Nonlinear QCD Evolution with Machine Learning for the Electron–Ion Collider

The rapid rise of gluon densities in the small-x regime of Quantum Chromodynamics (QCD) drives nonlinear dynamics that are central to the science case of the upcoming Electron–Ion Collider (EIC). The goal of our work is to create machine-learning models that can quickly compute solutions for nuclear evolution using the Balitsky–Kovchegov (BK) and Balitsky–Fadin–Kuraev–Lipatov (BFKL) equations. These approaches describe the behavior of gluons inside protons and nuclei at high energies, but their numerical solution is computationally demanding, limiting the scope of precision global analyses. We develop fast, accurate machine learning emulators based on Multi-Layer Perceptrons (MLP) and Deep Operator Networks (DeepONet), trained directly on high-accuracy BK and BFKL solutions. The resulting models reproduce full QCD evolutions within milliseconds while preserving physics fidelity across broad kinematics. Preliminary benchmarks show excellent agreement with established solvers and open the door to real-time global fits. By transforming a major computational bottleneck into an interactive analysis-ready tool, this work highlights the synergy of AI/ML and nuclear theory for the EIC era.