Spatiotemporal GNNs

Terrestrial water storage (TWS) integrates snow, soil moisture, surface water, and groundwater and is a key indicator of how climate variability and human activity reshape the global water cycle. The GRACE and GRACE-FO satellite missions provide the only direct, globally consistent observations of TWS change, but their record only begins in 2002 which is too short for many climate-scale analyses. We present a deep learning application that reconstructs monthly GRACE-like TWS anomalies (TWSA) back to 1940 by learning the relationship between daily ERA5 meteorological forcing (precipitation, evapotranspiration, runoff) and monthly GRACE observations. In contrast to prior reconstruction approaches based on grid-cell-wise regression, CNNs, or LSTMs, we adapt a multi-variate time series graph neural network (MTGNN) architecture, which was originally developed for mobility and traffic forecasting on urban sensor networks to this satellite-geodesy task. Spatial dependencies are encoded in a static, interpretable hybrid adjacency matrix that combines geodesic proximity with lagged correlations of climatic time series, capturing both local hydrological coupling and large-scale teleconnections. The reconstruction achieves a grid-cell Pearson correlation of 0.69, a basin-mean correlation of 0.94, and a near-zero bias, and it reproduces the spatial fingerprints of the 2015/16 El Niño and 2020/21 La Niña events. A systematic comparison with established reconstruction approaches (GTWS-MLrec, RM-REC, GRAiCE) shows that the graph-based model is statistically competitive at basin scale, reaching a correlation within 0.025 of the best baseline while using only roughly half to a tenth of the predictors the other models require and revealing characteristic weaknesses in arid regions in all models. The complete implementation is publicly available at github.com/hcu-cml/MTGNN-TWS-Reconstruction-GRACE

Origin-Destination (OD) demand prediction is fundamental to intelligent transportation systems, yet real-world OD flows are often dynamically sparse, long-tailed, and characterized by heterogeneous zero-flow patterns. These properties make it difficult to distinguish whether an OD connection is active from how much demand it generates once activated. Many existing methods primarily treat OD prediction as a single flow regression task, which limits their ability to model low-frequency, intermittent, and long-tailed OD interactions. To address these challenges, we propose SAGMTL, a Structure-Aware Graph Multi-Task Learning framework for dynamic sparse OD demand prediction. SAGMTL decomposes OD prediction into structural state modeling and flow intensity estimation, jointly learning regional activity states, OD connection activity, and edge-level flow intensity within a unified framework. Specifically, a node-edge collaborative representation module captures regional semantics, temporal dynamics, and spatial priors through interactive node-edge updates, producing structure-aware representations for dynamic OD interactions. Based on these representations, SAGMTL estimates OD flows by jointly modeling stable demand patterns and short-term fluctuations. A multi-constraint objective further improves sparsity awareness and structural consistency. Experiments on three real-world urban mobility datasets from Beijing, Chengdu, and Nanjing show that SAGMTL achieves superior overall performance compared with state-of-the-art baselines. Further analysis demonstrates that explicitly modeling regional activity, connection states, and flow intensity improves the robustness of dynamic sparse OD demand prediction.

High-fidelity simulation of spatiotemporal dynamics is computationally prohibitive, necessitating efficient super-resolution techniques to reconstruct high-resolution data from coarse-grained inputs. Traditional data-driven methods often lack physical constraints, and simple physics-informed learning struggles with irregular spatial geometries and intricately evolving temporal dynamics. To tackle these challenges, we propose a Physics-augmented Koopman-enhanced Graph Convolutional Network (P-K-GCN) for spatiotemporal super-resolution on irregular geometries. Specifically, a continuous spline-based GCN is first designed to extract spatial dependencies directly from coarse graph, and Koopman operator theory is incorporated to project the nonlinear dynamics into a compact latent space where temporal progression is linearized. Second, we augment the optimization objective with a physics-based loss to force the data-driven reconstructions to adhere to physical laws for improving predictive fidelity and robustness. Finally, we provide a rigorous theoretical analysis, establishing that the physics augmentation and Koopman regularization mathematically guarantees a reduction in super-resolution error by diminishing Rademacher complexity and tightening generalization bounds. We evaluate our framework on reconstructing spatially high-resolution cardiac electrodynamics across a 3D heart geometry from sparse low-resolution measurements. Numerical experiments demonstrate that our method achieves superior accuracy compared to baseline models.

