Exploring hidden flow structures from sparse data through deep-learning-strengthened proper orthogonal decomposition

Proper orthogonal decomposition (POD) enables complex flow fields to be decomposed into linear modes according to their energy, allowing the key features of the flow to be extracted. However, traditional POD requires high-quality inputs, namely, high-resolution spatiotemporal data. To alleviate the dependence of traditional POD on the quality and quantity of data, this paper presents a POD method that is strengthened by a physics-informed neural network (PINN) with an overlapping domain decomposition strategy. The loss function and convergence of modes are considered simultaneously to determine the convergence of the PINN-POD model. The proposed framework is applied to the flow past a two-dimensional circular cylinder at Reynolds numbers ranging from 100 to 10 000 and achieves accurate and robust extraction of flow structures from spatially sparse observation data. The spatial structures and dominant frequency can also be extracted under high-level noise. These results demonstrate that the proposed PINN-POD method is a reliable tool for extracting the key features from sparse observation data of flow fields, potentially shedding light on the data-driven discovery of hidden fluid dynamics.