Towards Invariant Time Series Forecasting in Smart Cities

TL;DR

This work tackles the challenge of out-of-distribution generalization in location-aware time series forecasting for smart cities, where geographic domain shifts hinder cross-city predictions. It introduces InvarNet, comprising Invar-LSTM and Invar-Transformer, which leverage invariant risk minimization to learn representations that are stable across urban environments; predictions are produced via an invariant weight mechanism $w_{inv}$ so that $Y=H\circ w_{inv}$. The authors develop IRM-based training objectives, validate on synthetic data with environment-dependent noise and on real-world air-quality data from Beijing, Shenzhen, and Guangzhou, and demonstrate improved robustness over standard TS models, with transformer-based variants often performing best. The results suggest that enforcing invariance across locations enhances forecasting reliability in smart-city applications and can extend to climate modeling and urban planning tasks. The approach provides a scalable, causally aware framework for robust, cross-location time series forecasting in heterogeneous urban landscapes, with room for integrating regression extensions in future work. The core mathematical insight centers on invariant objectives, including $\min_\phi \sum_{e} \mathcal{R}^e(\phi) + \lambda \cdot \mathrm{Var}(\mathcal{R}^1(\phi), ..., \mathcal{R}^m(\phi))$ for variance-based risk extrapolation and IRM-style gradient penalties in the feature space.

Abstract

In the transformative landscape of smart cities, the integration of the cutting-edge web technologies into time series forecasting presents a pivotal opportunity to enhance urban planning, sustainability, and economic growth. The advancement of deep neural networks has significantly improved forecasting performance. However, a notable challenge lies in the ability of these models to generalize well to out-of-distribution (OOD) time series data. The inherent spatial heterogeneity and domain shifts across urban environments create hurdles that prevent models from adapting and performing effectively in new urban environments. To tackle this problem, we propose a solution to derive invariant representations for more robust predictions under different urban environments instead of relying on spurious correlation across urban environments for better generalizability. Through extensive experiments on both synthetic and real-world data, we demonstrate that our proposed method outperforms traditional time series forecasting models when tackling domain shifts in changing urban environments. The effectiveness and robustness of our method can be extended to diverse fields including climate modeling, urban planning, and smart city resource management.

Figures (6)

• Figure 1: Train a time series forecasting model (TSModel) using observational data from city A and subsequently applied it to forecast for city B and C.
• Figure 2: Invar-LSTM for Location-Aware Time Series Forecasting.
• Figure 3: Visualization of the Geographic Distribution of Cities.
• Figure 4: Temporal Invariance (Left Solid Line) and Spurious (Left Dotted Line) Relationship, Spatial Invariance (Right Solid Line) and Spurious (Right Dotted Line) Relationship.
• Figure 5: Test Error Variation in Env-Type=2 Setting.