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| 2004 | Dr. rer. nat., University of Bonn | | 2004 - 2006 | Postdoctoral Research Fellow, Australian National University, Canberra, ACT, Australia | | 2006 - 2011 | Postdoctoral Research Fellow / Junior Research Group Leader, DFG Research Center Matheon / TU Berlin | | Since 2011 | Professor (W2), University of Bonn and Fraunhofer Institute for Algorithms and Scientific Computing (SCAI), Sankt Augustin |
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My research area is numerical mathematics with emphasis on high-dimensional problems and machine learning. On the one hand the numerical treatment of high-dimensional applications, often in the form of partial differential equations from physics, chemistry, biology, or finance, with sparse grids and low rank tensor approximations and on the other hand the application of modern methods from computational mathematics into machine learning and data mining are the focal points of my research. For high-dimensional data analysis I am investigating nonlinear dimensionality methods.
The further investigation of machine learning approaches from a numerical mathematics viewpoint will provide additional insights for these algorithms, while recent probabilistic views on numerical methods from a machine learning viewpoint will extend the understanding on that side. The analysis of big data from numerical simulations with machine learning approaches will be another focal point, for many practical applications more sophisticated data analysis approaches for the complex numerical simulation data are needed. Furthermore, recent results provide a new mathematical way to integrate domain knowledge into the data analysis, further research on this is necessary, in particular for data arising from the natural sciences and engineering.
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BMBF VAVID - Vergleichende Analyse von ingenieurrelevanten Mess- und Simulationsdaten
ITEA3/BMBF Flex4Apps – Plattform für Anwendungsflexibilität in Cyber-Physical Systems
BmWi - MathEnergy
BMBF - P3ML - Projektgekoppelter, Potentialorientierter und Praxisintegrierter Erwerb von ML Engineering Wissen
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[ 1] Jochen Garcke, Axel Kröner
Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
J. Sci. Comput. , 70: (1): 1--28
2017
DOI: 10.1007/s10915-016-0240-7[ 2] Jia Liu, Dustin Feld, Yong Xue, Jochen Garcke, Thomas Soddemann
Multi-Core Processors and Graphics Processing Unit Accelerators for Parallel Retrieval of Aerosol Optical Depth from Satellite Data: Implementation, Performance and Energy Efficiency
IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 8: (5): 2306-2317
2015
DOI: 10.1109/JSTARS.2015.2438893[ 3] Olivier Bokanowski, Jochen Garcke, Michael Griebel, Irene Klompmaker
An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
J. Sci. Comput. , 55: (3): 575--605
2013
DOI: 10.1007/s10915-012-9648-x[ 4] Gregory Beylkin, Jochen Garcke, Martin J. Mohlenkamp
Multivariate regression and machine learning with sums of separable functions
SIAM J. Sci. Comput. , 31: (3): 1840--1857
2009
DOI: 10.1137/070710524[ 5] Markus Hegland, Jochen Garcke, Vivien Challis
The combination technique and some generalisations
Linear Algebra Appl. , 420: (2-3): 249--275
2007
DOI: 10.1016/j.laa.2006.07.014[ 6] J. Garcke, M. Griebel, M. Thess
Data mining with sparse grids
Computing , 67: (3): 225--253
2001
DOI: 10.1007/s006070170007[ 7] Jochen Garcke, Michael Griebel
On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique
J. Comput. Phys. , 165: (2): 694--716
2000
DOI: 10.1006/jcph.2000.6627[ 8] Jochen Garcke, Thomas Vanck
Importance Weighted Inductive Transfer Learning for Regression
Proceedings of ECMLPKDD 2014, Nancy
of Lecture Notes in Computer Science : 466-481
Publisher: Springer Berlin Heidelberg
2014
ISBN: 978-3-662-44847-2
DOI: 10.1007/978-3-662-44848-9_30[ 9] Alexander Paprotny, Jochen Garcke
On a Connection between Maximum Variance Unfolding, Shortest Path Problems and IsoMap
15th International Conference on Artificial Intelligence and Statistics (AISTATS 2012)
2012[ 10] S. Börm, J. Garcke
Approximating Gaussian Processes with H^2-matrices
Proceedings of 18th European Conference on Machine Learning, Warsaw, Poland, September 17-21, 2007. ECML 2007
4701 : 42--53
2007
DOI: 10.1007/978-3-540-74958-5_8 |
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