Deep Generative Models for Detector Signature Simulation: An Analytical Taxonomy

In modern collider experiments, the quest to explore fundamental interactions between elementary particles has reached unparalleled levels of precision. Signatures from particle physics detectors are low-level objects encoding the physics of collisions. The complete simulation of them in a detector is a memory and storage-intensive task. To address this computational bottleneck in particle physics, "Fast Simulation" has been introduced and refined over the years. The field has seen a surge in interest in surrogate modeling the detector simulation, fueled by the advancements in deep generative models. These models aim to generate responses that are statistically identical to the observed data. In this paper, we conduct a comprehensive and exhaustive taxonomic review of the existing literature on the simulation of detector signatures from both methodological and application-wise perspectives. Initially, we formulate the problem of detector signature simulation and discuss its different variations that can be unified. Next, we classify the state-of-the-art methods into four distinct categories based on their underlying model architectures, summarizing their respective generation strategies. We then identify and discuss three key application areas. Finally, we shed light on the challenges and opportunities that lie ahead in detector signature simulation, setting the stage for future research and development.

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.

New directions for surrogate models and differentiable programming for High Energy Physics detector simulation

The computational cost for high energy physics detector simulation in future experimental facilities is going to exceed the current available resources. To overcome this challenge, new ideas on surrogate models using machine learning methods are being explored to replace computationally expensive components. Additionally, differentiable programming has been proposed as a complementary approach, providing controllable and scalable simulation routines. In this document, new and ongoing efforts for surrogate models and differential programming applied to detector simulation are discussed in the context of the 2021 Particle Physics Community Planning Exercise (`Snowmass').

CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows

Recently, we introduced CaloFlow, a high-fidelity generative model for GEANT4 calorimeter shower emulation based on normalizing flows. Here, we present CaloFlow v2, an improvement on our original framework that speeds up shower generation by a further factor of 500 relative to the original. The improvement is based on a technique called Probability Density Distillation, originally developed for speech synthesis in the ML literature, and which we develop further by introducing a set of powerful new loss terms. We demonstrate that CaloFlow v2 preserves the same high fidelity of the original using qualitative (average images, histograms of high level features) and quantitative (classifier metric between GEANT4 and generated samples) measures. The result is a generative model for calorimeter showers that matches the state-of-the-art in speed (a factor of $10^4$ faster than GEANT4) and greatly surpasses the previous state-of-the-art in fidelity.

CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows

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 100% accuracy, while images generated from CaloFlow are able to fool the classifier much of the time. 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.

i-flow: High-dimensional Integration and Sampling with Normalizing Flows

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijective mappings between two distributions. i-flow can also be used to sample random points according to complicated distributions in high dimensions. We compare i-flow to other algorithms for high-dimensional numerical integration and show that i-flow outperforms them for high dimensional correlated integrals.