Output-based adaptive aerodynamic simulations using convolutional neural networks

Abstract

This paper presents a new method to perform output error estimation and mesh adaptation in computational fluid dynamics (CFD) using machine-learning techniques. The error of interest is the functional output error induced by the numerical discretization, including the finite computational mesh and approximation order. Given the data of adaptive flow simulations guided by adjoint-based error estimates, a surrogate model is trained to predict the output error and drive the mesh adaptation with only the low-fidelity solution as input. The goal is to generalize the error estimation and mesh adaptation knowledge from the simulation data at hand. The proposed method uses an encoder-decoder type convolutional neural network (CNN), supervised by both the adaptive error indicator field and the total output error, to capture both the local and global features related to the numerical error. To handle geometries and irregular meshes in adaptive simulations, topology mapping and local projection are introduced into traditional CNN models. The feasibility of the proposed machine-learning approach for error prediction and mesh adaptation is demonstrated in inviscid transonic flow simulations over airfoils. Both the output error and the localized adaptive indicators are well predicted by the trained CNN model, which is then used to drive the mesh adaptation as an alternative to standard adjoint-based methods. The good performance and relatively simple deployment encourage more study and development of the proposed method.