Neural Controlled Differential Equations (NCDE) provide a powerful continuous-time framework for forecasting time series, but standard graph-based extensions typically learn spatial structure purely from data, even in settings where a directed graph structure is known a priori. We introduce Informed Neural controlled Differential EQuationS (INDEQS), a modification to graph-based NCDE forecasting methods that incorporates prior knowledge of a directed graph at distinct architectural positions. INDEQS separates inner mixing of hidden states across graph nodes from outer mixing between vector field and control, and offers both a lightweight graph-constrained variant and a more expressive variant, learning additional graph connections from data via adaptive graph convolutions. To systematically study when graph informedness is beneficial in forecasting, we devise a continuous advection simulation on directed graphs, yielding synthetic spatio-temporal datasets with known ground-truth flow structure. We then evaluate INDEQS on two real-world tasks: river discharge forecasting on a hydrological network and traffic flow prediction on PeMS08. Across the synthetic and the river-discharge tasks, outer informedness consistently improves mean absolute error over an uninformed NCDE with comparable parameter count, particularly on larger graphs, while inner informedness offers a more parameter-efficient alternative when strict adherence to a known adjacency is desired. A comparison of discrete convolutional and continuous-time decoders further shows that continuous decoders yield better accuracy and greater temporal flexibility on real-world tasks. An implementation of INDEQS and the advection simulation is available at https://github.com/mitchi1/indeqs .

Top-soil organic carbon (SOC) prediction is fundamental to agricultural sustainability, land use policy and fertilization planning. Existing approaches face two limitations: they pair hand-crafted covariates with classical ML or single-modal deep models that miss rich spectral and temporal information, and grid-based architectures ignore the irregular spatial structure of field measurements. We introduce SpTGNN, a multi-modal spatio-temporal graph neural network addressing both. SpTGNN represents soil measurements as nodes in a heterogeneous graph with three edge types (spatial proximity, spectral similarity, elevation), and applies relational graph attention to learn separate patterns per relation. A fine-tuned TerraMind encoder extracts node features from Sentinel-2, Sentinel-1 and DEM signals, combined with per-sample environmental covariates and learned positional and temporal embeddings. A sparse Mixture-of-Experts module fuses the four streams via top-$k$ routing. Uncertainty is captured by pairing heteroscedastic regression (aleatoric) with deep ensembles (epistemic), and a Moran's $I$ penalty regularizes spatial autocorrelation. We evaluate on a global SOC corpus split into three regional instances ($\sim$49k samples globally, Africa $\sim$26k, Europe $\sim$14k). Our 5-member deep ensemble reports $R^2=0.762$, RMSE $=3.51\pm0.48$ g/kg and MAPE $=22.9\%$ on the Africa test split, improving over a tabular XGBoost baseline; the best single checkpoint reaches validation $R^2=0.864$. Ablations confirm the heterogeneous graph, MoE fusion and fine-tuned backbone each contribute substantively, and the ensemble UQ stack achieves post-calibration ECE of $0.031$ (hybrid) and $0.026$ ($β$-NLL). To our knowledge, this is the first framework to unify foundation-model feature extraction, heterogeneous graph attention and decomposed uncertainty quantification for SOC estimation.

Given their effectiveness in modeling the relational structure among network traffic flows, graph neural networks (GNNs) have been widely adopted in network intrusion detection systems (NIDSs). However, most existing GNN-based NIDS approaches focus on the relational structure of traffic flows, and treat them as temporally independent, which limits their ability to cope with evolving attack behaviors. Moreover, their reliance on supervised or semi-supervised learning often restricts generalization to unseen attacks. To address these limitations, we propose a novel self-supervised GNN-based framework. To the best of our knowledge, the proposed model is among the first self-supervised GNN-based NIDS models to explicitly leverage real timestamps, which provides faithful temporal dependencies for representation learning. We first construct a series of temporal graphs from network traffic flows according to their timestamps, and then employ an E-GraphSAGE and LSTM based encoder to fully extract temporal information and spatial dependencies of network traffic, without introducing time-costly attention mechanisms. A multi-view graph contrastive learning (GCL) scheme is introduced, where temporal, spatial, and feature contrasts are jointly performed to capture temporal continuity, preserve structural consistency, and improve the generalization and robustness of the learned representations, respectively. In addition, a gradient-norm-based adaptive weighting strategy is designed to optimize the contrastive loss weights. Experimental results on four representative NIDS datasets with real timestamps demonstrate that our method significantly outperforms existing self-supervised approaches and achieves performance comparable to the supervised state-of-the-art GNN method, while maintaining high computational efficiency.

