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.

Urban mobility data has significant connections with economic growth and plays an essential role in various smart-city applications. Due to privacy concerns and substantial data collection costs, fine-grained human mobility trajectories are challenging to make publicly available on a large scale. A promising solution to address this issue is trajectory synthesizing, which generates synthetic trajectories that preserve aggregate spatiotemporal distributions. However, existing works often neglect the road network structural constraints or rely on instance-level external supervision, thus limiting their scalability in generating fine-grained and high-fidelity trajectories. In this paper, we propose Cardiff, a coarse-to-fine Cascaded hybrid diffusion-based framework for fine-grained and structure-plausible trajectory generation. By leveraging the hierarchical nature of urban mobility, Cardiff decomposes the generation process into two cascaded levels, i.e., discrete road segment-level and continuous fine-grained GPS-level: (i) At the segment level, to reduce computational costs and redundancy in raw trajectories, we first encode the discrete road segments into low-dimensional latent embeddings and design a diffusion transformer-based latent denoising network for segment-level synthesis. (ii) Taking the first stage of generation as conditions, we then design a fine-grained GPS-level conditional denoising network with a noise augmentation mechanism to achieve road-network-constrained and fine-grained generation. The cascaded progressive generation yields high-fidelity fine-grained trajectories while adhering to road geometry and topology constraints. Experimental results on three large real-world trajectory datasets demonstrate that our method outperforms state-of-the-art baselines in various metrics. The code is available at~ https://github.com/urban-mobility-generation/Cardiff.

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 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.

Public transit systems are the backbone of urban mobility systems in the era of urbanization. The design of transit schedules is important for the efficient and sustainable operation of public transit. However, limited studies have considered demand uncertainties when designing transit schedules. To better address demand uncertainty issues inherent in public transit systems, this paper utilizes the robust optimization (RO) framework to generate robust transit schedules against demand uncertainty. A nominal (non-robust) optimization model for the transit frequency setting problem (TFSP) under a single transit line setting is first proposed. The model is then extended to the RO-based formulation to incorporate demand uncertainty, which has not been considered in the literature. The large-scale origin-destination (OD) matrices for real-world transit problems bring computational challenges in solving the optimization problem. To efficiently generate robust transit schedules, a Transit Downsizing (TD) approach is proposed to reduce the dimensionality of the problem. The proposed models are tested with real-world transit lines and data from the Chicago Transit Authority (CTA). Meanwhile, a stochastic programming (SP) framework is used to construct a benchmark stochastic TFSP model. Compared to the current transit schedule implemented by the CTA, the nominal TFSP model without considering demand uncertainty reduces passengers’ wait times while increasing in-vehicle travel times. After incorporating demand uncertainty, both stochastic and robust TFSP models reduce passengers’ wait times and in-vehicle travel times simultaneously. The robust transit schedules outperform the benchmark stochastic transit schedules by reducing both wait and in-vehicle travel times when demand is significantly uncertain.

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.

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.

With millions of people using ride-hailing platforms for daily travel, estimated time of arrival (ETA) has become a significant problem in intelligent transportation systems and attracted considerable attention recently. Deep learning-based ETA methods have achieved promising results using massive spatial-temporal data. However, we find that the prediction accuracy is not satisfactory in practical applications due to the prevalent data sparsity problems. Instead of focusing on the average prediction performance as many other methods, this study aims to alleviate the data sparsity problems in ETA to enhance user experience. In general, the data sparsity problems arise from two aspects. The first is the road network, where many links are only traversed by few floating cars. The second aspect is drivers, where many drivers’ trajectories are too scarce (e.g., with only 3 trip records). To alleviate the sparsity in road network, we propose a Road Network Metric Learning framework for ETA (RNML-ETA), where an auxiliary metric learning task is used to improve the link-embedding, especially for links with insufficient data. A novel triangle loss is proposed to improve metric learning effectiveness for links. Experiments on massive real-world data show that RNML-ETA outperforms competing methods by promoting the cold links with limited data. Furthermore, we propose a novel unified framework to Alleviate Data Sparsity problems in ETA (ADS-ETA) by extending RNML-ETA with an additional auxiliary task for driver ID embedding. Results with extensive experiments demonstrate that ADS-ETA can effectively alleviate the data sparsity problems caused by road network and driver sparsity.