A comparison of neural-network architectures to accelerate high-order h/p solvers

High-order solvers are accurate but computationally expensive as they require small time steps to advance the solution in time. In this work, we include a corrective forcing to a low-order solution to achieve high accuracy while advancing in time with larger time steps and achieving fast computations. This work is a continuation of our previous research [Manrique de Lara and Ferrer, "Accelerating high order discontinuous Galerkin solvers using neural networks: 1D Burgers' equation," Comput. Fluids 235, 105274 (2022) and F. Manrique de Lara and E. Ferrer, "Accelerating high order discontinuous Galerkin solvers using neural networks: 3D compressible Navier-Stokes equations," J. Comput. Phys. 489, 112253 (2023).], where we compare advanced neural networks: convolutional neural network (CNN) and long short-term memory (LSTM) networks to obtain the corrective forcing that corrects the low-order solution. The CNN exploits local spatial correlations while the LSTM accounts for temporal dependencies in the flow, expanding the validity of the low-order solution. Experimental results on the Taylor-Green vortex problem at Re = 1600, which includes laminar, transitional, and turbulent regimes, demonstrate significant accelerations of these advanced networks over the fully connected network.