An end-to-end generative diffusion model for heavy-ion collisions

Abstract

We train a generative diffusion model (DM) to simulate ultra-relativistic heavy-ion collisions from end to end. The model takes initial entropy density profiles as input and produces two-dimensional final particle spectra, successfully reproducing integrated and differential observables. It also captures higher-order fluctuations and correlations. These findings suggest that the generative model has successfully learned the complex relationship between initial conditions and final particle spectra for various shear viscosities, as well as the fluctuations introduced during initial entropy production and hadronization stages, providing an efficient framework for resource-intensive physical goals. The code and trained model are available at https://huggingface.co/Jing-An/DiffHIC/tree/main.

Figures (4)

• Figure 1: The workflow of DiffHIC. The brown block is the core noise prediction network, which is a typical U-net architecture. The blue and orange boxes are the up and down sampling blocks, respectively. Both are realized by ResNet Resnet. The boxes with "Att" represent the block performing the spatial attention computations attention. More details of the architecture are given in the Supplemental Material NetArchitecture. The green box is the bottleneck block.
• Figure 2: The centrality dependence of integrated anisotropy flow of the 2nd ($v_2$), 3rd ($v_3$) and the 4th ($v_4$) order. The filled symbols are the ground truth. The first column is the ideal hydrodynamic results. The second and third columns present the results with $\eta/s=0.1,\eta/s=0.2$, respectively.
• Figure 3: The $p_T$ dependence of anisotropy flow, across all centralities. The filled symbols are the ground truth. The first row is the ideal hydrodynamic results. The second and third rows present the results with $\eta/s=0.1,\eta/s=0.2$, respectively. In each plot, the red, blue, and green lines represent flow of the 2nd order ($v_2(p_T))$, the 3rd order ($v_3(p_T)$) and the 4th order ($v_4(p_T)$), respectively.
• Figure 4: The ratio between the generated results and ground truth in central events. The gray band is $1\pm 0.05$. From left to right, the different color regions correspond to flow from single-, 2-, 3-, 4-, 6-, and 8-particle correlations, respectively. Errors are estimated via the bootstrap method.