Physics-informed deep convolutional hierarchical encoder-decoder neural network for flow field prediction in wind farms

Wind Farm Layout Optimization (WFLO) is a critical step in wind farm design, focusing on determining the optimal placement of turbines to maximize the annual energy production (AEP) of wind farms. Calculating AEP as an objective function in WFLO often relies on computationally expensive computational fluid dynamics (CFD) simulations to calculate the flow field within the farm. In this study, we propose PI-DeepWFLO, a physics-informed deep convolutional hierarchical encoder-decoder neural network, as a surrogate model to predict flow fields for various turbine configurations, significantly reducing dependence on costly CFD simulations. PI-DeepWFLO is trained on labeled data using a customized physics-informed loss function that incorporates mass and momentum conservation laws. Our results show that the proposed PI-DeepWFLO accurately predicts spanwise and streamwise velocity fields ($R^2=0.955$), effectively capturing wake interactions between turbines. Furthermore, results show that PI-DeepWFLO is less sensitive to variations in network weight initialization and training datasets than purely data-driven alternatives, exhibiting a ten-fold lower $R^2$ variance over different re-samplings of the training dataset. A comparison of AEP values calculated from PI-DeepWFLO and CFD-generated flow fields demonstrates a median error of 1.25 % across test cases. Importantly, the Spearman’s Rank Correlation Coefficient between AEPs from CFD and PI-DeepWFLO flow fields is 1.0, confirming the PI-DeepWFLO’s suitability for AEP estimation in optimization studies. We illustrate PI-DeepWFLO’s performance in an application context by employing it as a surrogate model for a WFLO task.