Enhancing the Forecasting Capability of Multi-Model Blending Algorithms for Extreme Precipitation via Joint Use of Station and Gridded Observations

Accurate extreme precipitation forecasting is critical for disaster mitigation but remains challenging for numerical weather prediction (NWP) models due to systemic intensity underestimation and spatial displacement. Traditional precipitation multi-model blending algorithms perform pixel-by-pixel blending on the forecast field based on weights, which may lead to the expansion of precipitation areas and the smoothing of extreme values. This study proposes an U-Net based two-stage framework: probability classification followed by value reconstruction, to blend forecasts from six major NWP models. A novel station-grid joint supervision mechanism is introduced by integrating observations from 2411 national meteorological stations in China into the loss function, simultaneously constraining spatial structures and peak intensities. Evaluations using independent samples from the 2025 flood season demonstrate that our model significantly outperforms both individual NWPs and current operational products. For rainstorms (>=50 mm), the Threat Score (TS) improved by 38.4% compared to the best NWP. Notably, for extreme events (>=100 mm) driven by extratropical cyclones and the subtropical high, the model successfully elevated the TS to above 0.1, transforming forecasts from having negligible reference value into those with certain operational utility. Furthermore, the model exhibits data-driven spatial correction capabilities, effectively realigning systematic rainbelt displacements with actual precipitation centers. The inclusion of station observations specifically enhanced the TS for rainstorms by 10.4% and effectively balanced the Bias. These results highlight the efficacy of multi-source joint supervision in enhancing the capture of extreme precipitation events.

DAE-KAN: A Kolmogorov-Arnold Network Model for High-Index Differential-Algebraic Equations

Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to Multi-Layer Perceptrons (MLPs) due to their superior function-fitting abilities in data-driven modeling. In this paper, we propose a novel framework, DAE-KAN, for solving high-index differential-algebraic equations (DAEs) by integrating KANs with Physics-Informed Neural Networks (PINNs). This framework not only preserves the ability of traditional PINNs to model complex systems governed by physical laws but also enhances their performance by leveraging the function-fitting strengths of KANs. Numerical experiments demonstrate that for DAE systems ranging from index-1 to index-3, DAE-KAN reduces the absolute errors of both differential and algebraic variables by 1 to 2 orders of magnitude compared to traditional PINNs. To assess the effectiveness of this approach, we analyze the drift-off error and find that both PINNs and DAE-KAN outperform classical numerical methods in controlling this phenomenon. Our results highlight the potential of neural network methods, particularly DAE-KAN, in solving high-index DAEs with substantial computational accuracy and generalization, offering a promising solution for challenging partial differential-algebraic equations.