M2FMoE: Multi-Resolution Multi-View Frequency Mixture-of-Experts for Extreme-Adaptive Time Series Forecasting

Forecasting time series with extreme events is critical yet challenging due to their high variance, irregular dynamics, and sparse but high-impact nature. While existing methods excel in modeling dominant regular patterns, their performance degrades significantly during extreme events, constituting the primary source of forecasting errors in real-world applications. Although some approaches incorporate auxiliary signals to improve performance, they still fail to capture extreme events' complex temporal dynamics. To address these limitations, we propose M 2 FMoE, an extremeadaptive forecasting model that learns both regular and extreme patterns through multi-resolution and multi-view frequency modeling. It comprises three modules: (1) a multiview frequency mixture-of-experts module assigns experts to distinct spectral bands in Fourier and Wavelet domains, with cross-view shared band splitter aligning frequency partitions and enabling inter-expert collaboration to capture both dominant and rare fluctuations; (2) a multi-resolution adaptive fusion module that hierarchically aggregates frequency features from coarse to fine resolutions, enhancing sensitivity to both short-term variations and sudden changes; (3) a temporal gating integration module that dynamically balances longterm trends and short-term frequency-aware features, improving adaptability to both regular and extreme temporal patterns. Experiments on real-world hydrological datasets with extreme patterns demonstrate that M 2 FMoE outperforms state-of-the-art baselines without requiring extreme-event labels. Code are available at: https://github.com/Yaohui- Huang/M2FMoE .