I am interested in the mathematical foundations of deep learning. This includes stochastic optimization algorithms (speed of convergence, implicit bias), approximation theory (in particular depth separation phenomena) and uses of deep learning in scientific computing (e.g. solving partial differential equations). The techniques involved in my research often involve stochastic processes, statistical learning theory, functional analysis, partial differential equations and measure theory.
I also maintain an interest in applied analysis, in particular geometric variational problems and their application in materials science.
Education & Training
- PhD, Durham University, UK