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On model emulation and closure tests for 3+1D relativistic heavy-ion collisions

Hendrik Roch, Syed Afrid Jahan, Chun Shen

TL;DR

The paper tackles the challenge of extracting physics from expensive (3+1)D relativistic heavy-ion collision simulations by systematically comparing Gaussian Process emulators (PCGP, PCSK, and Scikit GP) within a Bayesian calibration framework. It introduces PCA-based reductions for high-dimensional outputs and functional inputs, and evaluates how training choices, data transformations, and active learning affect emulator accuracy and posterior inferences. Closure tests show that PCGP and PCSK yield sharply peaked posteriors near the true parameters with smaller information-loss $\Delta$ than Scikit GP, and that active learning significantly reduces emulator uncertainty in the physically relevant posterior region. The study provides practical guidance for emulator-driven Bayesian inference in heavy-ion physics, including recommendations on active-learning points, data transformations, and functional-parameter handling, with open-source code to enable replication.

Abstract

In nuclear and particle physics, reconciling sophisticated simulations with experimental data is vital for understanding complex systems like the Quark Gluon Plasma (QGP) generated in heavy-ion collisions. However, computational demands pose challenges, motivating using Gaussian Process emulators for efficient parameter extraction via Bayesian calibration. We conduct a comparative analysis of Gaussian Process emulators in heavy-ion physics to identify the most adept emulator for parameter extraction with minimal uncertainty. Our study contributes to advancing computational techniques in heavy-ion physics, enhancing our ability to interpret experimental data and understand QGP properties.

On model emulation and closure tests for 3+1D relativistic heavy-ion collisions

TL;DR

The paper tackles the challenge of extracting physics from expensive (3+1)D relativistic heavy-ion collision simulations by systematically comparing Gaussian Process emulators (PCGP, PCSK, and Scikit GP) within a Bayesian calibration framework. It introduces PCA-based reductions for high-dimensional outputs and functional inputs, and evaluates how training choices, data transformations, and active learning affect emulator accuracy and posterior inferences. Closure tests show that PCGP and PCSK yield sharply peaked posteriors near the true parameters with smaller information-loss than Scikit GP, and that active learning significantly reduces emulator uncertainty in the physically relevant posterior region. The study provides practical guidance for emulator-driven Bayesian inference in heavy-ion physics, including recommendations on active-learning points, data transformations, and functional-parameter handling, with open-source code to enable replication.

Abstract

In nuclear and particle physics, reconciling sophisticated simulations with experimental data is vital for understanding complex systems like the Quark Gluon Plasma (QGP) generated in heavy-ion collisions. However, computational demands pose challenges, motivating using Gaussian Process emulators for efficient parameter extraction via Bayesian calibration. We conduct a comparative analysis of Gaussian Process emulators in heavy-ion physics to identify the most adept emulator for parameter extraction with minimal uncertainty. Our study contributes to advancing computational techniques in heavy-ion physics, enhancing our ability to interpret experimental data and understand QGP properties.
Paper Structure (19 sections, 13 equations, 13 figures, 4 tables)

This paper contains 19 sections, 13 equations, 13 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Bayesian Inference
  3. Gaussian Process Emulators
  4. GP Emulator Comparison
  5. Training Setup
  6. PCA Transformation for Functional Model Parameters
  7. Test Metrics for Model Emulators
  8. Emulator Validation
  9. Training Size Dependence for Model Emulation Performance
  10. Benchmark Emulation Performance
  11. Logarithmic transformation to training datasets
  12. PCA Transformation to Functional Model Parameters
  13. Active Learning Approach
  14. Closure Tests
  15. MCMC Setups
  16. ...and 4 more sections

Figures (13)

  • Figure 1: (Color Online) The averaged RMS errors for emulators $\mathcal{E}$ (left) and the quality of uncertainty estimation measure $\mathcal{H}$ (right) for three different example observables. The top row shows the first observable from the 7.7 GeV $\langle p_{\rm T}\rangle$ dataset, and the middle row is taken from the first observable in the 200 GeV ${\rm d}N/{\rm d}y$ dataset. The bottom row shows an observable at midrapidity from the 200 GeV $v_2(\eta)$ dataset.
  • Figure 2: (Color Online) The averaged RMS errors $\mathcal{E}$ for the three different types of GP emulators. Different training sets are separated by black lines. All emulators are trained with the same 970 LHD points.
  • Figure 3: (Color Online) The metric for emulator uncertainty estimation $\mathcal{H}$ for the three different types of GP emulators. Black lines separate different training sets. All emulators are trained with the same 970 LHD points.
  • Figure 4: (Color Online) The averaged RMS error $\mathcal{E}$ for the PCSK emulator trained with (open symbols) and without (solid markers) logarithmic transformation to particle multiplicities observables. Both emulators are trained with the same 970 LHD points and validated with the remaining 30 points in the initial design. Black lines separate different sets of observables.
  • Figure 5: (Color Online) Same layout as in Fig. \ref{['fig:E_GP_LOG_PCSK']} but for the metric for emulator uncertainty estimation $\mathcal{H}$.
  • ...and 8 more figures