Traffic state prediction is a fundamental task in intelligent transportation systems. In practical applications, some regions suffer from limited traffic observations due to insufficient sensing infrastructure, making cross-domain knowledge transfer an important solution for data-scarce traffic prediction. However, existing cross-domain traffic prediction methods still face several limitations, including coarse-grained source-target adaptation, limited capability in handling unseen target-domain patterns, and insufficient modeling of continuous traffic dynamics under irregular or heterogeneous temporal conditions. To address these issues, this paper proposes a continuous cross-domain traffic prediction framework, termed Memory-Augmented Graph Liquid Time-Constant Network (MA-GLTC). Specifically, we first construct spatio-temporal units (STUs) to decompose traffic networks into transferable local units, enabling fine-grained knowledge alignment across domains. Then, a graph liquid time-constant network (GLTC) is developed to model graph-coupled traffic evolution in continuous time. Different from generic graph neural ODE-based models, GLTC introduces graph-coupled recurrent conductance into liquid time-constant dynamics, allowing node states to evolve with leakage, adaptive time constants, and neighborhood-aware feedback. Furthermore, a Memory-based Transfer Storage (MTS) mechanism is designed to preserve source-domain knowledge, retrieve matched traffic patterns, and update reliable target-domain patterns when unseen states emerge. Experiments on five public traffic datasets demonstrate that MA-GLTC consistently outperforms representative innerdomain and cross-domain baselines in both short-term and longterm prediction tasks. Compared with the second-best method, MA-GLTC reduces the average prediction errors by 3.02%, 0.33%, 8.92%, 10.09%, and 2.11%, respectively.

Autonomous driving systems rely on precise trajectory prediction to plan safe and efficient movement. Graph Neural Networks (GNNs) have become a promising approach for modelling spatiotemporal interactions among road agents. However, designing GNN architectures for trajectory prediction remains non-standardized, with little guidance on which graph layers effectively capture spatial interactions and temporal dynamics. This paper offers a detailed comparative study of 19 graph layer types, focusing on their spatial and temporal processing capabilities to discover the most effective architectures for trajectory prediction. Within the explored hyperparameter setting, we highlight five standout layer combinations, with ARMA, Chebyshev, and topology-aware layers consistently performing better than others. Beyond performance metrics, our findings yield practical design principles: sum-based aggregation is more effective than mean-based methods, multi-head attention mechanisms enable richer interactions, and assigning different weights to different hop distances significantly improves prediction accuracy. These findings offer useful guidance for designing more interpretable and effective trajectory prediction models.

Spatio-Temporal forecasting is crucial in diverse fields, such as transportation, climate, and energy. Urban spatio-temporal data exhibits temporal mirage: similar short-window inputs have divergent future trends, and vice versa. Existing spatio-temporal graph neural networks (STGNNs) cannot effectively identify such mirages. We argue that the core reason lies in the short-window inputs that have incomplete period observation, heterogeneous global spatial correlation, and cross-period superposition causality. To bridge this gap, we develop a novel Multi- Period Pattern Pre-training (MP3), a plug-and-play pre-training plugin for distinguishing temporal mirages. MP3 presents two core innovations: (1) The multi-period pattern learning is designed to learn multi-period patterns from long time series. Specifically, multi-period temporal modeling leverages edge convolution to identify different multi-period patterns. Multi-period spatial modeling uses a bottleneck project and a global memory bank to capture heterogeneous global spatial relations efficiently. Cross-period pattern interaction employs a causality-enhanced Transformer to capture dependencies across different period patterns. (2) This plugin can seamlessly integrate into existing STGNN backbones to strengthen their forecasting performance. The experiment on five STGNN baselines across five real-world datasets (including a large-scale dataset CA) verify the effectiveness, superior scalability and strong adaptability of MP3, which brings consistent and robust performance improvements across all evaluated baselines. On average, MP3 reduces the MAE 4.7% and the RMSE 5.0%. The code can be available at https://github.com/YAN-outlook/MP3.

