Prof. Dr. Jochen Garcke

Biography

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. Academic Career 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

Research Interest

Research Area J One focus of my research area is scientific computing with emphasis on high-dimensional problems. This includes 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 product approaches.