Inferring Nuclear Radial Parameters from Initial-State Information in Heavy-Ion Collisions Using Deep Neural Networks

The geometric structure of atomic nuclei plays an important role in shaping the initial conditions of high-energy nuclear collisions and the subsequent evolution of the quark–gluon plasma. In this work, we develop a multimodal deep-learning framework to infer the Woods–Saxon radius ($R_0$) and diffuseness parameter ($a$) from initial-state information. Using the TRENTo model for relativistic $^{238}$U+$^{238}$U collisions, we construct a dataset covering multiple combinations of $R_0$ and $a$, and perform parameter regression by combining two-dimensional entropy-density distributions with event-level scalar observables, including multiplicity and eccentricities $\varepsilon_2$–$\varepsilon_5$. The results show that the proposed framework can effectively recover the Woods–Saxon parameters from initial-state information. Joint multi-event inputs suppress statistical fluctuations and improve regression performance by enhancing the extraction of collective information. The inversion accuracy exhibits a pronounced centrality dependence: $R_0$ is best constrained in central collisions, whereas $a$ shows the strongest sensitivity in the mid-peripheral region and becomes less well constrained in ultra-central and peripheral collisions. These findings indicate that the initial-state geometry retains useful information about nuclear radial structure and provide a baseline for future studies that incorporate transport evolution and experimental final-state observables.