Spatio-temporal forecasting is critical in applications such as traffic prediction, energy demand modeling, and weather monitoring. While Graph Attention Networks (GATs) are popular for modeling spatial dependencies, they rely on predefined adjacency structures and dynamic attention scores, introducing inductive biases and computational overhead that can obscure interpretability. We propose InterGAT, a simplified alternative to GAT that replaces masked attention with a fully learnable, symmetric node interaction matrix, capturing latent spatial relationships without relying on fixed graph topologies. Our framework, InterGAT-GRU, which incorporates a GRU-based temporal decoder, outperforms the baseline GAT-GRU in forecasting accuracy, achieving at least a 21% improvement on the SZ-Taxi dataset and a 6% improvement on the Los-Loop dataset across all forecasting horizons (15 to 60 minutes). Additionally, we observed reduction in training time by 60-70% compared to GAT-GRU baseline. Crucially, the learned interaction matrix reveals interpretable structure: it recovers sparse, topology-aware attention patterns that align with community structure. Spectral and clustering analyses show that the model captures both localized and global dynamics, offering insights into the functional topology driving predictions. This highlights how structure learning can simultaneously support prediction, computational efficiency, and topological interpretabil-ity in dynamic graph-based domains.
Spatio-temporal forecasting is crucial in many domains, such as transportation, meteorology, and energy. However, real-world scenarios frequently present challenges such as signal anomalies, noise, and distributional shifts. Existing solutions primarily enhance robustness by modifying network architectures or training procedures. Nevertheless, these approaches are computationally intensive and resource-demanding, especially for large-scale applications. In this paper, we explore a novel test-time computing paradigm, namely learning with calibration, ST-TTC, for spatio-temporal forecasting. Through learning with calibration, we aim to capture periodic structural biases arising from non-stationarity during the testing phase and perform real-time bias correction on predictions to improve accuracy. Specifically, we first introduce a spectral-domain calibrator with phase-amplitude modulation to mitigate periodic shift and then propose a flash updating mechanism with a streaming memory queue for efficient test-time computation. ST-TTC effectively bypasses complex training-stage techniques, offering an efficient and generalizable paradigm. Extensive experiments on real-world datasets demonstrate the effectiveness, universality, flexibility and efficiency of our proposed method.
Accurate predictions of spatio-temporal systems' states are crucial for tasks such as system management, control, and crisis prevention. However, the inherent time variance of spatio-temporal systems poses challenges to achieving accurate predictions whenever stationarity is not granted. To address non-stationarity frameworks, we propose a Distribution and Relation Adaptive Network (DRAN) capable of dynamically adapting to relation and distribution changes over time. While temporal normalization and de-normalization are frequently used techniques to adapt to distribution shifts, this operation is not suitable for the spatio-temporal context as temporal normalization scales the time series of nodes and possibly disrupts the spatial relations among nodes. In order to address this problem, we develop a Spatial Factor Learner (SFL) module that enables the normalization and de-normalization process in spatio-temporal systems. To adapt to dynamic changes in spatial relationships among sensors, we propose a Dynamic-Static Fusion Learner (DSFL) module that effectively integrates features learned from both dynamic and static relations through an adaptive fusion ratio mechanism. Furthermore, we introduce a Stochastic Learner to capture the noisy components of spatio-temporal representations. Our approach outperforms state of the art methods in weather prediction and traffic flows forecasting tasks. Experimental results show that our SFL efficiently preserves spatial relationships across various temporal normalization operations. Visualizations of the learned dynamic and static relations demonstrate that DSFL can capture both local and distant relationships between nodes. Moreover, ablation studies confirm the effectiveness of each component.
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.
