Profile

Michael Griebel
Date of birth: 13 Jan 1960
Academic career
1985
1985 - 1990
1989
1990 - 1993
1993
1994 - 1995
1995
1995 - 1995
2000
2009
Since 1996
Since 2003
Since 2010
Diploma in Computer Science, TU Munich (advisor: F. L. Bauer)
Research Assistant, Institute for Informatics,
TU Munich
PhD in Computer Science, TU Munich (advisor:
C. Zenger)
Assistant Professor (C1), Institute for Informatics, TU Munich
Habilitation in Computer Science, TU Munich
(advisor: C. Zenger)
Assistant Professor (C2, Wissenschaftlicher
Oberassistent), Institute for Informatics, TU Munich
Venia Legendi in Computer Science, TU Munich
Priv.-Doz., Institute for Informatics, TU Munich
Visiting Professor, University of California, San
Diego, CA, USA
Visiting Professor, Paris Diderot University (Paris 7), France
Professor (C4) of Scientific Computing and Numerical Simulation, University of Bonn
Director, Institute for Numerical Simulation, University of Bonn
Director, Fraunhofer-Institute for Algorithms and
Scientific Computing (SCAI), Bonn
Honours
2004
2007
2017
Fellow, Institute for Pure and Applied Mathematics, University of California, Los
Angeles, CA, USA
International Fellow, Australian Research Council (ARCIF), University of New
South Wales, Sydney, NSW, Australia
John von Neumann Visiting Professorship, TU Munich
Offers
1995
1998
1998
2002
Invited Lectures
C4 professorship in numerical mathematics, Düsseldorf
C4 professorship in simulation of large systems, Stuttgart
Research position at the Lawrence Livermore National Laboratory, California,
USA
C4 professorship in technomathematics, TU Kaiserslautern joint with leading
position at the Fraunhofer Institute for Industrial Mathematics (Fraunhofer-Institut
für Techno- und Wirtschaftsmathematik, ITWM)
2006
2006
2006
2006
2007
2007
2008
2008
2009
2010
2012
2016
International Congress on the Applications of Mathematics, Santiago de Chile,
Chile
World Congress on Computational Mechanics, Los Angeles, CA, USA
International Congress of Mathematicians, Madrid, Spain
Numerical Methods in Finance. An AMaMeF Conference, INRIA, Rocquencourt,
France
ENUMATH, Graz, Austria
European Postgraduate Fluid Dynamics Conference, Birmingham, England, UK
IUTAM, Symposium on Modeling Nanomaterials and Nanosystems, Aalborg,
Denmark
Summer School on Nanotechnology and Mathematics, Santiago de Compostela, Spain
Algorithms and Complexity for Continuous Problems, Dagstuhl, Wadern
Zürich Summer School, Sparse Tensor Discretizations of High-Dimensional Problems, Switzerland
ESF-JSPS Frontier Science Conference for Young Researchers: Mathematics
for Innovation Large and Complex Systems, Tokyo, Japan
SIAM Conference on Uncertainty Quantification, Lausanne, Switzerland
Research profile
A main focus of current research is the approximation of high-dimensional functions and the
solution of partial differential equations in high dimensions. Our central tool in this respect is
the dimension-adaptive sparse grid method and its generalizations. Another focus is the development of efficient numerical methods for the treatment of two-phase-flow problems and for
the simulation of materials on the atomistic and the continuous scale with special emphasis
on nano-technology. Finally, adaptive discretizations for partial differential equations, multi-level
solvers of the arising linear systems and their parallelization have been investigated.
A main focus of future research will be numerical data analysis. This involves high dimensional regression, density estimation and classification problems in high-dimensional spaces. The
emphasis will be on the development of new numerical techniques and on proposing stable algorithms as well as on establishing theoretical results. The research will be driven by real data
applications in econometrics and finance and by data-oriented problems from material science.
Since data often stem from a low-dimensional manifold embedded in ambient space, we aim
at exploiting this structure by applying adaptive sparse grid algorithms for the h-version, the
p-version and the kernel-based versions of approximation. Moreover, we will develop nonlinear
methods beyond the Hilbert space setting. To this end, we will replace the conventional Euclidean cost function by more appropriate distance measures such as Banach space norms or
Bregman divergences. Here, we again aim at deriving both, a theoretical foundation and stability conditions with error estimates for practical purposes. Finally, we plan to study the relation
of our nonlinear methods to deep neural networks.
