Energy usage prediction is important for various real-world applications, including grid management, infrastructure planning, and disaster response. Although a plethora of deep learning approaches have been proposed to perform this task, most of them either overlook the essential spatial correlations across households or fail to scale to individualized prediction, making them less effective for accurate fine-grained user-level prediction. In addition, due to the dynamic and uncertain nature of energy usage caused by various factors such as extreme weather events, quantifying uncertainty for reliable prediction is also significant, but it has not been fully explored in existing work. In this paper, we propose a unified framework called TrustEnergy for accurate and reliable user-level energy usage prediction. There are two key technical components in TrustEnergy, (i) a Hierarchical Spatiotemporal Representation module to efficiently capture both macro and micro energy usage patterns with a novel memory-augmented spatiotemporal graph neural network, and (ii) an innovative Sequential Conformalized Quantile Regression module to dynamically adjust uncertainty bounds to ensure valid prediction intervals over time, without making strong assumptions about the underlying data distribution. We implement and evaluate our TrustEnergy framework by working with an electricity provider in Florida, and the results show our TrustEnergy can achieve a 5.4% increase in prediction accuracy and 5.7% improvement in uncertainty quantification compared to state-of-the-art baselines.

As a typical problem of Spatiotemporal Resource Management, Time Series Supplier Allocation (TSSA) poses a complex NP-hard challenge, aimed at refining future order dispatching strategies to satisfy the trade-off between demands and maximum supply. The Black-Litterman (BL) model, which comes from financial portfolio management, offers a new perspective for the TSSA by balancing expected returns against insufficient supply risks. However, the BL model is not only constrained by manually constructed perspective matrices and spatio-temporal market dynamics but also restricted by the absence of supervisory signals and unreliable supplier data. To solve these limitations, we introduce the pioneering Deep Black-Litterman Model for TSSA, which innovatively adapts the BL model from financial domain to supply chain context. Specifically, DBLM leverages Spatio-Temporal Graph Neural Networks (STGNNs) to capture spatio-temporal dependencies for automatically generating future perspective matrices. Moreover, a novel Spearman rank correlation is designed as our DBLM supervise signal to navigate complex risks and interactions of the supplier. Finally, DBLM further uses a masking mechanism to counteract the bias of unreliable data, thus improving precision and reliability. Extensive experiments on two datasets demonstrate significant improvements of DBLM on TSSA.

Spatiotemporal prediction plays a critical role in numerous real-world applications such as urban planning, transportation optimization, disaster response, and pandemic control. In recent years, researchers have made significant progress by developing advanced deep learning models for spatiotemporal prediction. However, most existing models are deterministic, i.e., predicting only the expected mean values without quantifying uncertainty, leading to potentially unreliable and inaccurate outcomes. While recent studies have introduced probabilistic models to quantify uncertainty, they typically focus on a single phenomenon (e.g., taxi, bike, crime, or traffic crashes), thereby neglecting the inherent correlations among heterogeneous urban phenomena. To address the research gap, we propose a novel Graph Neural Network with Uncertainty Quantification, termed UQGNN for multivariate spatiotemporal prediction. UQGNN introduces two key innovations: (i) an Interaction-aware Spatiotemporal Embedding Module that integrates a multivariate diffusion graph convolutional network and an interaction-aware temporal convolutional network to effectively capture complex spatial and temporal interaction patterns, and (ii) a multivariate probabilistic prediction module designed to estimate both expected mean values and associated uncertainties. Extensive experiments on four real-world multivariate spatiotemporal datasets from Shenzhen, New York City, and Chicago demonstrate that UQGNN consistently outperforms state-of-the-art baselines in both prediction accuracy and uncertainty quantification. For example, on the Shenzhen dataset, UQGNN achieves a 5% improvement in both prediction accuracy and uncertainty quantification.

Graph Neural Networks (GNNs) deliver strong classification results but often suffer from poor calibration performance, leading to overconfidence or underconfidence. This is particularly problematic in high-stakes applications where accurate uncertainty estimates are essential. Existing post-hoc methods, such as temperature scaling, fail to effectively utilize graph structures, while current GNN calibration methods often overlook the potential of leveraging diverse input information and model ensembles jointly. In the paper, we propose Graph Ensemble Temperature Scaling (GETS), a novel calibration framework that combines input and model ensemble strategies within a Graph Mixture-of-Experts (MoE) architecture. GETS integrates diverse inputs, including logits, node features, and degree embeddings, and adaptively selects the most relevant experts for each node’s calibration procedure. Our method outperforms state-of-the-art calibration techniques, reducing expected calibration error (ECE) by $\geq$ 25% across 10 GNN benchmark datasets. Additionally, GETS is computationally efficient, scalable, and capable of selecting effective input combinations for improved calibration performance. The implementation is available at https://github.com/ZhuangDingyi/GETS/.

