Dr Daniel Platt
Mentor
King's College London
Daniel is a postdoc at King's College London working on differential geometry. He obtained my PhD from Imperial College London for his thesis on gauge theory in dimension 7 on problems that are motivated by string theory. Because of this, he is interested in big datasets of Calabi-Yau manifolds. Apart from this, Lie groups and group actions are important for the kind of geometry that he studies and he is also interested in applications of differential geometry to group invariant machine learning.
Project
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 [1]. 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 [2].
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.
References
[1] Group invariant machine learning by fundamental domain projections, Benjamin Aslan, Daniel Platt, David Sheard, arXiv 2022
[2] Calabi-Yau data