Editorships
• Numerische Mathematik (Managing Editor)
• Springer Lecture Notes in Computational Science and Engineering
• Springer Texts in Computational Science and Engineering
Research Area J A main focus of research is the approximation of high-dimensional functions
and the solution of partial differential equations in high dimensions. Also, data analysis problems are of interest here. Our central tool in this respect is the dimension-adaptive sparse grid
method and its generalizations. Another focus is the development of efficient numerical methods for the treatment of two-phase-flow problems and for the simulation of materials on the
atomistic and the continuous scale with special emphasis on nano-technology. Finally, adaptive
discretizations for partial differential equations, multi-level solvers of the arising linear systems
and their parallelization are under investigation.
Selected PhD students
Frank Kiefer (2001): “Multiskalen-Verfahren für Konvektions-Diffusions Probleme”,
now Programme Director, DFG
Jochen Garcke (2004): “Maschinelles Lernen durch Funktionsrekonstruktion mit verallgemeinerten dünnen Gittern”,
now Professor, University of Bonn
Jan Hamaekers (2009): “Tensor Product Multiscale Many-Particle Spaces with Finite-Order
Weights for the Electronic Schödinger Equation”,
now Head of Department ”Virtual Material Design”, Fraunhofer SCAI
Habilitations
Gerhard Zumbusch (2001), now Professor, University of Jena
Thomas Gerstner (2007), now Professor, University of Frankfurt
Marc Alexander Schweitzer (2008), now Professor, University of Bonn
Christian Rieger (2016)
Selected publications
[BG04]
[BG09]
[GG03]
[GH10a]
[GH10b]
[GK09]
[GO95]
[GO07]
[Gri94]
[Gri06]
[GW06]
B UNGARTZ, Hans-Joachim ; G RIEBEL, Michael: Sparse grids. In: Acta Numer. 13 (2004), S. 147–269. –
ISSN 0962–4929
B RAUN, Jürgen ; G RIEBEL, Michael: On a constructive proof of Kolmogorov’s superposition theorem. In:
Constr. Approx. 30 (2009), Nr. 3, S. 653–675. – ISSN 0176–4276
G ERSTNER, T. ; G RIEBEL, M.: Dimension-adaptive tensor-product quadrature. In: Computing 71 (2003),
Nr. 1, S. 65–87. – ISSN 0010–485X
G RIEBEL, M. ; H AMAEKERS, J.: Tensor Product Multiscale Many-Particle Spaces with Finite-Order Weights
for the Electronic Schrödinger Equation. In: Zeitschrift für Physikalische Chemie 224 (2010), S. 527–543
G RIEBEL, Michael ; H OLTZ, Markus: Dimension-wise integration of high-dimensional functions with applications to finance. In: J. Complexity 26 (2010), Nr. 5, S. 455–489. – ISSN 0885–064X
G RIEBEL, M. ; K NAPEK, S.: Optimized general sparse grid approximation spaces for operator equations.
In: Math. Comp. 78 (2009), Nr. 268, S. 2223–2257. – ISSN 0025–5718
G RIEBEL, M. ; O SWALD, P.: On the abstract theory of additive and multiplicative Schwarz algorithms. In:
Numer. Math. 70 (1995), S. 163–180. – Also as SFB-Report 342/6/93 A, Institut für Informatik, Technische
Universität München, 1993
G RIEBEL, M. ; O ELTZ, D.: A sparse grid space-time discretization scheme for parabolic problems. In:
Computing 81 (2007), Nr. 1, S. 1–34. – ISSN 0010–485X
G RIEBEL, Michael: Multilevel algorithms considered as iterative methods on semidefinite systems. In:
SIAM J. Sci. Comput. 15 (1994), Nr. 3, S. 547–565. – ISSN 1064–8275. – Iterative methods in numerical linear algebra (Copper Mountain Resort, CO, 1992)
G RIEBEL, Michael: Sparse grids and related approximation schemes for higher dimensional problems. In:
Foundations of computational mathematics, Santander 2005 Bd. 331. Cambridge Univ. Press, Cambridge,
2006, S. 106–161
G RIEBEL, M. ; W OZNIAKOWSKI, H.: On the optimal convergence rate of universal and non-universal algorithms for multivariate integration and approximation. In: Mathematics of Computation 75(255) (2006), S.
1259–1286