# TSSM: Triaxial State Space Model for Global Station Weather Forecasting with Temporal-Variable-Historical Modeling

arXiv: https://arxiv.org/abs/2607.13101 · HTML: https://mlsanity.com/paper/2607.13101/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 68 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 30 of 37)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [ClimaX: A foundation model for weather and climate](https://mlsanity.com/paper/2301.10343/) (2023)
- [Skillful Precipitation Nowcasting using Deep Generative Models of Radar](https://mlsanity.com/paper/2104.00954/) (2021)
- [FuXi: A cascade machine learning forecasting system for 15-day global weather forecast](https://mlsanity.com/paper/2306.12873/) (2023)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [Earthformer: Exploring Space-Time Transformers for Earth System Forecasting](https://mlsanity.com/paper/2207.05833/) (2022)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [From News to Forecast: Integrating Event Analysis in LLM-Based Time Series Forecasting with Reflection](https://mlsanity.com/paper/2409.17515/) (2024)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [Time-FFM: Towards LM-Empowered Federated Foundation Model for Time Series Forecasting](https://mlsanity.com/paper/2405.14252/) (2024)
- [Skillful Twelve Hour Precipitation Forecasts using Large Context Neural Networks](https://mlsanity.com/paper/2111.07470/) (2021)
- [Merlin: Multi-View Representation Learning for Robust Multivariate Time Series Forecasting with Unfixed Missing Rates](https://mlsanity.com/paper/2506.12459/) (2025)
- [xLSTM-Mixer: Multivariate Time Series Forecasting by Mixing via Scalar Memories](https://mlsanity.com/paper/2410.16928/) (2024)

## Abstract (arXiv)

Global Station Weather Forecasting (GSWF) is pivotal for localized and extreme weather prediction over key regions. Despite efforts to exploit look-back windows, existing methods show limited accuracy gains and struggle with extreme events and error accumulation. These limitations stem from overreliance on short-term patterns, which are insufficient to capture chaotic weather dynamics, especially under partial observations. To address this problem, we propose a novel Triaxial State Space Model (TSSM) with a history-enhanced Temporal-VariableHistorical paradigm, which incorporates period-aligned historical weather data to compensate for long-term, large-scale periodic, and full-window weather patterns beyond the temporal lookback window. Specifically, TSSM stacks historical samples into period-aligned batches, where forecasting is causally supported by historical and current observations. Temporal, variable, and historical scanning are designed to capture axial temporal dependencies, variable correlations, and historical evolution. This structure is hierarchically shared to model seasonal to extreme events while alleviating misalignment across historical patterns. TSSM achieves SOTA performance on Weather-5K, the largest station weather dataset to date, with 10% and 61% gains in accuracy and extreme event metrics, and obtains 95% best or second-best results on human-involved datasets. Its advantages are more pronounced in long-horizon and iterative forecasting, reaching a 37.5% gain at 240h and up to 103.5% under a 48h times 5 iterative setting. Moreover, TSSM retains > 90% performance under up to 80% missing observations, compared with < 43% for baselines, demonstrating robustness and practical potential for reliable GSWF in global in-situ observation networks.