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Generative modeling - Electromagnetic shower of a calorimeter - - PowerPoint PPT Presentation

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Generative modeling - Electromagnetic shower of a calorimeter Paul KLEIN 24 th of April 2017 Issue : Simulations (Geant4 Package) are time consuming and CPU intensive REAL LIFE SIMULATION VS ~ O(10 9 ) events/year ~ O(0,1) event/min ~

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Generative modeling

  • Electromagnetic shower of a

calorimeter

Paul KLEIN

24th of April 2017

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Issue : Simulations (Geant4 Package) are time consuming and CPU intensive

REAL LIFE ~ O(109) events/year ~ O(1000) events/min

VS

SIMULATION ~ O(0,1) event/min

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1) Specifications, Dataset, Simplification of the problem 2) Generative Adversarial Networks (GAN) 3) A GAN example : Jupyter Notebook 4) Some results : comparisons between Real/Generated simulations 5) Work in progress

SECTIONS

24th of April 2017 SystML Meeting

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1) Specifications, Dataset

EM shower in the Electromagnetic Calorimeter

The calorimeter is represented as the brown . area on the scheme → meas asure res part article energ rgy ( energy ) deposits in the cell of the calorimeter

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1) Specifications, Dataset

CONTEXT : Measurements in the Calorimeter

The calorimeter is represented as the brown . area on the scheme → meas asure res part article energ rgy ( energy ) deposits in the cell of the calorimeter

Structure of the barrel electromagnetic calorimeter

Direction of the particle

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1) Specifications, Dataset

Simulation of EM showers : Position of the problem

1 incident particle → 109 particles in the shower → have to generate 10*109 variables in total in the Simulation HUGE COMPUTATIONS ! USE GANs to generate fastly EM showers (no scientific expertise, inexpensive to run once they have been trained)

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1) Specifications, Dataset

CONTEXT :Simulation Dataset

  • Monte-Carlo data (MC)
  • Single-photon Particle Gun
  • ~ 44K events
  • For each event, we have the energy per cell of the calorimeter
  • We only focus on a cluster of 89 cells of the calorimeter for each event
  • Select a calorimeter region to avoid edge effects

TO SUM UP, we have 89 floats for each event corresponding to the simulated energy deposits in the cluster

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2) Generative Adversarial Networks (GAN)

z ~ {N(0,1)}m

Architecture of a GAN

ŝ = G(z) s Attached label -1 Attached label 1

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2) Generative Adversarial Networks (GAN)

How could we train a GAN ?

Training a GAN is really based on the idea that we . alternatively train the Discriminator and the Generator Train the Discriminator Classic BACKPROPAGATION Train the Generator ? Consider the network {Generator + Discriminator}, and freeze Discriminator weights

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2) Generative Adversarial Networks (GAN)

Choice of the loss : Wasserstein distance

Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein GAN / arXiv:1701,07875v1 [stat,ML]

Use Wasserstein distance to calculate the loss instead of Jensen- Shannon or Kullback Leibler divergence Discriminator will have a continuous and almost everywhere differentiable wasserstein distance.

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3) A GAN Example : Jupyter Notebook

Formal WGAN procedure

Discriminator training Generator training

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4) Comparison between simulated and generated data

Reminder about calorimeter geometry

Calorimeter is organised in 4 layers. Each of them has a special geometry

  • f cell.

1) Pre-sampler 2) Strip 3) Middle 4) Back

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4) Comparison between simulated and generated data

Mean cells intensities (Middle)

REAL DATA GENERATED DATA

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4) Comparison between simulated and generated data

5 10 15 20 1

True averaged Pixels intensities - Strip

101 102 103 5 10 15 20 1

Generated averaged Pixels intensities - Strip

101 102 103

Mean cells intensities (Strip)

REAL DATA GENERATED DATA

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4) Comparison between simulated and generated data

Mean cells intensities (Back)

REAL DATA GENERATED DATA

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4) Comparison between simulated and generated data

Mean cells intensities (Pre-Sampler)

REAL DATA GENERATED DATA

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4) Comparison between simulated and generated data

Averaged Eta per layer

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4) Comparison between simulated and generated data

Averaged Phi per layer

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4) Comparison between simulated and generated data

RMS (for eta) – per layer

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4) Comparison between simulated and generated data

Total Energy per event

Here we « enforced » the discriminator to learn several parameters such as mean energy of the event

All histograms have been normed

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4) Comparison between simulated and generated data

Total Energy per event

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5) Work in progress

  • Conditional GAN (energy as input → generate an EM shower)
  • Really simple architecture to generate those samples (only Dense layers)

→ Use convolutions, see the problem as a 3D image →use a hierarchical structure to build the GAN, based on the successive

layers of he calorimeter

  • Modify the loss (Enhanced WGAN)

Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky et all / arXiv:1704,00028v1 [cs.LG]

  • Quantify in a mathematical way distances between distributions
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APPENDIX

RMS Formula

, where wi = e_i xi = eta_i