A Novel Hybrid Deep Learning Method for Predicting the Flow Fields of Biomimetic Flapping Wings

The physics governing the fluid dynamics of bio-inspired flapping wings is effectively characterized by partial differential equations (PDEs). Nevertheless, the process of discretizing these equations at spatiotemporal scales is notably time consuming and resource intensive. Traditional PDE-based computations are constrained in their applicability, which is mainly due to the presence of numerous shape parameters and intricate flow patterns associated with bionic flapping wings. Consequently, there is a significant demand for a rapid and accurate solution to nonlinear PDEs, to facilitate the analysis of bionic flapping structures. Deep learning, especially physics-informed deep learning (PINN), offers an alternative due to its great nonlinear curve-fitting capability. In the present work, a hybrid coarse-data-driven physics-informed neural network model (HCDD-PINN) is proposed to improve the accuracy and reliability of predicting the time evolution of nonlinear PDEs solutions, by using an order-of-magnitude-coarser grid than traditional computational fluid dynamics (CFDs) require as internal training data. The architecture is devised to enforce the initial and boundary conditions, and incorporate the governing equations and the low-resolution spatiotemporal internal data into the loss function of the neural network, to drive the training. Compared to the original PINN with no internal data, the training and predicting dynamics of HCDD-PINN with different resolutions of coarse internal data are analyzed on the problem relevant to the two-dimensional unsteady flapping wing, which involves unsteady flow features and moving boundaries. Additionally, a hyper-parametrical study is conducted to obtain an optimal model for the problem under consideration, which is then utilized for investigating the effects of the snapshot and fraction of the coarse internal data on the HCDD-PINN's performances. The results show that the proposed framework has a sufficient stability and accuracy for solving the considered biomimetic flapping-wing problem, and its great potential means that it can be considered as an alternative to accelerate or replace traditional CFD solvers in the future. The interested variables of the flow field at any instant can be rapidly obtained by the trained HCDD-PINN model, which is superior to the traditional CFD method that usually needs to be re-run. For the three-dimensional and optimization problems of flapping wings, the advantages of the proposed method are supposedly even more apparent.