Dr Benjamin Aslan
University College London
Benjamin is a recent PhD graduate from University College London in differential geometry. His research aims to understand higher dimensional geometric structures, that are models for spacetime in string theory, by the lower-dimensional objects it contains. He is also interested in applications of geometry to equivariant and invariant machine learning.
Group invariant machine learning for Calabi-Yau polyhedra
There are many group invariant machine learning models, i.e. learnable functions that give the same output if the input is acted on by a group. One novel approach is using fundamental domain projections - an approach which is particularly useful if the group which acts is very large . There are many large string theory datasets with large symmetry groups, which make good benchmarks for group invariant machine learning models. One such example is the Kreuzer-Skarke dataset of Calabi-Yau three-folds coming from reflexive polyhedra and their Hodge numbers .
In this project, we will apply invariant machine learning via fundamental domain projections to the Kreuzer-Skarke dataset and compare this with other group invariant machine learning techniques (e.g. data augmentation and deep sets), as well models that are not group invariant.
 Group invariant machine learning by fundamental domain projections, Benjamin Aslan, Daniel Platt, David Sheard, arXiv 2022
 Calabi-Yau data