Spatiotemporal data modeling has long been a fundamental task across disciplines such as climate & environmental science, and transportation engineering.A typical goal is to estimate unknown information at specific spatiotemporal points based on partially observed data-for example, interpolating weather conditions at unmeasured locations, reconstructing missing historical records, or forecasting the future trajectories of financial markets.These are all core tasks within the broader scope of spatiotemporal modeling.This tutorial (1 hours) introduces a cohesive view of spatiotemporal data modeling, tracing the evolution from traditional statistical approaches to modern deep learning paradigms.We begin by revisiting Kriging and time series decomposition to highlight the essential assumptions and strengths of these classical methods.Next, we explore low-rank matrix and tensor completion techniques, which leverage the structured patterns of spatiotemporal data.We then elaborate on spatiotemporal graph neural networks, which characterize complex dependencies by integrating graph structures with dynamic temporal features.Finally, we discuss recent advances in applying large foundation models to spatiotemporal tasks, including their capabilities and current limitations.Throughout the tutorial, we emphasize how lessons from traditional methods-such as the importance of locality, periodicity, and smoothness priors-can inspire new directions for developing and fine-tuning foundation models in the spatiotemporal domain.We conclude by outlining key challenges and opportunities in bridging classical wisdom with emerging AI capabilities.

Spatiotemporal systems are ubiquitous in a large number of scientific areas, representing underlying knowledge and patterns in the data. Here, a fundamental question usually arises as how to understand and characterize these spatiotemporal systems with a certain data-driven machine learning framework. In this work, we introduce an unsupervised pattern discovery framework, namely, dynamic autoregressive tensor factorization. Our framework is essentially built on the fact that the spatiotemporal systems can be well described by the time-varying autoregression on multivariate or even multidimensional data. In the modeling process, tensor factorization is seamlessly integrated into the time-varying autoregression for discovering spatial and temporal modes/patterns from the spatiotemporal systems in which the spatial factor matrix is assumed to be orthogonal. To evaluate the framework, we apply it to several real-world spatiotemporal datasets, including fluid flow dynamics, international import/export merchandise trade, and urban human mobility. On the international trade dataset with dimensions {country/region, product type, year}, our framework can produce interpretable import/export patterns of countries/regions, while the low-dimensional product patterns are also important for classifying import/export merchandise and understanding systematical differences between import and export. On the ridesharing mobility dataset with dimensions {origin, destination, time}, our framework is helpful for identifying the shift of spatial patterns of urban human mobility that changed between 2019 and 2022. Empirical experiments demonstrate that our framework can discover interpretable and meaningful patterns from the spatiotemporal systems that are both time-varying and multidimensional.

Quantifying uncertainty is crucial for robust and reliable predictions. However, existing spatiotemporal deep learning mostly focuses on deterministic prediction, overlooking the inherent uncertainty in such prediction. Particularly, highly-granular spatiotemporal datasets are often sparse, posing extra challenges in prediction and uncertainty quantification. To address these issues, this paper introduces a novel post-hoc Sparsity-aware Uncertainty Calibration (SAUC) framework, which calibrates uncertainty in both zero and non-zero values. To develop SAUC, we firstly modify the state-of-the-art deterministic spatiotemporal Graph Neural Networks (ST-GNNs) to probabilistic ones in the pre-calibration phase. Then we calibrate the probabilistic ST-GNNs for zero and non-zero values using quantile approaches. Through extensive experiments, we demonstrate that SAUC can effectively fit the variance of sparse data and generalize across two real-world spatiotemporal datasets at various granularities. Specifically, our empirical experiments show a 20% reduction in calibration errors in zero entries on the sparse traffic accident and urban crime prediction. Overall, this work demonstrates the theoretical and empirical values of the SAUC framework, thus bridging a significant gap between uncertainty quantification and spatiotemporal prediction.

Recent studies have significantly improved the prediction accuracy of travel demand using graph neural networks. However, these studies largely ignored uncertainty that inevitably exists in travel demand prediction. To fill this gap, this study proposes a framework of probabilistic graph neural networks (Prob-GNN) to quantify the spatiotemporal uncertainty of travel demand. This Prob-GNN framework is substantiated by deterministic and probabilistic assumptions, and empirically applied to the task of predicting the transit and ridesharing demand in Chicago. We found that the probabilistic assumptions (e.g. distribution tail, support) have a greater impact on uncertainty prediction than the deterministic ones (e.g. deep modules, depth). Among the family of Prob-GNNs, the GNNs with truncated Gaussian and Laplace distributions achieve the highest performance in transit and ridesharing data. Even under significant domain shifts, Prob-GNNs can predict the ridership uncertainty in a stable manner, when the models are trained on pre-COVID data and tested across multiple periods during and after the COVID-19 pandemic. Prob-GNNs also reveal the spatiotemporal pattern of uncertainty, which is concentrated on the afternoon peak hours and the areas with large travel volumes. Overall, our findings highlight the importance of incorporating randomness into deep learning for spatiotemporal ridership prediction. Future research should continue to investigate versatile probabilistic assumptions to capture behavioral randomness, and further develop methods to quantify uncertainty to build resilient cities.

