# Beyond Fixed Variables: Expanding-variate Time Series Forecasting via Flat Scheme and Spatio-temporal Focal Learning

arXiv: https://arxiv.org/abs/2502.15296 · HTML: https://mlsanity.com/paper/2502.15296/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 45 references that are in the map.
- First posted on arXiv 21 Feb 2025.

## Builds on (most cited first, 30 of 31)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [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)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [WeatherBench: A benchmark dataset for data-driven weather forecasting](https://mlsanity.com/paper/2002.00469/) (2020)
- [Unsupervised Representation Learning for Time Series with Temporal Neighborhood Coding](https://mlsanity.com/paper/2106.00750/) (2021)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Contrast Everything: A Hierarchical Contrastive Framework for Medical Time-Series](https://mlsanity.com/paper/2310.14017/) (2023)
- [TimesURL: Self-supervised Contrastive Learning for Universal Time Series Representation Learning](https://mlsanity.com/paper/2312.15709/) (2023)
- [MSGNet: Learning Multi-Scale Inter-Series Correlations for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2401.00423/) (2023)
- [TrafficStream: A Streaming Traffic Flow Forecasting Framework Based on Graph Neural Networks and Continual Learning](https://mlsanity.com/paper/2106.06273/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning to Factorize and Adapt: A Versatile Approach Toward Universal Spatio-Temporal Foundation Models](https://mlsanity.com/paper/2601.12083/) (2026)
- [From XXLTraffic to EvoXXLTraffic: Scaling Traffic Forecasting to Sensor-Evolving Networks](https://mlsanity.com/paper/2605.29768/) (2026)

## Abstract (arXiv)

Multivariate Time Series Forecasting (MTSF) has long been a key research focus. Traditionally, these studies assume a fixed number of variables, but in real-world applications, Cyber-Physical Systems often expand as new sensors are deployed, increasing variables in MTSF. In light of this, we introduce a novel task, Expanding-variate Time Series Forecasting (EVTSF). This task presents unique challenges, specifically (1) handling inconsistent data shapes caused by adding new variables, and (2) addressing imbalanced spatio-temporal learning, where expanding variables have limited observed data due to the necessity for timely operation. To address these challenges, we propose STEV, a flexible spatio-temporal forecasting framework. STEV includes a new Flat Scheme to tackle the inconsistent data shape issue, which extends the graph-based spatio-temporal modeling architecture into 1D space by flattening the 2D samples along the variable dimension, making the model variable-scale-agnostic while still preserving dynamic spatial correlations through a holistic graph. We introduce a novel Spatio-temporal Focal Learning strategy that incorporates a negative filter to resolve potential conflicts between contrastive learning and graph representation, and a focal contrastive loss as its core to guide the framework to focus on optimizing the expanding variables. We benchmark EVTSF performance using three real-world datasets and compare it against three potential solutions employing SOTA MTSF models tailored for EVSTF. Experimental results show that STEV significantly outperforms its competitors, particularly on expanding variables. Notably, STEV, with only 5% of observations from the expanding period, is on par with SOTA MTSF models trained with complete observations. Further exploration of various expanding strategies underscores the generalizability of STEV in real-world applications.