Events

EU Regional School -Raul F. Tempone Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr. Raul F. Tempone - On Monte Carlo and Multilevel Monte Carlo

Computer, Electrical and Mathematical Science and Engineering Division
King Abdullah University of Science and Technology, Kingdom of Saudi Arabia

Abstract

We describe and analyze the Monte Carlo (MC, Multi-Index Monte Carlo (MIMC) and the Multi-Index Stochastic Collocation  (MISC) method for computing statistics of the solution of a PDE with random data. MIMC is both a stochastic version of the combination technique introduced by Zenger, Griebel and collaborators and an extension of the Multilevel Monte Carlo (MLMC) method first described by Heinrich and Giles. Instead of using first-order differences as in MLMC, MIMC uses mixed differences to reduce the variance of the hierarchical differences dramatically. These mixed differences yield new and improved complexity results, which are natural generalizations of Giles's MLMC analysis, and which increase the domain of problem parameters for which we achieve the optimal convergence. On the same vein, MISC is a deterministic combination technique based on mixed differences of spatial approximations and quadratures over the space of random data. Provided enough mixed regularity, MISC can achieve better complexity than MIMC. Moreover, we show that, in the optimal case, the convergence rate of MISC is only dictated by the convergence of the deterministic solver applied to a one-dimensional spatial problem. We propose optimization procedures to select the most effective mixed differences to include in MIMC and MISC. Such optimization is a crucial step that allows us to make MIMC and MISC computationally efficient. We show the effectiveness of MIMC and MISC in some computational tests using the mimclib open source library, including PDEs with random coefficients and Stochastic Interacting Particle Systems.  
 
References: 
1-   ”Multi-Index Stochastic Collocation for random PDEs”, by A. L. Haji Ali, F. Nobile, L. Tamellini and R. Tempone. Computers and Mathematics with  Applications, Vol. 306,  pp. 95--122, 2016.
 
2-   “Multi-index Stochastic Collocation convergence rates for random PDEs with parametric regularity, by A. Haji-Ali, F. Nobile, L. Tamellini, R. Tempone. Foundations of Computational Mathematics”, Vol. 16(6), Pages 1555-1605, 2016.
 
3-    “Multi Index Monte Carlo: When Sparsity Meets Sampling”, by A.-L. Haji-Ali, F. Nobile, and R. Tempone. Numerische Mathematik, Vol. 132(4), Pages 767–806, 2016. 
 
4- "Multilevel and Multi-index Monte Carlo methods for McKean-Vlasov equations”, by  A. L. Haji Ali and R. Tempone. ArXiv:1610.09934, October 2016.  To appear in Statistics and Computing, 2017.
 
5- "Sparse approximation of multilinear problems with applications to kernel-based methods in UQ", by F. Nobile, R. Tempone, and S. Wolfers. ArXiv:1609.00246, August 2016.  

Aachen Conference on Computaional Engineering Science 2017

Location: RWTH Super-C Building, Templergraben 57, 52056 Aachen, Germany

in Honor of Wolfgang Dahmen

The Aachen Conference on Computational Engineering Science (AC.CES) brings together leading experts in theory, method development, and applications related to problems in computational engineering. The main objectives of the conference are to present cutting-edge research and to facilitate interdisciplinary collaboration. The conference consists of a series of plenary sessions featuring invited talks by leading experts. The plenary lectures will be complemented by a poster session.

In 2017 the conference will be held in honor of Wolfgang Dahmen to celebrate his numerous contributions in Applied Mathematics.
 

Conference Topics:

  • Approximation Theory
  • High Dimensional Problems
  • Imaging / Electron Microscopy
  • Numerical Methods for PDEs

More information and tickets can be found here.

I³MS - Klawonn Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr. Axel Klawonn - Towards Computing on the Extreme Scale in Nonlinear Solid Mechanics

Chair of Numerical Mathematics and Scientific Computing, University of Cologne

Abstract

TBA

CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Marquardt Seminar

Location: SUPERC, 6th Floor, Generali Room, 52062 Aachen

Prof. Dr.-Ing. Wolfgang Marquardt - Energiewende - Opportunities for Systems Modelling and Optimization

Chairman of the Board of Directors Forschungszentrum Jülich GmbHForschungszentrum Jülich GmbH

Abstract

The transformation of the energy system poses not only political and socio-economic but also technical challenges. The envisioned completereplacement of nuclear and fossil energies by renewable energies is not possible with existing technological solutions. Novel concepts and technology options for decarbonisation, decentralization and digitalization
are required. Breakthroughs can only be expected if research and development broadly addresses the specific needs of a future energy system which is fully based on renewable sources. Given the complexity of the problem as well as the ambitious timeline announced by policy makers requires accelerated research processes which provide transformative knowledge and systemic solutions, which are "first time right".  Systems modeling and numerical optimization are key enablers in this respect. The lecture will introduce the ambitious goals of the Energiewende in Germany and the
resulting technological key challenges. The stabilization of the grid by appropriate design as well as reactive and proactive operational strategies will be exemplarily used to motivate the need for advanced optimization-based computational techniques and to illustrate their potential.
 
 

I³MS - Tempone Seminar

Location: AICES Seminar Room 115, 1st floor, Schinkelstr. 2, 52062 Aachen

Prof. Dr. Raul F. Tempone - A Potpourri of Results from the KAUST Uncertainty Quantification Center

King Abdullah University of Science and Technology, Kingdom of Saudi Arabia
 

Abstract

In this talk, we will present several results produced at the KAUST Strategic Research Initiative for Uncertainty Quantification.

These include, among others, contributions on Multi-level and Multi-index sampling techniques that address both direct and

inverse problems. We may also discuss efficient methods for Bayesian Inverse Problems and Optimal Experimental Design.