Parametric unsteady flow modeling by using meta learning

Abstract

Parametric unsteady flow modeling plays a significant role in the fluid dynamics, since the unsteady flow problems are usually involved with complex physical phenomena. Currently, in the study of data-driven unsteady flow modeling, the convolutional neural network based autoencoder (CNN-AE) model has been widely used. While, its application in engineering field has been limited due to challenges that the CNNs are expensive to be trained and the generalization performance of CNN-AE model needs to be improved. Therefore, based on the CNN-AE model, a meta-learning framework is introduced in the present work for parametric unsteady flow modeling. Specifically, both the model-agnostic meta-learning (MAML) and the reptile methods are used to learn the correlations between flow fields under various physical parameters. First, a meta-initialization CNN-AE model is established, with the training data-set under various physical parameters. Then, for a new physical parameter, the meta-initialization CNN-AE model will be finetuned by using few snapshots in a new task with limited epochs. Finally, the proposed CNN-AE based meta-learning framework is validated in two canonical unsteady flow problems with moving boundaries, including oscillating cylinder and flapping airfoil. The results have shown that the CNN-AE based meta-leaning framework can greatly accelerate the adaptation of CNN-AE model in new physical parameters, which can greatly enhance the generalization performance of CNN-AE model.