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

Huyen Ngoc Tran, Dung Trung Tran, Hong Nguyen, Xuan Vu Phan, Nam-Phong Nguyen

Abstract

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.

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

Abstract

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.

Paper Structure

This paper contains 12 sections, 6 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Data Preprocessing and Feature Engineering
  5. Proposed Framework: Matrix Profile-Guided MoE
  6. Hybrid Objective Function
  7. Experiments and Results
  8. Experimental Settings
  9. Comparative Performance
  10. Ablation Study
  11. Limitations and Future Work
  12. Conclusion

Figures (3)

  • Figure 1: Schematic overview of the proposed MP-MoE framework. Panel A (left) illustrates the inference workflow where the learnable gating network processes large-scale physical features to assign importance weights to fixed NWP experts dynamically. Panel B (right) details the training strategy using a hybrid loss function. Unlike standard MSE, which imposes severe penalties for temporal shifts, the proposed matrix profile-guided objective scans a symmetric search window to minimize structural distance, thereby prioritizing shape fidelity over rigid alignment.
  • Figure 2: Comparative visualization of forecast trajectories. The proposed MP-MoE ($\lambda=0.6$, solid red line) effectively captures high-intensity peaks and rapid onsets compared to the ground truth (black dashed line), whereas traditional baselines exhibit significant peak-shaving effects in the Ban Nhung and Song Chay basins.
  • Figure 3: Sensitivity analysis (at Ban Nhung) of the hyperparameter $\lambda$ which regulates the trade-off between the intensity-based MSE loss and the Modified MP loss. The dual-axis chart shows MAE and CSI-M on the left axis, and DTW distance on the right axis.