In this work, we present COGENT, a continuous graph emulator with Neural Ordinary Differential Equations for long-term physical forecasting on irregular geospatial meshes. COGENT encodes a finite history of system states and associated forcing fields and external forcings with a graph-based history encoder, producing node-wise context vectors that capture both local spatial interactions and temporal evolution. These context vectors initialize and condition a latent Neural Ordinary Differential Equation whose dynamics are driven by interpolated future forcings and explicit relative rollout time. By modeling the forecast trajectory as a continuous latent dynamical system, COGENT can generate predictions at arbitrary future times rather than being restricted to a fixed temporal discretization. A residual decoder maps the resulting latent trajectories back to future physical states, enabling direct multi-step forecasting without repeatedly feeding predicted states back into the model. This formulation combines graph-based spatial representation, history-conditioned latent dynamics, and continuous-time rollout in a unified framework for mesh-based physical simulation emulation. In order to stabilize training with long-horizon supervision, we also propose effective rollout-horizon sampling and a progressive rollout-horizon scheduling strategy. We evaluate COGENT on transient ice-sheet simulations generated by the Ice-sheet and Sea-level System Model, demonstrating improved long-range stability over autoregressive graph baselines. These results suggest that continuous graph Neural ODEs provide a promising methodology for scalable physical forecasting on irregular geospatial meshes, particularly in applications that require stable long-horizon predictions and the ability to query system states at arbitrary times.

Asynchronous, event-based graph neural networks (AEGNNs) have recently emerged as an efficient paradigm for processing the sparse and high-temporal-resolution data from event cameras. In this paper, we propose quantum analog AEGNNs (QA-AEGNNs), a novel framework to implement an AEGNN on a neutral-atom quantum computer. Neutral-atom quantum processors offer a programmable analog quantum computing platform based on controllable Rydberg-atom interactions. To this end, we map the streaming event data to an array of trapped neutral atoms, where each atom represents a graph node (event) and is positioned such that geometric proximity reflects the spatio-temporal neighborhood of events. The native Rydberg Hamiltonian of the quantum processor is programmed to mirror the message-passing computations of the AEGNN, with atomic qubit states serving as node feature embeddings and inter-atom interactions realizing graph edges. Furthermore, we propose a hybrid quantum-classical training scheme in which the analog Hamiltonian parameters (e.g., laser pulse amplitudes and detunings) are optimized using classical feedback to learn the quantum AEGNN model from data. Our approach leverages the continuous Hamiltonian dynamics and massive parallelism of neutral-atom quantum systems to natively execute event-based graph computations with potential accuracy improvements

Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations. We propose a coupled LSTM-GNN framework that links the temporal and spatial aspects of local stress field reconstruction. A Long Short-Term Memory network encodes macroscopic stress-strain sequences into a compact hidden state that captures the path-dependent constitutive response, while a physics-informed Graph Neural Network reconstructs the spatially-resolved stress field at each time step. We introduce a relative weighting strategy with linear warm-up to balance the data-driven reconstruction loss and a discrete divergence-based equilibrium penalty. This resolves the scale mismatch that prevents fixed-weight formulations from converging in the elasto-plastic regime. The model is trained on 10,000 non-proportional loading paths applied to a periodic plate-with-a-hole microstructure and von Mises elasto-plasticity. The model achieves three orders of magnitude speedup over finite element simulations and generalizes to loading sequences twice the training length, with 1.9% cumulative error. Because the graph relies on mesh connectivity instead of the specific element type, one trained surrogate can be applied directly without retraining to meshes with different element types and to both coarser and finer resolutions, while in all cases reproducing the high-fidelity quad-element FE field used during training. Indeed, the message passing characteristics inherent to GNN and MeshGraphNet architecture render the model mesh-agnostic. Analysis of the LSTM hidden states suggests a low-dimensional structure related to the internal state variables of the constitutive model.

