Dr. Tizian Wenzel

Within deep learning, my research focuses on feature learning and alignment phenomena, which are central to understanding how and why modern deep learning methods—most prominently neural networks—work. For several of these questions, kernel methods provide powerful analytical tools, for instance through the neural tangent kernel.

In the area of kernel-based approximation, I work on greedy kernel algorithms, where I have introduced novel classes of greedy methods and established strong, and in some cases optimal, convergence results. In addition, I have developed data-adapted and deep kernel methods—such as two-layered kernels—that are capable of outperforming standard kernel approaches in machine-learning tasks where feature learning is essential. More recently, I derived sharp direct and inverse results for kernel interpolation with finitely smooth kernels, enabling a systematic theory for understanding (asymptotically) optimal kernel shape-parameter.

My work in numerical analysis combines reduced basis methods, kernel-based techniques, and machine learning approaches, leading, for example, to certified surrogate models. Further contributions focus on transferring the developed theoretical tools—particularly kernel-based methods—to the analysis and numerical solution of partial differential equations.

Throughout my research, potential applications have consistently been kept in focus. Successful applications include surrogate modeling of the human spine, data-driven prediction of turbulent flows, surrogate models for surface kinetics in reactor simulations, and the development of local smoothness detection algorithms.