Unlocking the Full Potential of Data: From Applied Analysis and Optimisation to Applications
Recent and rapid breakthroughs in contemporary biology, climate science, and data science have unveiled a spectrum of intricate mathematical challenges which can be tackled through the fusion of applied and numerical analysis, as well as optimisation. In this talk, I will begin by delving into a class of interacting particle models with anisotropic interaction forces and their corresponding continuum limit. These models find their inspiration in the simulation of fingerprint patterns, which play a critical role in databases in forensic science and biometric applications. I will showcase our recent findings, including the development of a mean-field optimal control algorithm to tackle an inverse problem arising in parameter identification. Transitioning from interaction-focused models to the realm of transport networks, I will introduce an optimization approach tailored for a unique coupling of differential equations that arises in the context of biological network formation. Additionally, I will provide insights into my recent research in data science, encompassing topics such as image segmentation, non-convex optimisation algorithms for machine learning, Wasserstein Generative Adversarial Networks (WGANs), score-based diffusion models and semi-supervised learning techniques.
Lisa Kreusser is an Assistant Professor in Applied Mathematics and a Fellow of the Institute of Mathematical Innovation at the University of Bath since 2021. Prior to that, she completed her PhD in mathematics as a Vice-Chancellor’s Scholar at the University of Cambridge (2015-2019) and was a Junior Research Fellow at Magdalene College, University of Cambridge (2019-2021). Her research lies at the intersection of mathematical modelling, applied & numerical analysis, optimisation as well as data science and machine learning with diverse applications, particularly in biology and climate science. Recent awards include the Reinhart Heinrich Award of the European Society for Mathematical and Theoretical Biology, the Smith-Knight & Rayleigh-Knight Prize for outstanding research in Mathematics at the University of Cambridge and her selection as a Rising Star in Computational & Data Sciences by Texas’s Oden Institute.