Physics-Informed Neural Network for Solving the Heavy Quark Diffusion in the Expanding QCD Medium

We employ Physics-Informed Neural Networks (PINNs) to investigate the dynamical evolution of heavy quarks within the expanding hot QCD medium generated in relativistic heavy-ion collisions. The heavy quark dynamics are first modeled under the assumption of complete kinetic thermalization, followed by a more realistic study of non-thermal diffusion governed by the Fokker-Planck (FP) equation. In both scenarios, the background evolution of the hot QCD medium is encoded into the coefficients of the diffusion equations. These equations are solved within the PINN framework, where the initial conditions, physical constraints from the dynamical equation, and probability conservation are incorporated into the loss function.We also compare the performance of the FP-PINN with a supervised five-dimensional DNN trained on labeled data generated from Langevin-based reference distributions.This work provides a valuable reference for applying PINN-based models to particle diffusion in phase space, laying the foundation for future studies of heavy quarkonium production via realistic non-thermal heavy-quark coalescence.