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Machine learning approach to QCD kinetic theory

Sergio Barrera Cabodevila, Aleksi Kurkela, Florian Lindenbauer

TL;DR

The paper addresses the bottleneck of computing collision kernels in the Effective Kinetic Theory (EKT) of QCD by replacing Monte Carlo kernel evaluations with neural-network surrogates that exploit the locality of the Boltzmann equation, allowing per-cell kernel computation with the same network. It trains two independent neural networks to learn $C_{1\leftrightarrow2}$ and $C_{2\leftrightarrow2}$ from Monte Carlo data, using CGC-inspired initial conditions and symmetry-based data reductions to build a large training set, including a mapping of $p^3 f - p^3 f_{eq}$ to $p^3 C$. The results show that the networks can reproduce 1D and 3D evolutions with energy conservation and correct thermalization trends, achieving about a $10^3$ speed-up over the full Monte Carlo evolution (with some degradation near equilibrium). This method enables practical event-by-event QCD kinetic theory simulations and phenomenological studies, supported by publicly available datasets and models.

Abstract

The effective kinetic theory (EKT) of QCD provides a possible picture of various non-equilibrium processes in heavy- and light-ion collisions. While there have been substantial advances in simulating the EKT in simple systems with enhanced symmetry, eventually, event-by-event simulations will be required for a comprehensive phenomenological modeling. As of now, these simulations are prohibitively expensive due to the numerical complexity of the Monte Carlo evaluation of the collision kernels. In this talk, we show how the evaluation of the collision kernels can be performed using neural networks paving the way to full event-by-event simulations.

Machine learning approach to QCD kinetic theory

TL;DR

The paper addresses the bottleneck of computing collision kernels in the Effective Kinetic Theory (EKT) of QCD by replacing Monte Carlo kernel evaluations with neural-network surrogates that exploit the locality of the Boltzmann equation, allowing per-cell kernel computation with the same network. It trains two independent neural networks to learn and from Monte Carlo data, using CGC-inspired initial conditions and symmetry-based data reductions to build a large training set, including a mapping of to . The results show that the networks can reproduce 1D and 3D evolutions with energy conservation and correct thermalization trends, achieving about a speed-up over the full Monte Carlo evolution (with some degradation near equilibrium). This method enables practical event-by-event QCD kinetic theory simulations and phenomenological studies, supported by publicly available datasets and models.

Abstract

The effective kinetic theory (EKT) of QCD provides a possible picture of various non-equilibrium processes in heavy- and light-ion collisions. While there have been substantial advances in simulating the EKT in simple systems with enhanced symmetry, eventually, event-by-event simulations will be required for a comprehensive phenomenological modeling. As of now, these simulations are prohibitively expensive due to the numerical complexity of the Monte Carlo evaluation of the collision kernels. In this talk, we show how the evaluation of the collision kernels can be performed using neural networks paving the way to full event-by-event simulations.

Paper Structure

This paper contains 4 sections, 3 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Training data
  3. Choosing the ANN architecture
  4. Results

Figures (2)

  • Figure 1: Number (left) and energy (right) densities time evolutions for different initial conditions in the isotropic/1D case. Solid lines with error bars correspond to the neural network predictions, while the dashed lines are computed with the Monte Carlo algorithm. Figure obtained from BarreraCabodevila:2025ogv.
  • Figure 2: Different moments of the distribution defined in Eq. \ref{['eq:momentsadim']} as a function of time for two different initial conditions. Figure obtained from BarreraCabodevila:2025ogv.