Extending a Physics-informed Machine-learning Network for Superresolution Studies of Rayleigh–Bénard Convection

Abstract

Advancing our understanding of astrophysical turbulence is bottlenecked by the limited resolution of numerical simulations that may not fully sample scales in the inertial range. Machine-learning (ML) techniques have demonstrated promise in upscaling resolution in both image analysis and numerical simulations (i.e., superresolution). Here we employ and further develop a physics-constrained convolutional neural network ML model called “MeshFreeFlowNet” (MFFN) for superresolution studies of turbulent systems. The model is trained on both the simulation images and the evaluated partial differential equations (PDEs), making it sensitive to the underlying physics of a particular fluid system. We develop a framework for 2D turbulent Rayleigh–Bénard convection generated with the Dedalus code by modifying the MFFN architecture to include the full set of simulation PDEs and the boundary conditions. Our training set includes fully developed turbulence sampling Rayleigh numbers ( Ra ) of Ra = 10 ^6 –10 ^10 . We evaluate the success of the learned simulations by comparing the power spectra of the direct Dedalus simulation to the predicted model output and compare both ground-truth and predicted power spectral inertial range scalings to theoretical predictions. We find that the updated network performs well at all Ra studied here in recovering large-scale information, including the inertial range slopes. The superresolution prediction is overly dissipative at smaller scales than that of the inertial range in all cases, but the smaller scales are better recovered in more turbulent than laminar regimes. This is likely because more turbulent systems have a rich variety of structures at many length scales compared to laminar flows.

Keywords

• Interstellar medium