### **MIT Distinguished Seminar Series in**** Computational Science and Engineering**

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

**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 *

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.