Abstract
The different physical phenomena of particle physics and general relativity have some overlapping concepts
and mathematical formulations that make them amenable to the universal function approximation
abilities of deep neural networks (NNs) that are agnostic to the nature of the problem or the type of
analysis considered.
In Beyond the Standard Model (BSM) phenomenology, we focus on improving searches for the supersymmetry
counterpart of the muon (i.e. the “smuon”), an elusive task because of this particle’s low
expected production rate at the LHC Run 2. Past multilepton-and-missing-energy searches for smuons
have been inconclusive and, as such, have motivated the need for more in-depth event selection techniques
to improve search sensitivity.
On a different note, we consider black hole (BH) perturbation theory in general relativity. The
challenge here is to numerically solve some analytically intractable eigenvalue problems, in particular,
the perturbation equations of Kerr and Schwarzschild-Tangherlini BHs. The solutions that emerge are
quasinormal mode (QNM) frequencies that serve as templates for the BH spectroscopy of gravitational
wave signals. Specifically, to accurately determine a BH’s mass and spin using BH perturbation theory,
recent work on Kerr BH simulations has motivated the importance of overtones, i.e. QNM frequencies
with higher damping rates than the fundamental mode. Additionally, we can study the dynamics of
photon spheres of Schwarzschild-Tangherlini BHs from their QNMs, for varying dimensionality.
On a third topic conceptually related to the first (i.e. BSM phenomenology) and mathematically
related to the second (i.e. solving eigenvalue problems), we consider BSM in extra dimensions featuring
new particles whose masses are described by Kaluza-Klein spectra; that is, the eigenvalue spectra of
Laplacians in curved extra-dimensional spaces (the most interesting and least trivial of which are negatively
curved). Of particular interest is the “twisted-torus” denoted as M3 (significant in dark matter
phenomenology) and extra-dimensional spaces with properties in common with M3.
We successfully implemented NN classifiers to improve smuon searches over the existing jet-vetobased
cut-and-count and boosted decision-tree event selection approaches. This was achieved by using
a large training sample of backgrounds and signals (needed for accurate statistics), training NNs on two
signal regions (i.e., low- and high-smuon-mass regions), and optimising precision over recall. To measure
sensitivity, exclusion limits for searches in the LHC Runs 2 and 3, and the upcoming HL-LHC experiment
were obtained. At a final stage, potential gains in sensitivity were investigated in the more challenging,
highly compressed region by using a novel NN-based architecture (i.e. TabNet).
In the numerical analysis challenges of BH perturbation theory and BSM phenomenology, physicsinformed
neural networks (PINNs) were used as numerical solvers. We showed that PINNs could approximate
Kerr and Schwarzschild-Tangherlini BH QNMs with < 1% relative error, for at least the low-lying
overtone frequencies in the former case, compared to Leaver’s continued fraction method. Similary, we
used PINNs to accurately solve (generally with < 0.5% relative error) the Laplacian on twisted-periodic
spaces with aspects in common with M3, which includes the Möbius strip. Although M3 proved more
challenging to solve using PINNs, we provided recommendations for a pragmatic PINN implementation
for further consideration of this problem.
Overall, the problems considered in this thesis were each found amenable to the deep NN treatment,
with favourable performance in both classification and differential equation solving for simple setups
and enhanced performance (comparable or exceeding traditional methods) for more customised, physicsinspired
setups.