Deep learning approaches to extract nuclear deformation parameters from initial-state information in heavy-ion collisions

TL;DR

This paper investigates how well nuclear deformation parameters can be extracted from initial-state data in heavy-ion collisions using deep learning, highlighting the importance of ensemble averaging and probabilistic inference.

Contribution

It introduces a comprehensive analysis combining permutation-invariant networks and normalizing flows to quantify deformation parameters from initial collision states.

Findings

Deformation information is encoded in initial states and becomes more identifiable with ensemble averaging.

Normalizing flows provide calibrated uncertainty estimates for deformation parameters.

Multi-event averaging is crucial for suppressing fluctuations and extracting deformation signals.

Abstract

The deformation of heavy nuclei leaves characteristic imprints on the initial conditions of relativistic heavy-ion collisions. However, event-by-event fluctuations make the quantitative extraction of this information challenging. This study examines the identifiability of the quadrupole ($\beta_2$) and hexadecapole ($\beta_4$) deformation parameters from nucleon configurations sampled from a deformed Woods-Saxon distribution commonly used in initial-state modeling of heavy-ion collisions. As a baseline, we first establish an upper bound on the "intrinsic identifiability" of deformation information at the most microscopic level by constructing permutation-invariant point-cloud networks under controlled multi-event grouping. We then extend the analysis to the more realistic initial entropy-density profiles generated by the TRENTo model, where both standard regression and simulation-based inference (SBI) with conditional normalizing flows are employed to reconstruct the deformation parameters from ensembles of event images supplemented with global attributes. Multi-event averaging is found to be essential in this setting for suppressing stochastic fluctuations and revealing the underlying deformation information. While standard regression efficiently captures the central trends of deformation through point estimates, SBI provides calibrated posterior distributions, offering a more complete and robust characterization of uncertainty. Collectively, our results demonstrate that deformation information is effectively encoded in the initial state and becomes increasingly identifiable with sufficient ensemble averaging, laying a solid foundation for future extensions toward more complete dynamical modeling and final-state observables.