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. © 2024 The Author(s)     «

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 u...     »

Funding text 1 Financial support by the Deutsche Forschungsgemeinschaft, project number 525796191, within SPP 2410 Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness (CoScaRa) is gratefully acknowledged. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer JUWELS [40] at J\u00FClich Supercomputing Centre (JSC). Funding text 2 Financial support by the Deutsche Forschungsgemeinschaft, project number 525796191, within SPP 2410 Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness (CoScaRa) is gratefully acknowledged.      «

Funding text 1 Financial support by the Deutsche Forschungsgemeinschaft, project number 525796191, within SPP 2410 Hyperbolic Balance Laws in Fluid Mechanics: Complexity, Scales, Randomness (CoScaRa) is gratefully acknowledged. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer JUWELS [40] at J\u00FClich Supercomputing Centre (JSC). Funding text 2 Financial support by t...     »