graph-based spatio-temporal forecasting

Existing graph deep learning approaches for multivariate time series forecasting predominantly focus on architectural innovations, lacking systematic methodology studies on problem formalization, model design principles, and evaluation paradigms. This paper introduces the first unified methodology framework for graph-enhanced time series forecasting. It formally defines the forecasting problem by modeling dynamic inter-variable dependencies via learnable graph structures. It establishes principled design guidelines integrating graph neural networks (GNNs), spatiotemporal modeling, and deep temporal models (e.g., TCN and Informer variants). Furthermore, it proposes a reproducible evaluation protocol with built-in mechanisms to ensure interpretability and scalability. The framework shifts forecasting model development from empiricism toward first-principles reasoning, providing standardized guidance for relation-aware global modeling and articulating key open challenges. (149 words)

To address high model complexity and poor interpretability in long-term multivariate time series forecasting, this paper proposes Lite-STGNN, a lightweight spatiotemporal graph neural network. Methodologically, it introduces (1) a decomposition-driven lightweight spatiotemporal coupling architecture that jointly performs trend-seasonal decomposition and temporal modeling; and (2) a conservative temporal gating mechanism combined with low-rank Top-K sparse graph learning to preserve locality, enhance interpretability, and enable dynamic topology discovery. Evaluated on four benchmark datasets for 720-step-ahead forecasting, Lite-STGNN achieves state-of-the-art accuracy. It reduces parameter count by 62% and accelerates training by 3.8× over Transformer-based baselines. Ablation studies quantify performance gains of 4.6% and 3.3% attributable to the spatial module and Top-K graph learning, respectively.

Addressing spatiotemporal forecasting under high sensor missingness (e.g., in traffic and meteorology), this paper proposes a novel graph-enhanced spatiotemporal modeling architecture. Methodologically, it introduces a first-of-its-kind 3D MLP-Mixer structure, integrated with graph-structure-aware patch-level subgraph partitioning encoding, jointly capturing local spatial dependencies and long-range spatiotemporal–feature correlations. A missingness-aware mechanism is further incorporated to enhance robustness under sparse observations. Experiments on four benchmark datasets—AQI, ENGRAD, PV-US, and METR-LA—demonstrate that the method significantly outperforms state-of-the-art approaches under high missingness (>50%), especially in long-horizon forecasting (12–24 steps), exhibiting superior generalization and enhanced long-range dependency modeling. The core contribution lies in the deep integration of subgraph partitioning encoding with spatiotemporal MLP-Mixer, establishing a scalable and highly robust paradigm for missingness-intensive spatiotemporal forecasting.

Real-world spatiotemporal data arrive in streams, and the underlying graph structure dynamically expands—posing dual challenges for online forecasting: inefficient model retraining and catastrophic forgetting. To address this, we propose the first prompt-tuning framework for dynamic spatiotemporal graphs, grounded in two principles—*expansion* and *compression*. Our method employs a reusable, continuous prompt pool to retain historical knowledge while enabling rapid adaptation to newly added nodes or time intervals. It integrates lightweight prompt fine-tuning of spatiotemporal graph neural networks, dynamic prompt pool management, and joint optimization. Evaluated on multiple real-world traffic and environmental datasets, our approach consistently outperforms state-of-the-art methods. Crucially, it achieves superior prediction accuracy, training efficiency, and cross-scenario generalization while introducing fewer than 0.5% additional parameters.

Existing model evaluation methods for spatiotemporal data—characterized by co-occurring missingness and heterogeneity, strong nonlinearity, and nonstationarity—lack interpretability and robustness. Method: We propose the first assumption-free, distribution-agnostic residual correlation diagnostic framework. It quantifies residual dependence structures across spatiotemporal dimensions via spatiotemporal graph modeling and asymptotically distribution-free autocorrelation statistics, enabling precise localization of local underfitting regions. Crucially, it imposes no prior assumptions on data distribution or underlying dynamics and natively supports interpretability assessment for sparse observations and nonlinear models—including spatiotemporal graph neural networks. Results: Extensive validation on synthetic and real-world datasets demonstrates that our framework accurately identifies performance-weak subregions, significantly enhancing the targeting and efficiency of model iteration.

This work addresses the performance degradation of graph-structured multivariate time series forecasting under data-scarce and cross-domain transfer scenarios by proposing a structure-aware context selection mechanism within a transfer-oriented spatiotemporal graph learning framework. The approach incorporates an explicit graph context pruning strategy as an inductive bias, leveraging information-theoretic measures and correlation-based criteria to select informative subgraphs and features. This selection module is seamlessly integrated into a spatiotemporal convolutional architecture, enhancing both sample efficiency and out-of-distribution generalization. Evaluated under low-data transfer settings on large-scale traffic benchmark datasets, the proposed model significantly outperforms existing baseline methods.

This study addresses the modeling, generation, and prediction of dynamic network trajectories—such as time-varying graph structures observed in electroencephalography, gene regulatory networks, or financial markets. The authors propose embedding sequences of time-varying sparse precision matrices into Euclidean space via the log-Euclidean metric and introduce, for the first time, a conditional flow matching (CFM) model to learn their distribution. A geometry-aware decoder is integrated to guarantee the positive definiteness of generated matrices, and a history-based extrapolation strategy is developed for fine-tuned forecasting. Experiments on EEG motor imagery, chaotic dynamical systems, and gene expression datasets demonstrate that the generated trajectories preserve class-discriminative structures and significantly outperform baseline methods that directly model raw signals in predicting future connectivity patterns.

This work addresses the “temporal illusion” challenge in urban spatiotemporal forecasting, where nearly identical short-term inputs can lead to drastically divergent future evolutions—a phenomenon that existing spatiotemporal graph neural networks (STGNNs) struggle to discern. To enhance model robustness and generalization, we propose MP3, a plug-and-play multi-period pattern pretraining plugin. MP3 employs edge convolution to model multi-scale temporal dynamics, bottleneck projection combined with a global memory bank to capture heterogeneous spatial dependencies, and a causally enhanced Transformer to characterize cross-period temporal relationships. The plugin seamlessly integrates into mainstream STGNN architectures and consistently improves performance across five real-world datasets, reducing average MAE by 4.7% and RMSE by 5.0%, thereby significantly strengthening resilience against temporal illusions.