Physics-informed neural networks for angular-momentum conservation in computational relativistic spin hydrodynamics

Theoretical developments in relativistic spin hydrodynamics, which describes the macroscopic transport of spin angular momentum alongside other fundamental conserved quantities, have progressed rapidly since the experimental observation of the global spin polarization of $\Lambda$ hyperons in relativistic heavy-ion collision experiments. However, numerical simulations of relativistic spin hydrodynamics remain largely unaddressed due to computational challenges, particularly the accurate numerical conservation of total angular momentum. In this work, we propose the use of physics-informed neural networks (PINNs) for computational relativistic spin hydrodynamics. As a concrete application, we consider a rotating fluid confined within a cylindrical container. We show that angular-momentum conservation can be accurately achieved in the PINNs-based numerical framework. Furthermore, we investigate the spin-orbit conversion induced by the rotational viscous effect, which is the intrinsic dissipative process of relativistic spin hydrodynamics. Our analysis numerically identifies the mismatch between the transverse thermal vorticity and the spin potential as the driving mechanism of the spin-orbit conversion.