Data-driven benchmarks have led to significant progress in key scientific modeling domains including weather and structural biology. Here, we introduce the Zebrafish Activity Prediction Benchmark (ZAPBench) to measure progress on the problem of predicting cellular-resolution neural activity throughout an entire vertebrate brain. The benchmark is based on a novel dataset containing 4d light-sheet microscopy recordings of over 70,000 neurons in a larval zebrafish brain, along with motion stabilized and voxel-level cell segmentations of these data that facilitate development of a variety of forecasting methods. Initial results from a selection of time series and volumetric video modeling approaches achieve better performance than naive baseline methods, but also show room for further improvement. The specific brain used in the activity recording is also undergoing synaptic-level anatomical mapping, which will enable future integration of detailed structural information into forecasting methods.
Spatiotemporal forecasting is critical in applications such as traffic prediction, climate modeling, and environmental monitoring. However, the prevalence of missing data in real-world sensor networks significantly complicates this task. In this paper, we introduce the Temporal Graph MLP-Mixer (T-GMM), a novel architecture designed to address these challenges. The model combines node-level processing with patch-level subgraph encoding to capture localized spatial dependencies while leveraging a three-dimensional MLP-Mixer to handle temporal, spatial, and feature-based dependencies. Experiments on the AQI, ENGRAD, PV-US and METR-LA datasets demonstrate the model's ability to effectively forecast even in the presence of significant missing data. While not surpassing state-of-the-art models in all scenarios, the T-GMM exhibits strong learning capabilities, particularly in capturing long-range dependencies. These results highlight its potential for robust, scalable spatiotemporal forecasting.
In many problem settings that require spatio-temporal forecasting, the values in the time-series not only exhibit spatio-temporal correlations but are also influenced by spatial diffusion across locations. One such example is forecasting the concentration of fine particulate matter (PM2.5) in the atmosphere which is influenced by many complex factors, the most important ones being diffusion due to meteorological factors as well as transport across vast distances over a period of time. We present a novel Spatio-Temporal Graph Neural Network architecture, that specifically captures these dependencies to forecast the PM2.5 concentration. Our model is based on an encoder-decoder architecture where the encoder and decoder parts leverage gated recurrent units (GRU) augmented with a graph neural network (TransformerConv) to account for spatial diffusion. Our model can also be seen as a generalization of various existing models for time-series or spatio-temporal forecasting. We demonstrate the model's effectiveness on two real-world PM2.5 datasets: (1) data collected by us using a recently deployed network of low-cost PM$_{2.5}$ sensors from 511 locations spanning the entirety of the Indian state of Bihar over a period of one year, and (2) another publicly available dataset that covers severely polluted regions from China for a period of 4 years. Our experimental results show our model's impressive ability to account for both spatial as well as temporal dependencies precisely.
Next-generation reservoir computing (NG-RC) has attracted much attention due to its excellent performance in spatio-temporal forecasting of complex systems and its ease of implementation. This paper shows that NG-RC can be encoded as a kernel ridge regression that makes training efficient and feasible even when the space of chosen polynomial features is very large. Additionally, an extension to an infinite number of covariates is possible, which makes the methodology agnostic with respect to the lags into the past that are considered as explanatory factors, as well as with respect to the number of polynomial covariates, an important hyperparameter in traditional NG-RC. We show that this approach has solid theoretical backing and good behavior based on kernel universality properties previously established in the literature. Various numerical illustrations show that these generalizations of NG-RC outperform the traditional approach in several forecasting applications.
Large-scale human mobility exhibits spatial and temporal patterns that can assist policymakers in decision making. Although traditional prediction models attempt to capture these patterns, they often interfered by non-periodic public events, such as disasters and occasional celebrations. Since regular human mobility patterns are heavily affected by these events, estimating their causal effects is critical to accurate mobility predictions. Although news articles provide unique perspectives on these events in an unstructured format, processing is a challenge. In this study, we propose a causality-augmented prediction model, called CausalMob, to analyze the causal effects of public events. We first utilize large language models (LLMs) to extract human intentions from news articles and transform them into features that act as causal treatments. Next, the model learns representations of spatio-temporal regional covariates from multiple data sources to serve as confounders for causal inference. Finally, we present a causal effect estimation framework to ensure event features remain independent of confounders during prediction. Based on large-scale real-world data, the experimental results show that the proposed model excels in human mobility prediction, outperforming state-of-the-art models.
