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

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. Additionally, 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. To evaluate the effectiveness of STEV, we benchmark EVTSF performance on three real-world datasets from various domains and compare it against three potential solutions employing state-of-the-art (SOTA) MTSF models tailored for EVSTF. Experimental results show that STEV significantly outperforms its competitors, especially in handling expanding variables. Notably, STEV, with only 5% of observations during the expanding period, is on par with SOTA MTSF models trained with complete data. Further exploration of various expanding scenarios underscores the generalizability of STEV in real-world applications.