Differentiable Turbulence II

• URL: http://arxiv.org/abs/2307.13533v1
• Date: Tue, 25 Jul 2023 14:27:49 GMT
• Title: Differentiable Turbulence II
• Authors: Varun Shankar, Romit Maulik, Venkatasubramanian Viswanathan
• Abstract summary: We develop a framework for integrating deep learning models into a generic finite element numerical scheme for solving the Navier-Stokes equations. We show that the learned closure can achieve accuracy comparable to traditional large eddy simulation on a finer grid that amounts to an equivalent speedup of 10x.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Differentiable fluid simulators are increasingly demonstrating value as useful tools for developing data-driven models in computational fluid dynamics (CFD). Differentiable turbulence, or the end-to-end training of machine learning (ML) models embedded in CFD solution algorithms, captures both the generalization power and limited upfront cost of physics-based simulations, and the flexibility and automated training of deep learning methods. We develop a framework for integrating deep learning models into a generic finite element numerical scheme for solving the Navier-Stokes equations, applying the technique to learn a sub-grid scale closure using a multi-scale graph neural network. We demonstrate the method on several realizations of flow over a backwards-facing step, testing on both unseen Reynolds numbers and new geometry. We show that the learned closure can achieve accuracy comparable to traditional large eddy simulation on a finer grid that amounts to an equivalent speedup of 10x. As the desire and need for cheaper CFD simulations grows, we see hybrid physics-ML methods as a path forward to be exploited in the near future.

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