A Search for Non-Resonant $HH\rightarrow4b$ at $\sqrt{s} = 13$ TeV with the ATLAS detector -- or -- $2b$, and then another $2b$... now that's the thesis question.

The Standard Model (SM) characterizes the fundamental building blocks of nature, with its experimental characterization culminating with the discovery of the Higgs boson a decade ago. While subsequent Higgs measurements have thus far confirmed the SM predictions, a critical test for our understanding of electroweak symmetry breaking is to study the shape of the Higgs potential by measuring the Higgs self-coupling, which can be probed by searching for events with two Higgs bosons ($HH$). This thesis presents a search for $HH$ production with each Higgs subsequently decaying into two $b$-quarks. The extremely small predicted $HH$ signal, coupled with a complex background that cannot be simulated from first principles, makes this analysis an ideal test bed for machine learning applications. This thesis details both the optimization of the $HH\rightarrow4b$ analysis, and the development and validation of ML-based approaches for background estimation with a neural reweighting method and a novel hierarchical interpolation model with normalizing flows and Gaussian Processes. The $HH\rightarrow4b$ analysis sets an observed (expected) upper limit on the $HH$ SM cross-section of 5.4 (8.1), a 30% improvement on the previous analysis strategy. We additionally constrain the Higgs self-coupling in the $\kappa$ framework with observed (expected) limits of [-3.9, 11.1] ( [-4.6, 10.8] ). Furthermore, as the identification of $b$-quark jets is crucial for $HH$ physics searches, this thesis also contributes to the development of $b$-jet identification algorithms building on recent advancements in machine learning. Studies optimizing a Recurrent Neural Network, RNNIP, culminated in the recommended DL1r ATLAS Run 2 tagger, and a forward-looking Deep Sets algorithm, DIPS, provides a strong baseline for future b-tagging optimizations.