MP-MoE: Matrix Profile-Guided Mixture of Experts for Precipitation Forecasting

Precipitation forecasting remains a persistent challenge in tropical regions like Vietnam, where complex topography and convective instability often limit the accuracy of Numerical Weather Prediction (NWP) models. While data-driven post-processing is widely used to mitigate these biases, most existing frameworks rely on point-wise objective functions, which suffer from the ``double penalty'' effect under minor temporal misalignments. In this work, we propose the Matrix Profile-guided Mixture of Experts (MP-MoE), a framework that integrates conventional intensity loss with a structural-aware Matrix Profile objective. By leveraging subsequence-level similarity rather than point-wise errors, the proposed loss facilitates more reliable expert selection and mitigates excessive penalization caused by phase shifts. We evaluate MP-MoE on rainfall datasets from two major river basins in Vietnam across multiple horizons, including 1-hour intensity and accumulated rainfall over 12, 24, and 48 hours. Experimental results demonstrate that MP-MoE outperforms raw NWP and baseline learning methods in terms of Mean Critical Success Index (CSI-M) for heavy rainfall events, while significantly reducing Dynamic Time Warping (DTW) values. These findings highlight the framework's efficacy in capturing peak rainfall intensities and preserving the morphological integrity of storm events.