Metal additive manufacturing enables the fabrication of complex parts, but achieving consistent build quality remains challenging due to interactions induced by repeated layer-wise melting, solidification, and reheating across the 3D build. Advanced sensing provide a great opportunity to collect rich observations of the actual manufacturing process for real-time quality monitoring and control. Yet, existing methods often have limited ability to represent multi-layer interactions and quantify their contributions to quality. In this paper, we develop a novel spatiotemporal graph transformer for modeling 3D neighborhood interactions and learn their effects on build quality in metal additive manufacturing. Specifically, we first introduce a weighted network representation of the manufacturing process, where fusing locations are modeled as nodes, and their spatial- and process-dependent relationships are encoded as edge weights. This representation also enables the integration of multimodal data (e.g., geometric design, process settings, and in-situ sensing data) into a unified structure for downstream learning tasks. Building on this network, we further design a dual-attention graph transformer that captures both within-node feature dependencies and cross-node neighborhood interactions for quality representation learning. Experimental results show that the proposed framework significantly outperforms image-based, sequence-based, and graph-based models in characterizing process-quality relationships. More importantly, the incorporation of cross-layer interactions is critical for improving quality prediction performance. This framework is broadly applicable to other tasks involving network modeling and graph-based representation learning.

Spatio-temporal graph neural networks (STGNNs) have become the dominant approach for traffic prediction, yet their computational requirements pose challenges for practical deployment in intelligent transportation systems (ITS). While recent work has proposed efficient alternatives to STGNNs, a fundamental question remains unexplored: are these architectures themselves over-parameterised? We examine this question using the Spatio-Temporal Graph Convolutional Network (STGCN), one of the most widely adopted models in this domain. Through systematic experiments across four diverse traffic datasets, we compare 1-block, 2-block (standard), and 3-block STGCN variants. Our findings reveal that the single-block architecture achieves optimal performance for short-term prediction (10 mins) on three of four datasets, while incurring only marginal degradation ($\leq$1.8% relative error) at longer horizons. Crucially, the 2-block variant incurs 61% higher CPU inference latency and 37% lower throughput relative to 1-block -- substantial overhead for resource-constrained ITS deployment. The 3-block architecture offers no favourable tradeoff, more than doubling computational cost for $<$0.5% relative improvement. These results suggest that the default 2-block STGCN may be over-parameterised for many applications, with implications for both practitioners deploying traffic prediction systems and researchers benchmarking efficiency-focused methods.

Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies. Graph neural networks (GNNs) provide a natural representation but typically rely on autoregressive rollouts and treat spatial and temporal dynamics separately, leading to error accumulation over long horizons. Existing approaches also focus on local interactions and short temporal contexts, limiting their ability to capture multi-hop dependencies and global structure. We introduce the Graph Mamba Operator (GraMO), a latent-space simulator that integrates state-space models with graph-based interaction learning. In contrast to prior work that sequences nodes or applies spatial and temporal updates in separate stages, GraMO couples graph-based interactions and temporal state updates within a single recurrence. The update is linear in the latent state, with input-dependent coefficients that adapt across regimes. We evaluate GraMO on N-body systems, motion capture, and robotics datasets, achieving the lowest error across benchmarks and the largest gains in long-horizon prediction.

This paper presents a unified system designed to support precision agriculture by integrating advanced weather prediction, crop recommendation, and a question-answering tool for farmers. We propose two deep learning models -- a Transformer-based Graph Neural Network and a Spatio-Temporal Graph Convolutional Network (STGCN) -- to forecast weather conditions for the next 30 days using data from 1,359 locations in Nepal. The STGCN outperforms the Transformer-based model in accuracy (MSE ~0.011 vs. 0.013), effectively modeling both spatial and temporal dependencies in climate data. These predictions are combined with static soil properties such as pH, moisture, and organic content to generate localized crop recommendations through a scoring algorithm that matches each crop's optimal growing conditions. Additionally, we develop a Retrieval-Augmented Generation (RAG) chatbot that leverages domain-specific agricultural documents to answer farmers' questions in natural language. The entire system is deployed via a mobile application, offering real-time suggestions and conversational support. User feedback confirms the system's usability and relevance, especially in rural settings where personalized farming guidance is limited. Overall, our approach demonstrates how combining machine learning models with local agricultural data can empower farmers with actionable insights, promoting more informed decisions, better crop yields, and increased resilience to climate variability.

