# Connecting implicit and explicit large eddy simulations of two-dimensional turbulence through machine learning

## TL;DR

This paper introduces a machine learning framework that dynamically chooses between implicit and explicit dissipation schemes in large eddy simulations of 2D turbulence, improving statistical accuracy without predefined turbulence models.

## Contribution

It presents a novel data-driven approach to adaptively select numerical dissipation schemes in LES based on DNS data, bridging implicit and explicit turbulence modeling.

## Key findings

- Enhanced statistical fidelity in LES results.
- Effective dynamic scheme selection based on learned criteria.
- Improved energy spectra and vorticity structures.

## Abstract

In this article, we utilize machine learning to dynamically determine if a point on the computational grid requires implicit numerical dissipation for large eddy simulation (LES). The decision making process is learnt through \emph{a priori} training on quantities derived from direct numerical simulation (DNS) data. In particular, we compute eddy-viscosities obtained through the coarse graining of DNS quantities and utilize their distribution to categorize areas that require dissipation. If our learning determines that closure is necessary, an upwinded scheme is utilized for computing the non-linear Jacobian. In contrast, if it is determined that closure is unnecessary, a symmetric and second-order accurate energy and enstrophy preserving Arakawa scheme is utilized instead. This results in a closure framework that precludes the specification of any model-form for the small scale contributions of turbulence but deploys an appropriate numerical dissipation from explicit closure driven hypotheses. This methodology is deployed for the Kraichnan turbulence test-case and assessed through various statistical quantities such as angle-averaged kinetic energy spectra and vorticity structure functions. Our framework thus establishes a direct link between the use of explicit LES ideologies for closure and numerical scheme-based modeling of turbulence leading to improved statistical fidelity of \emph{a posteriori} simulations.