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

## TL;DR

This paper explores deep generative models for physics event simulation, demonstrating that a density buffer improves the accuracy and speed of event generation, with applications in density estimation, anomaly detection, and importance sampling.

## Contribution

It introduces a density information buffer for VAEs that significantly enhances event generation accuracy and efficiency in physics simulations.

## Key findings

- Standard GANs and VAEs struggle to learn distributions precisely.
- Buffering density information enables accurate, fast event sampling.
- Applications include density estimation, anomaly detection, and phase space integration.

## 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 $e^+e^-\to Z \to l^+l^-$ and $p p \to t\bar{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.