The prediction of external flow field and hydrodynamic force with limited data using deep neural network

Predicting the external flow field with limited data or limited measurements has attracted long-time interests of researchers in many industrial applications. Physics informed neural network (PINN) provides a seamless framework for combining the measured data with the deep neural network, making the neural network capable of executing certain physical constraints. Unlike the data-driven model to learn the end-to-end mapping between the sensor data and high-dimensional flow field, PINN need no prior high-dimensional field as the training dataset and can construct the mapping from sensor data to high dimensional flow field directly. However, the extrapolation of the flow field in the temporal direction is limited due to the lack of training data. Therefore, we apply the long short-term memory (LSTM) network and physics-informed neural network (PINN) to predict the flow field and hydrodynamic force in the future temporal domain with limited data measured in the spatial domain. The physical constraints (conservation laws of fluid flow, e.g., Navier-Stokes equations) are embedded into the loss function to enforce the trained neural network to capture some latent physical relation between the output fluid parameters and input tempo-spatial parameters. The sparsely measured points in this work are obtained from computational fluid dynamics (CFD) solver based on the local radial basis function (RBF) method. Different numbers of spatial measured points (4–35) downstream the cylinder are trained with/without the prior knowledge of Reynolds number to validate the availability and accuracy of the proposed approach. More practical applications of flow field prediction can compute the drag and lift force along with the cylinder, while different geometry shapes are taken into account. By comparing the flow field reconstruction and force prediction with CFD results, the proposed approach produces a comparable level of accuracy while significantly fewer data in the spatial domain is needed. The numerical results demonstrate that the proposed approach with a specific deep neural network configuration is of great potential for emerging cases where the measured data are often limited.