Computational Challenges for Multi-Messenger Heavy-ion Physics*

High energy relativistic nuclear collisions create matter in an extremely hot and dense environment. Such matter exhibits near-perfect fluidity that emerges from many-body interactions among deconfined quarks and gluons, known as the Quark-Gluon Plasma (QGP). A wealth of high precision measurements at the Relativistic Heavy-Ion Collider (RHIC) and the Large Hadron Collider (LHC) have been driving our field to an era of multi-messenger characterization of the QGP properties. Like multi-messenger astronomy, different types of particles emitted from heavy-ion collisions carry unique dynamical information, complement each other. Hadrons with transverse momenta below 2 GeV interact collectively. Their momentum distributions and correlations encode QGP's thermal and transport properties. QCD jets and heavy quarks probe the color degrees of freedom of the QCD medium at different length scales. Electromagnetic (EM) radiation, such as photons and dileptons, is a unique soft penetrating probe for the entire medium evolution in heavy-ion collisions with a high sensitivity to the collisions' early-stage. This talk will lay out the computational challenges in theoretical aspects of multi-messenger heavy-ion physics. I will highlight recent theoretical and numerical advancements in 3+1D relativistic viscous hydrodynamics and the treatments of stochastic fluctuations. Such computational frameworks serve as a powerful tool to unravel QCD many-body physics from the complex dynamics of relativistic heavy-ion collisions.