Applications of deep learning to relativistic hydrodynamics

Relativistic hydrodynamics is a powerful tool to simulate the evolution of the quark gluon plasma(QGP) in relativistic heavy ion collisions. Using 10000 initial and final profiles generated from 2+1-d relativistic hydrodynamics VISH2+1 with MC- Glauberinitial conditions, we train a deep neural network based on stacked U-net, and use it to predict the final profiles associated with various initial conditions, including MC- Glauber, MC-KLN and AMPTand TRENTo. A comparison with the VISH2+1 results shows that the network predictions can nicelycapture the magnitude and inhomogeneous structures of the final profiles, and nicelydescribe the related eccentricity distributions $P(\varepsilon_n)$ (n=2, 3, 4). These results indicate that deep learning technique can capture the main features of the non-linear evolution of hydrodynamics, showing its potential to largely accelerate the event-by-event simulations of relativistic hydrodynamics.