Solver-in-the-loop approach to closure of shell models of turbulence

Fuente: arXiv
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Autores principales: Freitas, André, Um, Kiwon, Desbrun, Mathieu, Buzzicotti, Michele, Biferale, Luca
Formato: Preprint
Publicado: 2024
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author Freitas, André
Um, Kiwon
Desbrun, Mathieu
Buzzicotti, Michele
Biferale, Luca
author_facet Freitas, André
Um, Kiwon
Desbrun, Mathieu
Buzzicotti, Michele
Biferale, Luca
contents This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a neural network model to interact with the differential equation solver over time during the training process. The closure model is, then, naturally exposed to equations-informed input distributions by accounting for prior corrections over the temporal evolution in training. Such a characteristic makes this approach depart from the conventional a priori instantaneous training paradigm and often leads to a more accurate and stable closure model. Our study demonstrates that the closure learned via this a posteriori approach is able to reproduce high-order statistical moments of interest also in closures of high Reynolds number turbulence. Moreover, we investigate the performance of the learned model by experimenting with the effect of unrolling in time, which has remained for the most part unexplored in the literature. Finally, we discuss potential extensions of this approach to Navier-Stokes equations.
format Preprint
id arxiv_https___arxiv_org_abs_2411_13194
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Solver-in-the-loop approach to closure of shell models of turbulence
Freitas, André
Um, Kiwon
Desbrun, Mathieu
Buzzicotti, Michele
Biferale, Luca
Fluid Dynamics
Chaotic Dynamics
This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a neural network model to interact with the differential equation solver over time during the training process. The closure model is, then, naturally exposed to equations-informed input distributions by accounting for prior corrections over the temporal evolution in training. Such a characteristic makes this approach depart from the conventional a priori instantaneous training paradigm and often leads to a more accurate and stable closure model. Our study demonstrates that the closure learned via this a posteriori approach is able to reproduce high-order statistical moments of interest also in closures of high Reynolds number turbulence. Moreover, we investigate the performance of the learned model by experimenting with the effect of unrolling in time, which has remained for the most part unexplored in the literature. Finally, we discuss potential extensions of this approach to Navier-Stokes equations.
title Solver-in-the-loop approach to closure of shell models of turbulence
topic Fluid Dynamics
Chaotic Dynamics
url https://arxiv.org/abs/2411.13194