We propose and demonstrate the use of a Model-Assisted Generative Adversarial Network to produce simulated images that accurately match true images through the variation of underlying model parameters that describe the image generation process. The generator learns the parameter values that give images that best match the true images. Two case studies show the excellent agreement between the generated best match parameters and the true parameters. The best match parameter values that produce the most accurate simulated images can be extracted and used to re-tune the default simulation to minimise any bias when applying image recognition techniques to simulated and true images. In the case of a real-world experiment, the true data is replaced by experimental data with unknown true parameter values. The Model-Assisted Generative Adversarial Network uses a convolutional neural network to emulate the simulation for all parameter values that, when trained, can be used as a conditional generator for fast image production.
Several domains could benefit from the approach we present in this paper, but its best application is probably in physical experiments @cite_15 . Although GANs have not been broadly used in real-world scientific experiments, some promising work has been done on the production of @math images @cite_21 , GAN-based calorimeter simulations @cite_6 @cite_18 , and in the production of galaxy images @cite_0 . Contrary to the above studies, the GAN that we present in this paper could be, for instance, used to learn the optimal parameters needed by a Monte Carlo simulation for mimicking detector images in physics experiments.
@cite_18 @cite_21 @cite_6 @cite_0 @cite_15
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Detectors of High Energy Physics experiments, such as the ATLAS dectector [1] at the Large Hadron Collider [2], serve as cameras that take pictures of the particles produced in the collision events. One of the key detector technologies used for measuring the energy of particles are calorimeters. Particles will lose their energy in a cascade (called a shower) of electromagnetic and hadronic interactions with a dense absorbing material. The number of the particles produced in this showering process is subsequently measured across the sampling layers of the calorimeter. The deposition of energy in the calorimeter due to a developing shower is a stochastic process that can not be described from first principles and rather relies on a precise simulation of the detector response. It requires the modeling of particles interactions with matter at the microscopic level as implemented using the Geant4 toolkit [3]. This simulation process is inherently slow and thus presents a bottleneck in the ATLAS simulation pipeline [4]. The current work addresses this limitation. To meet the growing analysis demands, ATLAS already relies strongly on fast calorimeter simulation techniques based on thousands of individual parametrizations of the calorimeter response [5]. The algorithms currently employed for physics analyses by the ATLAS collaboration achieve a significant speedup over the full simulation of the detector response at the cost of accuracy. Current developments [6] [7] aim at improving the modeling of taus, jet-substructure-based boosted objects or wrongly identified objects in the calorimeter and will benefit from an improved detector description following data taking and a more detailed forward calorimeter geometry. Deep Learning techniques have been improving state of the art results in various science areas such as: astrophysics [8], cosmology [9] and medical imaging [10]. These techniques are able to describe complex data structures and scale well with highdimensionality problems. Generative models are powerful deep learning algorithms to map complex distributions into a lower dimensional space, to generate samples of higher dimensionality and to approximate the underlying probability densities. Among the most promising approaches are Variational Auto-Encoders [11] [12] and Generative Adversarial Networks [13]. In this context, the talk presents the first application of such models to the fast simulation of the calorimeter response in the ATLAS detector. This work [14] demonstrates the feasibility of using such algorithms for large scale high energy physics experiments in the future, and opens the possibility to complement current techniques. High Energy Physics (HEP) simulations are traditionally based on the Monte Carlo approach and generally rely on time consuming calculations. The present work investigates the use of Generative Adversarial Networks (GANs) as a fast alternative. Our approach treats the energy deposited by a particle inside a calorimeter detector as a three-dimensional image. True three-dimensional convolutions can be employed to capture the spatio-temporal correlation of shower energy depositions. Three-dimensional images are generated, conditioned on the energy of the incoming particle and validated against Monte Carlo simulation. The results show an agreement to full Mote Carlo simulations well within 10 thus proving that GAN can be used as a fast alternative for simulation of HEP detector response. In this paper, we propose the Self-Attention Generative Adversarial Network (SAGAN) which allows attention-driven, long-range dependency modeling for image generation tasks. Traditional convolutional GANs generate high-resolution details as a function of only spatially local points in lower-resolution feature maps. In SAGAN, details can be generated using cues from all feature locations. Moreover, the discriminator can check that highly detailed features in distant portions of the image are consistent with each other. Furthermore, recent work has shown that generator conditioning affects GAN performance. Leveraging this insight, we apply spectral normalization to the GAN generator and find that this improves training dynamics. The proposed SAGAN achieves the state-of-the-art results, boosting the best published Inception score from 36.8 to 52.52 and reducing Frechet Inception distance from 27.62 to 18.65 on the challenging ImageNet dataset. Visualization of the attention layers shows that the generator leverages neighborhoods that correspond to object shapes rather than local regions of fixed shape. We provide a bridge between generative modeling in the Machine Learning community and simulated physical processes in high energy particle physics by applying a novel Generative Adversarial Network (GAN) architecture to the production of jet images—2D representations of energy depositions from particles interacting with a calorimeter. We propose a simple architecture, the Location-Aware Generative Adversarial Network, that learns to produce realistic radiation patterns from simulated high energy particle collisions. The pixel intensities of GAN-generated images faithfully span over many orders of magnitude and exhibit the desired low-dimensional physical properties (i.e., jet mass, n-subjettiness, etc.). We shed light on limitations, and provide a novel empirical validation of image quality and validity of GAN-produced simulations of the natural world. This work provides a base for further explorations of GANs for use in faster simulation in high energy particle physics.