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Toward using GANs in astrophysical Monte-Carlo simulations

Ahab Isaac, Wesley Armour, Karel Adámek

TL;DR

The paper addresses the computational cost of Monte Carlo sampling in astrophysical spectra by using Generative Adversarial Networks to sample from the Maxwell-Jüttner distribution $P_ ext{MJ}(eta)$ that describes relativistic electron speeds. A GAN with a two-hidden-layer generator (400 neurons per layer) and a discriminator (40 and 20 neurons) is trained per value of $\Theta$, with the MJ distribution normalized to $[-1,1)$ to match the $\tanh$ activation. The results show that single-sample KS tests cannot distinguish generated samples from true MJ samples for several $\Theta$ values, but aggregating many samples reveals correlations due to mode collapse, and KS tests fail in that regime; Wasserstein GAN attempts did not resolve this. The work demonstrates the feasibility of neural sampling to speed up astrophysical Monte Carlo simulations but highlights challenges (mode collapse and hyperparameter handling) that require future refinement and broader training.

Abstract

Accurate modelling of spectra produced by X-ray sources requires the use of Monte-Carlo simulations. These simulations need to evaluate physical processes, such as those occurring in accretion processes around compact objects by sampling a number of different probability distributions. This is computationally time-consuming and could be sped up if replaced by neural networks. We demonstrate, on an example of the Maxwell-Jüttner distribution that describes the speed of relativistic electrons, that the generative adversarial network (GAN) is capable of statistically replicating the distribution. The average value of the Kolmogorov-Smirnov test is 0.5 for samples generated by the neural network, showing that the generated distribution cannot be distinguished from the true distribution.

Toward using GANs in astrophysical Monte-Carlo simulations

TL;DR

The paper addresses the computational cost of Monte Carlo sampling in astrophysical spectra by using Generative Adversarial Networks to sample from the Maxwell-Jüttner distribution that describes relativistic electron speeds. A GAN with a two-hidden-layer generator (400 neurons per layer) and a discriminator (40 and 20 neurons) is trained per value of , with the MJ distribution normalized to to match the activation. The results show that single-sample KS tests cannot distinguish generated samples from true MJ samples for several values, but aggregating many samples reveals correlations due to mode collapse, and KS tests fail in that regime; Wasserstein GAN attempts did not resolve this. The work demonstrates the feasibility of neural sampling to speed up astrophysical Monte Carlo simulations but highlights challenges (mode collapse and hyperparameter handling) that require future refinement and broader training.

Abstract

Accurate modelling of spectra produced by X-ray sources requires the use of Monte-Carlo simulations. These simulations need to evaluate physical processes, such as those occurring in accretion processes around compact objects by sampling a number of different probability distributions. This is computationally time-consuming and could be sped up if replaced by neural networks. We demonstrate, on an example of the Maxwell-Jüttner distribution that describes the speed of relativistic electrons, that the generative adversarial network (GAN) is capable of statistically replicating the distribution. The average value of the Kolmogorov-Smirnov test is 0.5 for samples generated by the neural network, showing that the generated distribution cannot be distinguished from the true distribution.
Paper Structure (4 sections, 1 equation, 2 figures)

This paper contains 4 sections, 1 equation, 2 figures.

Table of Contents

  1. Introduction
  2. Network and training
  3. Results
  4. Conclusions

Figures (2)

  • Figure 1: Comparison of histograms of true (blue) and generated (red) Maxwell-Jüttner distribution for different values of $\Theta$ parameter.
  • Figure 2: Visual representation of generated samples from Maxwell-Jüttner distribution with increasing value of $\Theta$. The randomness is good for lower values of $\Delta$, but for higher values of $\Theta$, we can see clear correlations.