Aziz Lakhal

My name is Aziz Lakhal, I began my PhD studies in July 2024 within the “Mathematical Methods in Computer Science” group. My research interests lie at the intersection of optimal transport, high-dimensional probability and (causal) artificial intelligence. My research is driven by the idea of leveraging the geometric structure of probability measures to better understand and develop AI algorithms. Accordingly, I investigate the theoretical and numerical implications of these structural assumptions. For example, we investigated during our first project, how the geometric interplay of linear functional constraints affects the convergence of generalised iterative fitting procedures. Yet, in another project we aim to construct a sensible notion of transport distance between causally structured probability measures with a particular focus on graph neural networks. Overall, I thrive on exploring modern and exciting problems from AI through the lens of well-established mathematical disciplines such as functional analysis, probability theory and convex optimisation. My long-term goal is to broaden the capabilities of AI in the natural sciences, enabling breakthroughs in fields like computational biology and personalised medicine