Residual-connected physics-informed neural network for anti-noise wind field reconstruction

Physics-informed neural network (PINN)-based methods have recently been applied to reconstruct the spatiotemporal wind field based on LIDAR measurements. However, the accuracy of this reconstruction considerably degrades when LIDAR measurement noise exists. Unfortunately, LIDAR measurement noise is inevitable in the real world. To address this limitation, this paper proposes a novel anti-noise method to reconstruct the wind field based on real-world noisy LIDAR measurements. To this end, we first address the gradient vanishing problem in PINN's automatic differentiation process, which prevents the Navier-Stokes (NS) equations from being fully leveraged in wind field reconstruction. This problem is addressed by proposing a residual-connected PINN (RC-PINN) framework. Its advantage in solving the gradient vanishing problem is mathematically proven. Subsequently, by incorporating the NS equations into the RC-PINN, an anti-noise wind field reconstruction method is established. The key feature of this method is that, by employing the RC-PINN, the NS equations are more effectively utilized in the training process, thus improving its anti-noise capability. The numerical results show that, at a wide range of noise levels, the proposed method can achieve a significant improvement in reconstruction performance. Especially, at the noise level of commercially available LIDAR, the reconstruction results are quite satisfactory. Moreover, the proposed method can converge faster.