Computation of the Harish–Chandra–Itzykson–Zuber (HCIZ) integral appears as a theoretical bottleneck in many areas of theoretical physics and mathematics, from matrix models for Quantum Chromodynamics, to stochastic resetting problems and Free Probability Theory. Knowledge of its asymptotic expansion, which is notoriously hard to estimate, would be extremely useful. Recently, a hydrodynamic mapping of the problem giving rise to a set of coupled PDEs has been proposed, but their solutions are hard to obtain with standard numerical methods. This work presents the development and evaluation of ANaGRAM, a partial differential equation solver based on Physics-Informed Neural Networks (PINNs), with the explicit goal of solving the above mentioned PDEs.