Machine Learning techniques are not only highly efficient in getting more insights from particle physics or astrophysical experiments but also to deepen our understanding in theoretical particle physics. In this lecture I shall focus on one example, namely how we can use neural networks to approximate the metrics of extra-dimensional compact spaces, in particular so-called Calabi-Yau manifolds. I discuss how these solutions of Einstein's equations can be obtained by optimising appropriate energy functionals in an unsupervised way. I will discuss how this ML approach is suitable for generalisation to search for other types of metrics and how geometric quantities can be readily obtained using auto-differentiation.
This is based on arXiv:2012.04656 and arXiv:2211.12520 where the code base of our associated software package CYJAX can be found at https://github.com/ml4physics/cyjax and the documentation is available here https://cyjax.readthedocs.io/en/latest/.
This event is part of a series of lectures and tutorials on data science topics hosted by the Platform for Challenges in Data Science in the excellence cluster "Quantum Universe" between DESY and Universität Hamburg. It is intended specifically for the PhD students in the cluster but younger and more senior members are of course also welcome.
Gregor Kasieczka, Matthias Schröder