ML-ILES: End-to-end optimization of data-driven high-order Godunov-type finite-volume schemes for compressible homogeneous isotropic turbulence

In this work, we present a data-driven high-order Godunov-type finite-volume scheme for machine-learned implicit large-eddy simulations (ML-ILES) of compressible homogeneous isotropic turbulence. For the simulation of compressible flows, many Godunov-type finite-volume schemes combine high-order shock-capturing schemes with approximate Riemann solvers. Here, we devise neural network-based reconstruction operators which are trained to best approximate turbulent subgrid-scales. In particular, we use separate reconstruction neural networks for each physical flow quantity and show that an optimal reconstruction for ILES may require different reconstruction strategies for different flow quantities. The neural networks used in the reconstruction operator are trained end-to-end, using the automatically differentiable JAX-Fluids CFD solver. The training data set comprises coarse-grained spatio-temporal trajectories of compressible temporally decaying homogeneous isotropic turbulence. Comparisons with established ILES discretizations show encouraging results.