Joint Species Distribution Modeling (JSDM) is a key enabler for biodiversity monitoring and conservation planning. However, accurate JSDM faces two coupled challenges: environmental drivers and species distributions are inherently spatio-temporal, while species co-occurrence patterns exhibit complex non-linear community structure and severe long-tail imbalance driven by rare species. Existing approaches often address these factors in isolation, learning from static covariates or neglecting the historical trajectories of dynamic community structure. To overcome these limitations, we propose STELLAR (Spatio-Temporal Environmental Learning with Latent Alignment and Refinement), a novel framework that learns a shared latent space where dynamic habitat context and community structure are optimized jointly. Our approach integrates three complementary components: (1) a Graph-Temporal Encoder that employs graph attention and recurrent units to aggregate spatial neighborhood effects and capture the co-evolving historical dynamics of environmental context and community structure; (2) a Context-Anchored Latent Alignment mechanism that structures the latent space using a label-activated mixture prior and supervised contrastive learning, actively clustering species based on shared environmental preferences; and (3) an Imbalance-Aware Decoupled Decoding module that utilizes Asymmetric Loss to focus learning on hard, rare species samples, preventing mode collapse in the long tail. Experiments on the large-scale eBird dataset, curated with domain experts, demonstrate that our framework significantly outperforms state-of-the-art baselines, particularly in predicting rare species and revealing interpretable species interactions.

Accurate vessel traffic flow prediction is crucial for smart port operations and navigational safety. However, maritime traffic flow data are often highly sparse with intermittent bursts, making robust forecasting challenging. Under such conditions, conventional spatio-temporal graph neural networks (ST-GNNs) can degrade toward conservative near-zero predictions and fail to capture non-zero activity. Although zero-inflated negative binomial (ZINB) models partially address excess zeros, their two-part formulation can still remain conservative around abrupt transitions. To address these issues, we propose a model-agnostic learnable Tweedie head that can be attached as a plug-and-play output module to arbitrary ST-GNN backbones. Instead of likelihood-based Tweedie training, which typically requires surrogate objectives, our approach optimizes the closed-form Tweedie unit deviance and predicts the mean for point forecasting while learning a node-level variance power to capture heterogeneous variability across port areas. Experiments on a maritime traffic graph constructed from real-world AIS data in the Port of Los Angeles and Long Beach show that the proposed head consistently improves RMSE across multiple ST-GNN backbones, especially on non-zero events, leading to more reliable forecasts for practical maritime traffic control.

Multi-object tracking (MOT) from UAV imagery presents unique challenges: altitude varies across sequences, objects are small and densely packed, and frequent occlusion causes identity switches. Existing graph-based trackers assume fixed spatial context and treat all objects uniformly, ignoring the heterogeneous lifecycle states of detections, active tracklets, and lost targets. We propose HDST-GNN, a Heterogeneous Dynamic Spatiotemporal Graph Neural Network with three novel contributions. First, Altitude-Adaptive Edge Construction estimates a camera-altitude proxy from mean object area and adjusts the graph connectivity radius accordingly. Second, Heterogeneous Node Representation models detections (Type-D), confirmed tracklets (Type-T), and lost tracklets (Type-L) as distinct node types with dedicated projections and typed edge relations. Third, Occlusion-Gated Temporal Aggregation gates each node's attention contribution by its occlusion confidence, preventing occluded nodes from corrupting neighbour embeddings. HDST-GNN is trained end-to-end with a differentiable Sinkhorn head using joint cross-entropy and triplet loss. On VisDrone2019-MOT with oracle detections, HDST-GNN achieves 94.51% MOTA and 97.24% IDF1, outperforming SORT by +5.0 MOTA points and reducing identity switches by 81%. With real YOLOv8n detections, HDST-GNN reduces identity switches by 49% vs. SORT. Ablation studies confirm the independent contribution of each component.

