Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil

Abstract

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. Such models are known to incur huge off-line costs, however, which can sometimes outweigh their potential benefits. Furthermore, their prediction accuracy is known to be poor under transonic flow conditions. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks, and we demonstrate its ability to preserve accuracy with significantly lower offline and online costs. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in fast exploration of design space for diverse engineering applications. arXiv:1911.07943v2 [physics.flu-dyn] 12 Jan 2020 Ψ k (Au − f (u)) = 0.Since the reduced state variableũ ≈ Φ k u, this equation can be written as

A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

“…One way to utilize this abundance of data is the purely data-driven nonintrusive ROM (NIROM) approach. NIROMs have largely benefited from the widespread of open-source cutting edge and easy-to-use machine learning (ML) libraries, and cheap computational infrastructure to solely rely on data in order to build stable and accurate models, compared to their GROM counterparts [73][74][75][76][77][78][79][80][81][82][83]. However, purely data-driven tools often lack human interpretability and generalizability, and sometimes become prohibitively "data-hungry".…”

Non‐intrusive reduced order modeling: Geometrical framework, high‐order models, and a priori analysis of applicability

“…Up to date the method has been investigated in a wide range of applications, including fluid dynamics, 1,7‐9 fluid‐structure interactions, 5 blasting, 10 simple reservoir modeling, 11 melt flow, 12 car crash simulation, 13 and others. In recent years particular emphasis was put on NIROMs based on machine learning methods due to the increasing popularity of the latter 14‐16 . However, NIROM is typically introduced as an abstract ansatz (heuristic) and little attention has been given to the characteristics and intuitive understanding of the method itself.…”

Parameterized nonintrusive reduced‐order model for general unsteady flow problems using artificial neural networks

“…The accuracy achieved was shown to be comparable with intrusive ROMs based on POD and a Galerkin projection. A very recent application of ANNs is presented in Reference 27, where a parametric ROM is generated for the steady‐state inviscid transonic flow over a RAE 2822 aerofoil. The parametric space included eight independent parameters for modifying the aerofoil shape, the results showing that the neural network‐based model achieved accuracy comparable with intrusive ROM techniques.…”

“…It is seen that the focus in most of these works has been either to capture the nonlinear parameter space variation of a steady parameter‐dependent system, or to accurately capture the unsteady behavior of a nonlinear system. Indeed, the most common usage for ANNs in ROM frameworks are related to time evolution or data compression, examples of the latter being found in References 30,31, fewer works (such as Reference 27) focusing on the parametric space approximation. Work on ANN‐ROMs for time‐dependent phenomena involving arbitrarily large parameter spaces, as are common for many engineering design problems, is rarely covered in literature.…”