Urban spatio-temporal (ST) forecasting is crucial for various urban applications such as intelligent scheduling and trip planning. Previous studies focus on modeling ST correlations among urban locations in offline settings, which often neglect the non-stationary nature of urban ST data, particularly, distribution shifts over time. This oversight can lead to degraded performance in real-world scenarios. In this paper, we first analyze the distribution shifts in urban ST data, and then introduce DOST, a novel online continual learning framework tailored for ST data characteristics. DOST employs an adaptive ST network equipped with a variable-independent adapter to address the unique distribution shifts at each urban location dynamically. Further, to accommodate the gradual nature of these shifts, we also develop an awake-hibernate learning strategy that intermittently fine-tunes the adapter during the online phase to reduce computational overhead. This strategy integrates a streaming memory update mechanism designed for urban ST sequential data, enabling effective network adaptation to new patterns while preventing catastrophic forgetting. Experimental results confirm DOST's superiority over state-of-the-art models on four real-world datasets, providing online forecasts within an average of 0.1 seconds and achieving a 12.89% reduction in forecast errors compared to baseline models.
Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle to capture this variability. To address this, data-driven approaches learn parametric PDEs by sampling a very large variety of trajectories with varying PDE parameters. We first show that incorporating conditioning mechanisms for learning parametric PDEs is essential and that among them, $\textit{adaptive conditioning}$, allows stronger generalization. As existing adaptive conditioning methods do not scale well with respect to the number of parameters to adapt in the neural solver, we propose GEPS, a simple adaptation mechanism to boost GEneralization in Pde Solvers via a first-order optimization and low-rank rapid adaptation of a small set of context parameters. We demonstrate the versatility of our approach for both fully data-driven and for physics-aware neural solvers. Validation performed on a whole range of spatio-temporal forecasting problems demonstrates excellent performance for generalizing to unseen conditions including initial conditions, PDE coefficients, forcing terms and solution domain. $\textit{Project page}$: https://geps-project.github.io
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This inference cost is the major obstacle to deploying GNN models with \emph{online prediction} to reflect the potentially dynamic node features. To address this, we propose an approach to reduce the number of nodes that are included during aggregation. We achieve this through a sparse decomposition, learning to approximate node representations using a weighted sum of linearly transformed features of a carefully selected subset of nodes within the extended neighbourhood. The approach achieves linear complexity with respect to the average node degree and the number of layers in the graph neural network. We introduce an algorithm to compute the optimal parameters for the sparse decomposition, ensuring an accurate approximation of the original GNN model, and present effective strategies to reduce the training time and improve the learning process. We demonstrate via extensive experiments that our method outperforms other baselines designed for inference speedup, achieving significant accuracy gains with comparable inference times for both node classification and spatio-temporal forecasting tasks.
The widespread deployment of sensing devices leads to a surge in data for spatio-temporal forecasting applications such as traffic flow, air quality, and wind energy. Although spatio-temporal graph neural networks have achieved success in modeling various static spatio-temporal forecasting scenarios, real-world spatio-temporal data are typically received in a streaming manner, and the network continuously expands with the installation of new sensors. Thus, spatio-temporal forecasting in streaming scenarios faces dual challenges: the inefficiency of retraining models over newly arrived data and the detrimental effects of catastrophic forgetting over long-term history. To address these challenges, we propose a novel prompt tuning-based continuous forecasting method, following two fundamental tuning principles guided by empirical and theoretical analysis: expand and compress, which effectively resolve the aforementioned problems with lightweight tuning parameters. Specifically, we integrate the base spatio-temporal graph neural network with a continuous prompt pool, utilizing stored prompts (i.e., few learnable parameters) in memory, and jointly optimize them with the base spatio-temporal graph neural network. This method ensures that the model sequentially learns from the spatio-temporal data stream to accomplish tasks for corresponding periods. Extensive experimental results on multiple real-world datasets demonstrate the multi-faceted superiority of our method over the state-of-the-art baselines, including effectiveness, efficiency, universality, etc.
