Changhoon Song

Yesom Park, Changhoon Song, Myungjoo Kang

Physics-informed neural networks (PINNs) have recently emerged as effective methods for solving partial differential equations (PDEs) in various problems. Substantial research focuses on the failure modes of PINNs due to their frequent inaccuracies in predictions. However, most are based on the premise that minimizing the loss function to zero causes the network to converge to a solution of the governing PDE. In this study, we prove that PINNs encounter a fundamental issue that the premise is invalid. We also reveal that this issue stems from the inability to regulate the behavior of the derivatives of the predicted solution. Inspired by the \textit{derivative pathology} of PINNs, we propose a \textit{variable splitting} strategy that addresses this issue by parameterizing the gradient of the solution as an auxiliary variable. We demonstrate that using the auxiliary variable eludes derivative pathology by enabling direct monitoring and regulation of the gradient of the predicted solution. Moreover, we prove that the proposed method guarantees convergence to a generalized solution for second-order linear PDEs, indicating its applicability to various problems.

Changhoon Song, Teng Yuan Chang, Youngjoon Hong

Accurate forecasting of extreme weather events such as heavy rainfall or storms is critical for risk management and disaster mitigation. Although high-resolution radar observations have spurred extensive research on nowcasting models, precipitation nowcasting remains particularly challenging due to pronounced spatial locality, intricate fine-scale rainfall structures, and variability in forecasting horizons. While recent diffusion-based generative ensembles show promising results, they are computationally expensive and unsuitable for real-time applications. In contrast, deterministic models are computationally efficient but remain biased toward normal rainfall. Furthermore, the benchmark datasets commonly used in prior studies are themselves skewed--either dominated by ordinary rainfall events or restricted to extreme rainfall episodes--thereby hindering general applicability in real-world settings. In this paper, we propose exPreCast, an efficient deterministic framework for generating finely detailed radar forecasts, and introduce a newly constructed balanced radar dataset from the Korea Meteorological Administration (KMA), which encompasses both ordinary precipitation and extreme events. Our model integrates local spatiotemporal attention, a texture-preserving cubic dual upsampling decoder, and a temporal extractor to flexibly adjust forecasting horizons. Experiments on established benchmarks (SEVIR and MeteoNet) as well as on the balanced KMA dataset demonstrate that our approach achieves state-of-the-art performance, delivering accurate and reliable nowcasts across both normal and extreme rainfall regimes.