair, L. Scarabosio, C. Schillings, C. Schwab. Deterministic uncertainty
quantification in nano optics, 2014.
Theses
C. Schillings. Optimal aerodynamic design under uncertainties, PhD Thesis,
Universität Trier, 2011.
C. Schillings. Modeling of a fuel cell component in Matlab/Simulink using parameter
estimation and neuronal networks (in German), DiplomaThesis, 2006.
Teaching and Supervision
Term 14/15 Research Study Group Uncertainty Quantification designed for first year
PhD students (jointly with Dr. A. Teckentrup), University of Warwick.
Winter Term 14 Lecture Matrix Analysis and Algorithms (jointly with Dr. A. Teckentrup), University of Warwick.
since Sep 2014 Co-supervision of PhD student Matthew Dunlop, MAP estimators for Bayesian
inverse problems, University of Warwick.
Summer Term 14 Teaching Assistant Numerical Anaysis II (Ordinary Differential Equations),
ETH Zürich, Prof. Dr. P. Grohs.
Winter Term 13 Teaching Assistant Linear Algebra, ETH Zürich, Prof. Dr. K. Nipp.
Summer Term 13 Teaching Assistant Numerical Analysis of Stochastic Partial Differential
Equations, ETH Zürich, Prof. Dr. C. Schwab, Dr. A. Lang.
Winter Term 12 Teaching Assistant Linear Algebra, ETH Zürich, Prof. Dr. K. Nipp.
Summer Term 11 Lecture Mathematics for Students of Business Administration and
Mathematics, FOM Hochschule für Ökonomie & Management (University of Applied Sciences), Luxemburg.
Summer Term 11 Seminar Numerical Mathematics, Surrogate Models / Approximation Methods,
Universität Trier, Prof. Dr. V. Schulz.
Sep 2008 - Mar 2009 Co-supervision of Diploma thesis of Jörg Skalbania, Portfolio optimization
under uncertainties, Universität Trier.
Sep 2008 - Mar 2009 Co-supervision of Diploma thesis of Jochen Geiter, Optimal Hedging on futures
market, Universität Trier.
Dec 2008 - Jun 2009 Co-supervision of Diploma thesis of Thomas Melchior, Polynomial Chaos,
Application to CFD, Universität Trier.
Jan 2008 - Sep 2009 Co-supervision of Diploma thesis of Hannah Ilesan, MPEC problems with
applications in economics, Universität Trier.
Summer Term 08 Tutorial Numerical Mathematics III (Nonlinear Optimization), graduate level,
Universität Trier, Prof. Dr. V. Schulz.
Summer Term 08 Substitution of several lectures Numerical Mathematics III (Nonlinear
Optimization), graduate level, Universität Trier, Prof. Dr. V. Schulz.
Winter Term 07/08 Seminar Numerical Mathematics, Mathematics for 3D game programming and
computer graphics, Universität Trier, Prof. Dr. V. Schulz.
Summer Term 07 Tutorial Numerical Mathematics, Universität Trier, Prof. Dr. V. Schulz.
Winter Term 05/06 Tutorial Analysis for Students of Business Administration and Mathematics,
Universität Trier, Prof. Dr. W. Luh.
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