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.

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.

The enormously successful physics program at the LHC relies heavily on the availability of copious amounts of highly accurate simulated data. However, the use of Geant4 [1-3] for full detector simulations is a major computational bottleneck and severely limits the analysis capabilities of the LHC. This is forecast to worsen significantly with future LHC upgrades and the HL-LHC [4-8]. Recently, deep generative modeling has demonstrated great potential to speed up the most computationally expensive part of detector simulations, namely calorimeter showers [8-19]. By fitting the generative model to Geant4 shower images, the generative model learns (often implicitly) the underlying distribution that the Geant4 showers are drawn from and can then sample from it quickly. Most of the current approaches [8-18] are based on GAN or VAE architectures. Very recently, in [19], we proposed a fresh alternative, dubbed CaloFlow, based on normalizing flows (for recent reviews and original references, see e.g.

We introduce CaloFlow, a fast detector simulation framework based on normalizing flows. For the first time, we demonstrate that normalizing flows can reproduce many-channel calorimeter showers with extremely high fidelity, providing a fresh alternative to computationally expensive GEANT4 simulations, as well as other state-of-the-art fast simulation frameworks based on GANs and VAEs. Besides the usual histograms of physical features and images of calorimeter showers, we introduce a new metric for judging the quality of generative modeling: the performance of a classifier trained to differentiate real from generated images. We show that GAN-generated images can be identified by the classifier with nearly 100% accuracy, while images generated from CaloFlow are better able to fool the classifier. More broadly, normalizing flows offer several advantages compared to other state-of-the-art approaches (GANs and VAEs), including: tractable likelihoods; stable and convergent training; and principled model selection. Normalizing flows also provide a bijective mapping between data and the latent space, which could have other applications beyond simulation, for example, to detector unfolding.