Events

MIT Distinguished Seminar Series in Computational Science and Engineering

Thursday, May 12th | 12:00 PM* | 37-212

Kernel Approximations for Surrogate Modelling in Simulation Science
Bernard Haasdonk
Professor for Numerical Mathematics, University of Stuttgart
Institute of Applied Analysis and Numerical Simulation

Data-based approaches are gaining increasing attention for generating or improving simulation models in CSE. Application settings comprise modelling from data, i.e. measurements are given, and we aim to find a model, that can be used for simulation, or approximative surrogate modelling, where a model is given and a cheap surrogate model is constructed based on simulation data of the former.

In this presentation I focus on kernel methods for generating such models. These powerful techniques have proven to be successful in various applications in data-science such as pattern recognition, machine learning, bioinformatics, etc. In addition to relevant applicability, they also enable elegant mathematical analysis in so called reproducing kernel Hilbert spaces (RKHS).

In the context of simulation models, kernel methods can be used for sparse vectorial function approximation, for example by vectorial support vector regression or the vectorial kernel orthogonal greedy algorithm (VKOGA). For the VKOGA theoretical analysis can be given in terms of local optimality and convergence rates [2]. The resulting approximants allow efficient complexity reduction in projection-based model order reduction [1] or in multiscale problems as demonstrated on applications from biomechanics and porous media flow [3].

References:

[1] Wirtz, D. & Haasdonk, B.: Efficient a-posteriori error estimation for
nonlinear kernel-based reduced systems, Systems and Control Letters,
2012, 61, 203 - 211.

[2] Wirtz, D. & Haasdonk, B.: An Improved Vectorial Kernel Orthogonal Greedy Algorithm,
Dolomites Research Notes on Approximation, 2013, 6, 83-100.

[3] Wirtz, D.; Karajan, N. & Haasdonk, B.: Surrogate Modelling of multiscale models using
kernel methods, International Journal of Numerical Methods in Engineering,
2015, 101, 1-28.

*Lunch provided at 11:45 AM.