Fast prediction of the hydrodynamic QGP evolution in ultra-relativistic heavy-ion collisions using Fourier Neural Operators

Abstract: Recent research in machine learning has employed neural networks to learn mappings between function spaces on bounded domains termed ``neural operators''. As such, these operators can provide alternatives to standard numerical methods for partial differential equation (PDE) solutions. In particular, the Fourier Neural Operator (FNO) has been shown to map solutions for classical fluid flow problems with accuracy competitive with traditional PDE solvers and with much greater computing speed. This paper explores the first application of FNOs to model ultra-relativistic hydrodynamic flow of the quark-gluon plasma (QGP) generated in relativistic heavy-ion collisions. The application in ultra-relativistic flow is novel relative to classical flow, due to the hydrodynamic evolution of the QGP occurring in femtometer-scaled explosions characterized by rapid expansion cooling. In this study we investigate the applicability of FNOs as computationally fast alternatives to standard numerical PDE solvers. The FNO predictions are evaluated by comparing to standard PDE solutions, using \MUSIC in the \JETSCAPE Monte Carlo event generator framework. The performance of calculating established experimental observables for flow and jet quenching using FNOs in the MC framework are also reported.