As urban environments continue to evolve rapidly, accurately modeling the dynamic behaviour of Points of Interest is essential for supporting data-driven urban planning and commercial decision-making. While recent advancements in spatio-temporal graph learning have improved POI forecasting, most methods rely on proximity-based graphs and correlation-driven modeling, which overlook the functional dependencies between POIs and fail to capture the causal effects of urban interventions. In this paper, we introduce a novel research problem -- cold-start POI check-in forecasting, which aims to predict the future check-in pattern of a newly introduced POI, by modeling its temporal evolution and functional interactions with nearby POIs in a structured urban spatial context. To address these challenges, we propose CausalPOI, a spatio-temporal graph-based causal representation learning framework. CausalPOI leverages Spatio-Temporal Functional Interaction Graph to model semantic and spatial relationships between POIs, and constructs structurally aligned treatment and control graphs to simulate factual and counterfactual scenarios. Extensive experiments on real-world SafeGraph datasets demonstrate that CausalPOI significantly outperforms state-of-the-art baselines across the board, validating its effectiveness in spatio-temporal forecasting, semantic interaction modeling, and causal effect estimation, providing a more interpretable and actionable foundation for urban intervention analysis. Source code is available at Github.

Traffic forecasting is a fundamental component of intelligent transportation systems, yet remains challenging in real-world settings due to irregular sensor distributions and the high computational cost of modeling large-scale spatiotemporal dependencies. In practical traffic networks, sensors are unevenly distributed across regions, leading to non-uniform spatial structures that limit the effectiveness and scalability of existing graph-based and attention-based models. To address these challenges, we propose PatchSTG, a patch-based spatiotemporal graph Transformer designed for efficient forecasting on irregular sensor networks. The key idea is to introduce a hierarchical spatial representation that partitions sensors into balanced, locality-preserving patches based on geographic information. On top of this structure, a dual attention encoder alternates between intra-patch attention for capturing local interactions and inter-patch attention for modeling global dependencies, reducing computational complexity from quadratic to near-linear scaling. We evaluate PatchSTG on real-world traffic data from Rhode Island and additional large-scale datasets. Experimental results demonstrate that the proposed model achieves stable and competitive forecasting performance across multiple horizons, while significantly improving computational efficiency. Ablation studies further validate the effectiveness of spatial partitioning and dual attention in capturing both local and long-range traffic dynamics. These results suggest that patch-based spatiotemporal modeling provides a scalable and effective framework for traffic forecasting under irregular spatial settings.

Industrial Internet systems face increasing threats from sophisticated industrial control system (ICS) attacks, resulting in critical safety incidents. However, existing tools exhibit limited effectiveness in real-time anomaly detection due to the complex dependencies among sensors and actuators. To tackle this, we present IstGPT, the first industrial anomaly detection tool based on LLMs and graph learning to provide real-time protection against a wide range of ICS attacks. IstGPT achieves fine-grained and precise modeling on spatial-temporal dependencies in industrial cyber-physical systems. It first leverages industrial multi-modal knowledge, including operational data, technical documents, and system diagrams, to extract sensor-actuator dependency graphs via multi-stage prompt engineering. Then, LLM-Optimation iteratively refines the graph based on node accuracy, edge consistency, and logical coherence. Finally, IstGPT integrated improved graph neural networks with an encoder-decoder architecture to detect anomalies via reconstruction errors. We evaluate IstGPT against 12 state-of-the-art baselines on 9 datasets, including 2 public, 6 simulated, and a real-world robotic arm dataset. IstGPT achieves the best F1-scores and eTaF1 (a newer time-aware metric) across nine datasets. We further discuss the feasibility of deploying IstGPT in real-world industrial scenarios.

Modeling spatial dependencies is central to spatiotemporal data analysis using Graph Neural Networks (GNNs). Traditional methods rely on distance-based kernels with predefined parameters, which restricts model capacity. Although generic adaptive mechanisms (e.g., Graph Attention Networks) offer flexibility, they often fail to capture the underlying geometric structure, performing worse than distance-based models in data-sparse scenarios. Addressing this, we revisit the kernel parameterization problem and theoretically prove that misspecified kernel parameters introduce unavoidable approximation errors in GNNs. To overcome this, we propose AdaKernel, a simple yet effective approach that learns adaptive kernel parameters within the neural network. Unlike methods that learn graph structures from scratch, AdaKernel adopts a structure-preserving strategy that optimizes the scale of physical interactions rather than discarding them. Extensive experiments on Kriging, Imputation, and Forecasting demonstrate that AdaKernel consistently improves various GNN architectures and outperforms model-agnostic adaptive baselines, validating that accurately learned kernel parameters are superior to both fixed priors and fully latent graph structures.

