Deep Generative Models for Ultra-High Granularity Particle Physics Detector Simulation: A Voyage From Emulation to Extrapolation

Simulating ultra-high-granularity detector responses in Particle Physics represents a critical yet computationally demanding task. This thesis aims to overcome this challenge for the Pixel Vertex Detector (PXD) at the Belle II experiment, which features over 7.5M pixel channels-the highest spatial resolution detector simulation dataset ever analysed with generative models. This thesis starts off by a comprehensive and taxonomic review on generative models for simulating detector signatures. Then, it presents the Intra-Event Aware Generative Adversarial Network (IEA-GAN), a new geometry-aware generative model that introduces a relational attentive reasoning and Self-Supervised Learning to approximate an "event" in the detector. This study underscores the importance of intra-event correlation for downstream physics analyses. Building upon this, the work drifts towards a more generic approach and presents YonedaVAE, a Category Theory-inspired generative model that tackles the open problem of Out-of-Distribution (OOD) simulation. YonedaVAE introduces a learnable Yoneda embedding to capture the entirety of an event based on its sensor relationships, formulating a Category theoretical language for intra-event relational reasoning. This is complemented by introducing a Self-Supervised learnable prior for VAEs and an Adaptive Top-q sampling mechanism, enabling the model to sample point clouds with variable intra-category cardinality in a zero-shot manner. Variable Intra-event cardinality has not been approached before and is vital for simulating irregular detector geometries. Trained on an early experiment data, YonedaVAE can reach a reasonable OOD simulation precision of a later experiment with almost double luminosity. This study introduces, for the first time, the results of using deep generative models for ultra-high granularity detector simulation in Particle Physics.