  Generation of simulated detector response to collision products is crucial to
data analysis in particle physics, but computationally very expensive. One
subdetector, the calorimeter, dominates the computational time due to the high
granularity of its cells and complexity of the interactions. Generative models
can provide more rapid sample production, but currently require significant
effort to optimize performance for specific detector geometries, often
requiring many models to describe the varying cell sizes and arrangements,
without the ability to generalize to other geometries. We develop a
$\textit{geometry-aware}$ autoregressive model, which learns how the
calorimeter response varies with geometry, and is capable of generating
simulated responses to unseen geometries without additional training. The
geometry-aware model outperforms a baseline unaware model by over $50\%$ in
several metrics such as the Wasserstein distance between the generated and the
true distributions of key quantities which summarize the simulated response. A
single geometry-aware model could replace the hundreds of generative models
currently designed for calorimeter simulation by physicists analyzing data
collected at the Large Hadron Collider. This proof-of-concept study motivates
the design of a foundational model that will be a crucial tool for the study of
future detectors, dramatically reducing the large upfront investment usually
needed to develop generative calorimeter models.

Instrumentation and Detectors;Machine Learning;High Energy Physics - Experiment;High Energy Physics - Phenomenology;Data Analysis, Statistics and Probability