Spatio-temporal forecasting is a critical component of various smart city applications, such as transportation optimization, energy management, and socio-economic analysis. Recently, several automated spatio-temporal forecasting methods have been proposed to automatically search the optimal neural network architecture for capturing complex spatio-temporal dependencies. However, the existing automated approaches suffer from expensive neural architecture search overhead, which hinders their practical use and the further exploration of diverse spatio-temporal operators in a finer granularity. In this paper, we propose AutoSTF, a decoupled automatic neural architecture search framework for cost-effective automated spatio-temporal forecasting. From the efficiency perspective, we first decouple the mixed search space into temporal space and spatial space and respectively devise representation compression and parameter-sharing schemes to mitigate the parameter explosion. The decoupled spatio-temporal search not only expedites the model optimization process but also leaves new room for more effective spatio-temporal dependency modeling. From the effectiveness perspective, we propose a multi-patch transfer module to jointly capture multi-granularity temporal dependencies and extend the spatial search space to enable finer-grained layer-wise spatial dependency search. Extensive experiments on eight datasets demonstrate the superiority of AutoSTF in terms of both accuracy and efficiency. Specifically, our proposed method achieves up to 13.48x speed-up compared to state-of-the-art automatic spatio-temporal forecasting methods while maintaining the best forecasting accuracy.
The primary environmental health threat in the WHO European Region is air pollution, impacting the daily health and well-being of its citizens significantly. To effectively understand the impact, and dynamics of air quality a detailed investigation of different environmental, weather, and land cover indices is appropriate. To this end, this paper introduces three European cities’ spatiotemporal datasets, customized for air pollution monitoring at a regional level. The datasets are composed of major air quality, weather measurements and land use information. The duration is approximately from 2020 to 2023 with an hourly temporal resolution and a spatial resolution of 0.005°. The temporal and spatiotemporal datasets are publicly released aiming to provide a solid foundation for researchers, analysts, and practitioners to conduct in-depth analyses of air pollution dynamics.
Spatio-temporal forecasting is pivotal in numerous real-world applications, including transportation planning, energy management, and climate monitoring. In this work, we aim to harness the reasoning and generalization abilities of Pre-trained Language Models (PLMs) for more effective spatio-temporal forecasting, particularly in data-scarce scenarios. However, recent studies uncover that PLMs, which are primarily trained on textual data, often falter when tasked with modeling the intricate correlations in numerical time series, thereby limiting their effectiveness in comprehending spatio-temporal data. To bridge the gap, we propose RePST, a physics-aware PLM reprogramming framework tailored for spatio-temporal forecasting. Specifically, we first propose a physics-aware decomposer that adaptively disentangles spatially correlated time series into interpretable sub-components, which facilitates PLM to understand sophisticated spatio-temporal dynamics via a divide-and-conquer strategy. Moreover, we propose a selective discrete reprogramming scheme, which introduces an expanded spatio-temporal vocabulary space to project spatio-temporal series into discrete representations. This scheme minimizes the information loss during reprogramming and enriches the representations derived by PLMs. Extensive experiments on real-world datasets show that the proposed RePST outperforms twelve state-of-the-art baseline methods, particularly in data-scarce scenarios, highlighting the effectiveness and superior generalization capabilities of PLMs for spatio-temporal forecasting.
Spatio-temporal forecasting is crucial in transportation, logistics, and supply chain management. However, current methods struggle with large, complex datasets. We propose a dynamic, multi-modal approach that integrates the strengths of traditional forecasting methods and instruction tuning of small language models for time series trend analysis. This approach utilizes a mixture of experts (MoE) architecture with parameter-efficient fine-tuning (PEFT) methods, tailored for consumer hardware to scale up AI solutions in low resource settings while balancing performance and latency tradeoffs. Additionally, our approach leverages related past experiences for similar input time series to efficiently handle both intra-series and inter-series dependencies of non-stationary data with a time-then-space modeling approach, using grouped-query attention, while mitigating the limitations of traditional forecasting techniques in handling distributional shifts. Our approach models predictive uncertainty to improve decision-making. Our framework enables on-premises customization with reduced computational and memory demands, while maintaining inference speed and data privacy/security. Extensive experiments on various real-world datasets demonstrate that our framework provides robust and accurate forecasts, significantly outperforming existing methods.
