# More Sensors Only One Field: Rethinking Continual Spatio-Temporal Forecasting

arXiv: https://arxiv.org/abs/2609.31325 · HTML: https://mlsanity.com/paper/2609.31325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 25 Sep 2026.

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

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [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)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Fredformer: Frequency Debiased Transformer for Time Series Forecasting](https://mlsanity.com/paper/2406.09009/) (2024)
- [TrafficStream: A Streaming Traffic Flow Forecasting Framework Based on Graph Neural Networks and Continual Learning](https://mlsanity.com/paper/2106.06273/) (2021)
- [Continual Graph Learning: A Survey](https://mlsanity.com/paper/2301.12230/) (2023)
- [STAEformer: Spatio-Temporal Adaptive Embedding Makes Vanilla Transformer SOTA for Traffic Forecasting](https://mlsanity.com/paper/2308.10425/) (2023)
- [Efficient Traffic Prediction Through Spatio-Temporal Distillation](https://mlsanity.com/paper/2501.10459/) (2025)
- [Lifelong Learning on Evolving Graphs Under the Constraints of Imbalanced Classes and New Classes](https://mlsanity.com/paper/2112.10558/) (2021)
- [Expand and Compress: Exploring Tuning Principles for Continual Spatio-Temporal Graph Forecasting](https://mlsanity.com/paper/2410.12593/) (2024)
- [Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting](https://mlsanity.com/paper/2506.00635/) (2025)
- [Pseudo-Differential Neural Operator: Generalized Fourier Neural Operator for Learning Solution Operators of Partial Differential Equations](https://mlsanity.com/paper/2201.11967/) (2022)
- [Temporal Neural Operator for Modeling Time-Dependent Physical Phenomena](https://mlsanity.com/paper/2504.20249/) (2025)
- [STRAP: Spatio-Temporal Pattern Retrieval for Out-of-Distribution Generalization](https://mlsanity.com/paper/2505.19547/) (2025)
- [Decoupling Spatio-Temporal Prediction: When Lightweight Large Models Meet Adaptive Hypergraphs](https://mlsanity.com/paper/2505.19620/) (2025)

## Abstract (arXiv)

Continual spatio-temporal forecasting supports traffic management and environmental monitoring under evolving dynamics and expanding sensor networks. However, conventional graph-based continual learning methods tie forecasting representations to the current sensor layout, so sensor expansion can alter the representation of learned spatial relationships. Our key insight is that sensor expansion changes the evidence available about a process without necessarily changing the dynamics to be learned. We propose STFO (Spatio-Temporal Field Operator), which parameterizes forecasting knowledge as a shared field-evolution operator and handles changing sensor layouts through observation and query interfaces. Normalized coordinate-based aggregation lifts irregular sensor histories onto a fixed latent grid, enabling reuse of learned spatial maps across observation sets without sensor-specific parameters. To accommodate process drift, a spectral descriptor summarizes variation across spatial scales and conditions Fourier propagation and attention to adapt operator responses to the current spatial regime. Coordinate-based decoding queries the evolved field at sensor locations and combines spatial corrections with local-history predictions. Experiments on PEMS-Stream, CA-Stream, and AIR-Stream demonstrate state-of-the-art average forecasting performance. STFO-Large reduces average MAE over DOL by 8.4% on PEMS-Stream and 4.7% on CA-Stream. Our code is available at https://github.com/Xielewei/Spatio-Temporal-Field-Operator.