This study introduces enhancements to physics-constrained neural networks (PCNNs) that improve the accuracy and stability of hybrid short-term weather forecasting models. Building on the WeatherGFT architecture, three innovations are proposed. First, an upgraded numerical solver, combining a fifth-order weighted essentially non-oscillatory scheme (WENO-5), a beta-plane approximation, and subgrid-scale viscosity, permits a fourfold increase in the integration time step to 1200 s while reducing the daily mean squared error by up to 26%. Second, a unified autoregressive hybrid block replaces the original chain of 24 specialised modules, eliminating overfitting to specific lead times. Third, the physical core is integrated with two state-of-the-art neural backbones, resulting in PI-PredFormer and PI-IAM4VP. Evaluation on the WeatherBench South Pacific subset from 2000 to 2004 shows that these hybrids reduce root mean squared error at 1-12 h lead times by 8-22% compared to purely neural counterparts, while better preserving physical consistency. These results demonstrate that incremental refinement of hybrid components offers a practical route toward more accurate and efficient short-range weather forecasting.

翻译：本研究提出了对物理约束神经网络（PCNNs）的改进，旨在提升混合式短期天气预报模型的准确性与稳定性。基于WeatherGFT架构，本文提出三项创新。首先，一种结合五阶加权本质非振荡格式（WENO-5）、β平面近似和亚网格尺度粘性的升级版数值求解器，允许积分时间步长增加四倍至1200秒，同时将日均方误差降低高达26%。其次，采用统一的自回归混合模块替代原有的24个专用模块链，消除了对特定预报步长的过拟合。第三，将物理核心与两种最先进的神经网络骨干相集成，由此得到PI-PredFormer和PI-IAM4VP。在2000至2004年WeatherBench南海子集上的评估表明，与纯神经网络模型相比，这些混合模型在1至12小时预报步长上的均方根误差降低了8%至22%，同时更好地保持了物理一致性。这些结果表明，对混合组件进行渐进式优化是实现更精确、更高效短期天气预报的可行路径。