Artificial neural network subgrid models of 2D compressible magnetohydrodynamic turbulence

Abstract

We explore the suitability of deep learning to capture the physics of subgrid-scale ideal magnetohydrodynamics turbulence of 2-D simulations of the magnetized Kelvin-Helmholtz instability. We produce simulations at different resolutions to systematically quantify the performance of neural network models to reproduce the physics of these complex simulations. We compare the performance of our neural networks with gradient models, which are extensively used in the extensively in the magnetohydrodynamic literature. Our findings indicate that neural networks significantly outperform gradient models at reproducing the effects of magnetohydrodynamics turbulence. To the best of our knowledge, this is the first exploratory study on the use of deep learning to learn and reproduce the physics of magnetohydrodynamics turbulence.

Advances in Machine and Deep Learning for Modeling and Real-time Detection of Multi-Messenger Sources

“…It is expected that numerical relativity will meet these challenges within the next few years with the production of open source numerical relativity software that will bring together experts across the community. The adoption of deep learning to accelerate the description of physics that requires sub-grid scale precision, such as turbulence, is also in earnest development [30].…”

Deconvolutional artificial neural network models for large eddy simulation of turbulence

“…the unsolved velocity u * i and the SGS stress τ ij , etc.). They are the correlation coefficient C (Q), the relative error E r (Q), and the root-mean-square value R (Q), which are defined, respectively, by [52][53][54][55][56][57][58][59]…”

“…Ma et al established a natural analogy between recurrent neural network and the Mori-Zwanzig formalism, and proposed a systematic approach for developing long-term reduced models to predict the Kuramoto-Sivashinsky equations and the Navier-Stokes equations 48 . The ANN models built with the filtered velocity gradients as input variables show good performance for both the a priori and the a posteriori studies in the prediction of isotropic turbulence [50][51][52][53][54][55][56][57] and magneto-hydrodynamic turbulence 58 , but show no advantage over the Smagorinsky model in the a posteriori testing for the channel flow 59 . Raissi et al proposed a physical-informed neural network to learn the unclosed terms for turbulent scalar mixing 60 .…”

Binary Neutron Star Merger Simulations with a Calibrated Turbulence Model

“…An extension of the method to GRMHD, taking into account also terms that we neglected in our initial formulation (more on this below) was proposed in [84,85]. Rosofsky and Huerta [86] proposed to use machine learning to calibrate subgrid turbulence models for 2D MHD. Finally, a variant of the GRLES method was also implemented in the SpEC code by the SXS collaboration to perform 2D axisymmetric simulations [66].…”