VarP-GP: cost-efficient Bayesian emulation of quark-gluon plasma modeling with variable statistical precision

TL;DR

The VarP-GP emulator enables new multi-model and many-observable calibrations of QGP data and modeling, which would otherwise not be possible with achievable computing resources.

Abstract

We present VarP-GP, a new cost-efficient Bayesian emulator for expensive computational models with variable statistical precision. We focus on the interpretation of measurements of the quark-gluon plasma (QGP) generated in high-energy nuclear collisions, through comparison to numerical models using Bayesian Inference. Such inference calculations are computationally expensive and require surrogate model emulation, which is commonly implemented using Machine Learning (ML)--based Gaussian processes (GPs). Emulator training data are generated by Monte Carlo simulations whose numerical precision depends on the computational resources utilized; improved precision entails greater computational cost. This study utilizes JETSCAPE simulations of inclusive hadron and jet measurements in nuclear collisions at RHIC and the LHC. The VarP-GP emulator combines information from multiple simulation runs with varying precision across the model parameter space, taking advantage of the smoothness in that space of QCD-driven processes. Comparison to a traditional emulator approach shows a marked reduction in emulator uncertainty at fixed computational cost, indicating that knowledge of the overall contours of the parameter design space is more important for precise emulation than detailed information at a more limited number of design points. As an initial application of VarP-GP, a computationally-expensive model parameter sensitivity study of jet quenching data is reported. The VarP-GP emulator enables new multi-model and many-observable calibrations of QGP data and modeling, which would otherwise not be possible with achievable computing resources.

Figures (12)

• Figure 1: Schematic illustration of the stages of evolution of a high--energy heavy--ion collision which generates a Quark--Gluon Plasma. Figure from Arslandok:2023utm.
• Figure 2: Schematic visualization of the VarP-GP workflow.
• Figure 3: A toy example with $n=5$ design points. (Left) A poor pairing of design points with event counts in $\mathcal{M}$. (Right) An optimized pairing of design points with event counts in $\mathcal{M}$, using the proposed criterion from Eq. \ref{['eq:pair']}.
• Figure 4: Assessment of VarP-GP and HF-GP performance as a function of number of simulated events for emulator training. For each value of $p_\mathrm{T}$, an MSE is determined by comparing $R_{\mathrm{AA}}$ computed by VarP-GP and HF-GP to that of a reference high-fidelity calculation at 23 test design points. Each figure element shows the distribution of MSE across $p_\mathrm{T}$ values: thick black line is the median; colored box lower and upper limits are 25% and 75% quartiles; and vertical lines beyond the box limits correspond to the largest values within 1.5 times the inter-quartile range. Outliers are shown as individual points. The x-axis values are offset for clarity. Vertical colored arrows at the top of the figure indicate a single MSE value above the maximum y-axis range for a given number of training events. Left: hadron $R_{\mathrm{AA}}$; right: jet $R_{\mathrm{AA}}$. Orange: VarP-GP; purple: HF-GP.
• Figure 5: Aggregated $p_\mathrm{T}$-differential MSE (sum of MSE over all $p_\mathrm{T}$ bins) from Fig. \ref{['fig:differentialEmulationPerformance']}, as a function of the number of simulated events used for emulator training. Left: hadron $R_{\mathrm{AA}}$; right: jet $R_{\mathrm{AA}}$. Orange: VarP-GP; purple: HF-GP.