  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.
