Under the supervision of Prof. Markus Bachmayr, my current work focuses on the approximation of high-dimensional partial differential equations using low-rank techniques and neural networks. My research centers on
the development of nonlinear approximation spaces, including neural networks, adaptive meshes, and free-knot B-splines;
the construction of numerical schemes for solving partial differential equations within these spaces;
the analysis of stability, convergence, and approximation properties of the resulting methods.