Predicting high-fidelity data from coarse-mesh computational fluid dynamics corrected using hybrid twins based on optimal transport

Abstract

Nowadays, numerical simulation, such as computational fluid dynamics (CFD), has become an essential tool for scientific investigation and analysis of complex systems in engineering allowing high-fidelity Navier-Stokes resolution for realistic turbulent flows which cannot be solved analytically. However, although all the studies and development conducted to improve its accuracy and computational cost, CFD remains either not to be trusted completely or too expensive to run. Moreover, with the present data-based revolution, artificial intelligence and machine learning (ML) are acquiring indisputable importance in every field leading to data, theory, and simulation working together for computational efficiency and to increase accuracy. Among the very different applications of data in CFD, here we focus on data-driven correction of coarse simulations based on the knowledge of the error gap between coarse and high-fidelity simulations, also known as the "hybrid twin" rationale. On the one hand, coarse numerical simulations are computed as fast and cheap data, assuming their inherent error. On the other hand, some high-fidelity (HF) data is gathered to train the ML correction model which fills the coarse-HF gap. However, modeling this ignorance gap might be difficult in some fields such as fluids dynamics, where a regression over the localized solutions can lead to non physical interpolated solutions. Therefore, the Optimal Transport theory is followed, which provides a mathematical framework to measure distances between general objects. Such an OT-based "hybrid twin" methodology was already proposed in a previous article by the authors. However, even if in this article the methodology remains the same, the problem solved is conceptually different since we correct no longer the gap between experimental and numerical data but between coarse and high-fidelity simulations.

Keywords

• hybrid twin
• artificial intelligence
• optimal transport
• computational fluid dynamics