Spatio-temporal forecasting plays a crucial role in various sectors such as transportation systems, logistics, and supply chain management. However, existing methods are limited by their ability to handle large, complex datasets. To overcome this limitation, we introduce a hybrid approach that combines the strengths of open-source large and small-scale language models (LLMs and LMs) with traditional forecasting methods. We augment traditional methods with dynamic prompting and a grouped-query, multi-head attention mechanism to more effectively capture both intra-series and inter-series dependencies in evolving nonlinear time series data. In addition, we facilitate on-premises customization by fine-tuning smaller open-source LMs for time series trend analysis utilizing descriptions generated by open-source large LMs on consumer-grade hardware using Low-Rank Adaptation with Activation Memory Reduction (LoRA-AMR) technique to reduce computational overhead and activation storage memory demands while preserving inference latency. We combine language model processing for time series trend analysis with traditional time series representation learning method for cross-modal integration, achieving robust and accurate forecasts. The framework effectiveness is demonstrated through extensive experiments on various real-world datasets, outperforming existing methods by significant margins in terms of forecast accuracy.
In the geospatial domain, universal representation models are significantly less prevalent than their extensive use in natural language processing and computer vision. This discrepancy arises primarily from the high costs associated with the input of existing representation models, which often require street views and mobility data. To address this, we develop a novel, training-free method that leverages large language models (LLMs) and auxiliary map data from OpenStreetMap to derive geolocation representations (LLMGeovec). LLMGeovec can represent the geographic semantics of city, country, and global scales, which acts as a generic enhancer for spatio-temporal learning. Specifically, by direct feature concatenation, we introduce a simple yet effective paradigm for enhancing multiple spatio-temporal tasks including geographic prediction (GP), long-term time series forecasting (LTSF), and graph-based spatio-temporal forecasting (GSTF). LLMGeovec can seamlessly integrate into a wide spectrum of spatio-temporal learning models, providing immediate enhancements. Experimental results demonstrate that LLMGeovec achieves global coverage and significantly boosts the performance of leading GP, LTSF, and GSTF models. Our codes are available at \url{https://github.com/Umaruchain/LLMGeovec}.
Spatiotemporal forecasting of traffic flow data represents a typical problem in the field of machine learning, impacting urban traffic management systems. In general, spatiotemporal forecasting problems involve complex interactions, nonlinearities, and long-range dependencies due to the interwoven nature of the temporal and spatial dimensions. Due to this, traditional statistical and machine learning methods cannot adequately handle the temporal and spatial dependencies in these complex traffic flow datasets. A prevalent approach in the field combines graph convolutional networks and multi-head attention mechanisms for spatiotemporal processing. This paper proposes a wavelet-based temporal attention model, namely a wavelet-based dynamic spatiotemporal aware graph neural network (W-DSTAGNN), for tackling the traffic forecasting problem. Wavelet decomposition can help by decomposing the signal into components that can be analyzed independently, reducing the impact of non-stationarity and handling long-range dependencies of traffic flow datasets. Benchmark experiments using three popularly used statistical metrics confirm that our proposal efficiently captures spatiotemporal correlations and outperforms ten state-of-the-art models (including both temporal and spatiotemporal benchmarks) on three publicly available traffic datasets. Our proposed ensemble method can better handle dynamic temporal and spatial dependencies and make reliable long-term forecasts. In addition to point forecasts, our proposed model can generate interval forecasts that significantly enhance probabilistic forecasting for traffic datasets.