Understanding Origin-Destination (O-D) travel demand is crucial for transportation management. However, traditional spatial-temporal deep learning models grapple with addressing the sparse and long-tail characteristics in high-resolution O-D matrices and quantifying prediction uncertainty. This dilemma arises from the numerous zeros and over-dispersed demand patterns within these matrices, which challenge the Gaussian assumption inherent to deterministic deep learning models. To address these challenges, we propose a novel approach: the Spatial-Temporal Tweedie Graph Neural Network (STTD). The STTD introduces the Tweedie distribution as a compelling alternative to the traditional 'zero-inflated' model and leverages spatial and temporal embeddings to parameterize travel demand distributions. Our evaluations using real-world datasets highlight STTD's superiority in providing accurate predictions and precise confidence intervals, particularly in high-resolution scenarios. GitHub code is available online(https://github.com/STTDAnonymous/STTD).

This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as input to train learning algorithms. Different from previous studies, in this paper we propose a purely data-driven and model-free solution. We consider TSE as a spatiotemporal matrix completion/interpolation problem and apply spatiotemporal delay embedding to transform the original incomplete matrix into a fourth-order Hankel structured tensor. By imposing a low-rank assumption on this tensor structure, we can approximate and characterize both global patterns and local patterns in a data-driven manner. We use a truncated nuclear norm of a balanced spatiotemporal unfolding to approximate the tensor rank and develop an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve the problem. The proposed framework only involves two hyperparameters, spatial and temporal window lengths, which are easy to set given the degree of data sparsity. To validate the effectiveness of our proposed method, we conducted numerical experiments on real-world high-resolution trajectory data, which demonstrated its superiority in some challenging scenarios. The proposed method shows great potential for solving the TSE problem using sparse observations from mobile sensors and can be applied in various traffic applications.

Origin-Destination (O-D) travel demand prediction is a fundamental challenge in transportation. Recently, spatial-temporal deep learning models demonstrate the tremendous potential to enhance prediction accuracy. However, few studies tackled the uncertainty and sparsity issues in fine-grained O-D matrices. This presents a serious problem, because a vast number of zeros deviate from the Gaussian assumption underlying the deterministic deep learning models. To address this issue, we design a Spatial-Temporal Zero-Inflated Negative Binomial Graph Neural Network (STZINB-GNN) to quantify the uncertainty of the sparse travel demand. It analyzes spatial and temporal correlations using diffusion and temporal convolution networks, which are then fused to parameterize the probabilistic distributions of travel demand. The STZINB-GNN is examined using two real-world datasets with various spatial and temporal resolutions. The results demonstrate the superiority of STZINB-GNN over benchmark models, especially under high spatial-temporal resolutions, because of its high accuracy, tight confidence intervals, and interpretable parameters. The sparsity parameter of the STZINB-GNN has physical interpretation for various transportation applications.

Recent studies have demonstrated the great success of graph convolutional networks in short-term traffic forecasting (e.g., 15–30 min ahead) tasks by capturing dependencies in road network structure. Based on these models, long-term forecasting can be achieved by two approaches: (1) recursively generating a one-step-ahead prediction and (2) adapting the models to sequence-to-sequence (seq2seq) learning. However, in practice, these two approaches often show poor performance in long-term forecasting tasks. The recursive approach suffers from the error accumulation problem, as the model is trained based on one-step-ahead loss. On the other hand, seq2seq shows convergence issues that limit its application. To address the issues for long-term forecasting, in this paper, we propose a universal framework that directly transforms any existing state-of-the-art models for one-step-ahead prediction to achieve more accurate long-term forecasting. The proposed framework consists of two components—a base model and a bias block. The base model is assumed to be a well-trained state-of-the-art one-step-ahead forecasting model, and the bias block is constructed by a spatiotemporal graph neural network composed of gated temporal convolution layers and graph convolution layers. The base model and the bias block are residually-connected so that we can substantially reduce the training complexity. Extensive experiments are conducted on existing benchmark datasets. We experiment with several state-of-the-art models in the literature as base models, and our results demonstrate the ability of the proposed universal framework to greatly improve the long-term prediction accuracy for all models.

Time series forecasting and spatiotemporal kriging are the two most important tasks in spatiotemporal data analysis. Recent research on graph neural networks has made substantial progress in time series forecasting, while little attention has been paid to the kriging problem---recovering signals for unsampled locations/sensors. Most existing scalable kriging methods (e.g., matrix/tensor completion) are transductive, and thus full retraining is required when we have a new sensor to interpolate. In this paper, we develop an Inductive Graph Neural Network Kriging (IGNNK) model to recover data for unsampled sensors on a network/graph structure. To generalize the effect of distance and reachability, we generate random subgraphs as samples and the corresponding adjacency matrix for each sample. By reconstructing all signals on each sample subgraph, IGNNK can effectively learn the spatial message passing mechanism. Empirical results on several real-world spatiotemporal datasets demonstrate the effectiveness of our model. In addition, we also find that the learned model can be successfully transferred to the same type of kriging tasks on an unseen dataset. Our results show that: 1) GNN is an efficient and effective tool for spatial kriging; 2) inductive GNNs can be trained using dynamic adjacency matrices; 3) a trained model can be transferred to new graph structures and 4) IGNNK can be used to generate virtual sensors.