Unifying Simulation and Inference with Normalizing Flows

There have been many applications of deep neural networks to detector calibrations and a growing number of studies that propose deep generative models as automated fast detector simulators. We show that these two tasks can be unified by using maximum likelihood estimation (MLE) from conditional generative models for energy regression. Unlike direct regression techniques, the MLE approach is prior-independent and non-Gaussian resolutions can be determined from the shape of the likelihood near the maximum. Using an ATLAS-like calorimeter simulation, we demonstrate this concept in the context of calorimeter energy calibration.

SuperCalo: Calorimeter shower super-resolution

Calorimeter shower simulation is a major bottleneck in the Large Hadron Collider computational pipeline. There have been recent efforts to employ deep-generative surrogate models to overcome this challenge. However, many of best performing models have training and generation times that do not scale well to high-dimensional calorimeter showers. In this work, we introduce SuperCalo, a flow-based super-resolution model, and demonstrate that high-dimensional fine-grained calorimeter showers can be quickly upsampled from coarse-grained showers. This novel approach presents a way to reduce computational cost, memory requirements and generation time associated with fast calorimeter simulation models. Additionally, we show that the showers upsampled by SuperCalo possess a high degree of variation. This allows a large number of high-dimensional calorimeter showers to be upsampled from much fewer coarse showers with high-fidelity, which results in additional reduction in generation time.

Inductive CaloFlow

Simulating particle detector response is the single most expensive step in the Large Hadron Collider computational pipeline. Recently it was shown that normalizing flows can accelerate this process while achieving unprecedented levels of accuracy, but scaling this approach up to higher resolutions relevant for future detector upgrades leads to prohibitive memory constraints. To overcome this problem, we introduce Inductive CaloFlow (iCaloFlow), a framework for fast detector simulation based on an inductive series of normalizing flows trained on the pattern of energy depositions in pairs of consecutive calorimeter layers. We further use a teacher-student distillation to increase sampling speed without loss of expressivity. As we demonstrate with Datasets 2 and 3 of the CaloChallenge2022, iCaloFlow can realize the potential of normalizing flows in performing fast, high-fidelity simulation on detector geometries that are ~ 10 - 100 times higher granularity than previously considered.

CaloFlow for CaloChallenge Dataset 1

CaloFlow is a new and promising approach to fast calorimeter simulation based on normalizing flows. Applying CaloFlow to the photon and charged pion Geant4 showers of Dataset 1 of the Fast Calorimeter Simulation Challenge 2022, we show how it can produce high-fidelity samples with a sampling time that is several orders of magnitude faster than Geant4. We demonstrate the fidelity of the samples using calorimeter shower images, histograms of high level features, and aggregate metrics such as a classifier trained to distinguish CaloFlow from Geant4 samples.