# DSFNet: Learning Dual-Domain Spectral Operators for Multi-Modality Spatio-Temporal Forecasting in Urban Transportation Systems

arXiv: https://arxiv.org/abs/2606.07695 · HTML: https://mlsanity.com/paper/2606.07695/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Builds on (most cited first, 27 of 27)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [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)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [TSLANet: Rethinking Transformers for Time Series Representation Learning](https://mlsanity.com/paper/2404.08472/) (2024)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)
- [Spatial-Temporal-Decoupled Masked Pre-training for Spatiotemporal Forecasting](https://mlsanity.com/paper/2312.00516/) (2023)
- [Dynamic Frequency Domain Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/2312.11933/) (2023)
- [AutoSTF: Decoupled Neural Architecture Search for Cost-Effective Automated Spatio-Temporal Forecasting](https://mlsanity.com/paper/2409.16586/) (2024)
- [Multi-Modality Spatio-Temporal Forecasting via Self-Supervised Learning](https://mlsanity.com/paper/2405.03255/) (2024)
- [Gateformer: Advancing Multivariate Time Series Forecasting through Temporal and Variate-Wise Attention with Gated Representations](https://mlsanity.com/paper/2505.00307/) (2025)
- [Fine-Grained Traffic Inference from Road to Lane via Spatio-Temporal Graph Node Generation](https://mlsanity.com/paper/2507.19089/) (2025)
- [Spatio-temporal modeling and forecasting with Fourier neural operators](https://mlsanity.com/paper/2601.01813/) (2026)

## Abstract (arXiv)

Multi-Modality Spatio-Temporal Forecasting (MoSTF) extends traditional spatio-temporal forecasting by incorporating diverse traffic modalities. Despite significant recent strides in spatio-temporal modeling, existing approaches often fail to explicitly model the coupling relationships between different modality variables. Accurate MoSTF is challenging, as it requires modeling (1) temporal dynamic heterogeneity under exogenous influences and (2) heterogeneous spatial dependencies alongside complex cross-variable couplings. To address these challenges, we propose the Dual-Domain Spectral Filtering Network (DSFNet). Our framework employs dual-domain spectral filtering to capture heterogeneous spatial patterns and explicitly model the relationships between variables. Unlike graph-based message passing or dense attention over node-modality pairs, DSFNet factorizes space-modality interactions into feature-domain and spatial-domain spectral operators, enabling scalable modeling of nonlocal dependencies and cross-modality couplings. Furthermore, we introduce an external gating mechanism to adaptively regulate temporal dynamics under external influences. We validate our method through extensive experiments on five representative real-world traffic datasets. Compared with the second-best baselines, DSFNet reduces MAE by 3.21%-10.16% across these datasets. The results demonstrate that DSFNet significantly outperforms existing state-of-the-art baselines in accuracy while exhibiting efficiency and robustness.