Precision measurements and new physics searches at the Large Hadron Collider
require efficient simulations of particle propagation and interactions within
the detectors. The most computationally expensive simulations involve
calorimeter showers. Advances in deep generative modelling - particularly in
the realm of high-dimensional data - have opened the possibility of generating
realistic calorimeter showers orders of magnitude more quickly than
physics-based simulation. However, the high-dimensional representation of
showers belies the relative simplicity and structure of the underlying physical
laws. This phenomenon is yet another example of the manifold hypothesis from
machine learning, which states that high-dimensional data is supported on
low-dimensional manifolds. We thus propose modelling calorimeter showers first
by learning their manifold structure, and then estimating the density of data
across this manifold. Learning manifold structure reduces the dimensionality of
the data, which enables fast training and generation when compared with
competing methods.Comment: Accepted to the Machine Learning and the Physical Sciences Workshop
at NeurIPS 202