Event Generation and Statistical Sampling for Physics with Deep Generative Models and a Density Information Buffer

Abstract

We present a study for the generation of events from a physical process with deep generative models. The simulation of physical processes requires not only the production of physical events, but also to ensure these events occur with the correct frequencies. We investigate the feasibility of learning the event generation and the frequency of occurrence with Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs) to produce events like Monte Carlo generators. We study three processes: a simple two-body decay, the processes e + e − → Z → l + l − and pp → t t including the decay of the top quarks and a simulation of the detector response. We find that the tested GAN architectures and the standard VAE are not able to learn the distributions precisely. By buffering density information of encoded Monte Carlo events given the encoder of a VAE we are able to construct a prior for the sampling of new events from the decoder that yields distributions that are in very good agreement with real Monte Carlo events and are generated several orders of magnitude faster. Applications of this work include generic density estimation and sampling, targeted event generation via a principal component analysis of encoded ground truth data, anomaly detection and more efficient importance sampling, e.g. for the phase space integration of matrix elements in quantum field theories.

Variational Autoencoders for Jet Simulation

“…We begin by showing a linear interpolation of QCD and W boson jets in Figures 12 and 14 and the difference between the two classes of images in Figure 13. Each column represents a different latent space value (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) in descending order.…”

Differentiable Strong Lensing: Uniting Gravity and Neural Nets through Differentiable Probabilistic Programming

“…The assumed prior can drag z into unrealistic regions of parameter space far from the location preferred by the likelihood, where the corresponding decoded image µ d (z) does not look like a galaxy. A variety of methods have been proposed to address this problem, including constructing simple priors using q φ (z) [83,94], fitting q φ (z) with a second VAE after training the primary one [93], or using normalizing flows [95][96][97][98]. Here we follow the simpler approach of creating a weakly-informative prior for z by fitting a multivariate normal distribution to the set of encoded means of the training data {µ e x (i) } N i=1 and rescaling its covariance matrix by a factor of 9.…”

Uncertainties associated with GAN-generated datasets in high energy physics

“…For example, the usage of GANs to only perform detector/calorimeter simulation was explored in [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The use of GANs for simulating the underlying hard process was considered in [22][23][24], while the use of GANs for pileup description was explored in [25,26]. Recent works have also explored the idea of replacing the entire reconstructed-event generation pipeline with a GAN [21,22,25,[27][28][29][30].…”

“…The use of GANs for simulating the underlying hard process was considered in [22][23][24], while the use of GANs for pileup description was explored in [25,26]. Recent works have also explored the idea of replacing the entire reconstructed-event generation pipeline with a GAN [21,22,25,[27][28][29][30]. Each of these applications of GANs would differ in the nature of the training data used.…”