# Research on Wind Field Correction Method Integrating Position Information and Proxy Divergence

## TL;DR

This paper introduces PPWNet, a deep learning model that improves wind field correction by using sparse observations and physical consistency, outperforming existing methods.

## Contribution

PPWNet integrates position information and a physics-informed loss function for high-precision wind field correction using sparse data.

## Key findings

- PPWNet reduces MAE by 38.65% and RMSE by 28.93% compared to existing methods.
- The corrected wind field aligns better with observations in both speed and direction.
- Incorporating physical consistency and position data improves deep learning-based correction accuracy.

## Abstract

The accuracy of numerical model outputs strongly depends on the quality of the initial wind field, yet ground observation data are typically sparse and provide incomplete spatial coverage. More importantly, many current mainstream correction models rely on reanalysis grid datasets like ERA5 as the true value, which relies on interpolation calculation, which directly affects the accuracy of the correction results. To address these issues, we propose a new deep learning model, PPWNet. The model directly uses sparse and discretely distributed observation data as the true value, which integrates observation point positions and a physical consistency term to achieve a high-precision corrected wind field. The model design is inspired by biological intelligence. First, observation point positions are encoded as input and observation values are included in the loss function. Second, a parallel dual-branch DenseInception network is employed to extract multi-scale grid features, simulating the hierarchical processing of the biological visual system. Meanwhile, PPWNet references the PointNet architecture and introduces an attention mechanism to efficiently extract features from sparse and irregular observation positions. This mechanism reflects the selective focus of cognitive functions. Furthermore, this paper incorporates physical knowledge into the model optimization process by adding a learned physical consistency term to the loss function, ensuring that the corrected results not only approximate the observations but also adhere to physical laws. Finally, hyperparameters are automatically tuned using the Bayesian TPE algorithm. Experiments demonstrate that PPWNet outperforms both traditional and existing deep learning methods. It reduces the MAE by 38.65% and the RMSE by 28.93%. The corrected wind field shows better agreement with observations in both wind speed and direction, confirming the effectiveness of incorporating position information and a physics-informed approach into deep learning-based wind field correction.