Passenger count data from public transit systems reveals urban mobility patterns and is essential for planning, operation, and optimisation. However, non-linear spatiotemporal interdependencies across stops and lines make modelling and prediction challenging. Existing approaches often rely on fixed temporal, spatial, or stop-level formulations, limiting their ability to capture within-trip evolution and network context. This study proposes SMT-GraphFormer, a spatiotemporal multi-task graph transformer that frames trip-level transit prediction as sequence-to-sequence modelling. Given a line's stop sequence and trip-level context, the model predicts successive boarding and alighting counts, with delay and dwell time treated as encoder-side surrogate tasks. Key components include graph embeddings for multi-relational stop similarity, a context encoder for weather and temporal information, and a multi-gate mixture-of-experts module that produces task-specific decoder representations for boarding and alighting predictions. Evaluation on public bus transit data from Trondheim, Norway, shows that SMT-GraphFormer outperforms stop-level tabular benchmarks, with ablation studies examining each component's contribution. The sequential formulation yields substantial gains on alighting prediction ($+$0.24 in $R^2$) and consistent improvements on boarding, delay, and dwell, confirming the value of explicit trip-level sequential bias and inter-target dependencies. These findings demonstrate the potential of transformer-based sequence modelling for capturing complex spatiotemporal dynamics in public transit and underscore the value of architectures tailored to transit data rather than off-the-shelf tabular models. The proposed framework provides a horizon-agnostic basis for scenario analysis in digital twin environments, supporting informed decision-making by planners and transit operators.

Graph anomaly detection methods aim to distinguish anomalous nodes. While prior methods characterize anomalies through increased variation in the spectral energy distributions, they overlook those that result in decreased variation, i.e., camouflaged anomalies that appear normal. We show that this type of anomaly persists across multiple datasets and remains undetectable by existing spectral approaches. To address this limitation, we propose a node-level spectral energy formulation that is fully compatible with message passing and enables the detection of camouflaged anomalies. Building on this formulation, we introduce an energy-aware graph learning framework that models spectral shifts through energy-driven message passing in both static and time-series graphs. Besides, our unified architecture extends to temporal settings without introducing specialized sequence modules, enabling efficient learning under long sliding windows. Extensive experiments on large-scale benchmarks demonstrate the effectiveness and scalability of our approach.

Spatio-temporal graph-based models have typically been used to forecast new cases of infectious diseases such as COVID-19 and chickenpox outbreaks. However, the use of stochastic modelling into their learning process has been surprisingly under-investigated and rarely considered entire data sets of large countries. As a result, it is unknown whether these models would provide accurate forecasts in real-world disease spread scenarios. In this work, we propose a spatio-temporal stochastic graph-based architecture that integrates a stochastic formulation and uncertainty approximation process to forecast new infectious disease cases. We find that our approach can adapt to encode large and small population geographical networks within a single model architecture. Using two real-world data sets, COVID-19 in the US and chickenpox in Hungary, we report an enhanced effect of the proposed architecture across predictions of the 2022 first wave for COVID-19 in the US and comparative results of chickenpox waves during 2012-2014 in Hungary. By benchmarking with four spatio-temporal graph-based models, quantitative results show competitive overall weekly performance of the proposed approach on forecasting new cases for all 3,218 US counties and all 20 Hungary counties. The proposed approach can represent overall epidemic progression relative to baselines, though with a one-step delay; while exhibiting a reduced sensitivity to high-frequency and low-amplitude variability.

Spatio-temporal forecasting on sensor graphs is commonly tackled with a single backbone architecture applied uniformly across all nodes, although graph regions can exhibit different dynamics. Road segments differ in functional class, structure, and traffic behavior, suggesting that node-wise expert specialization can be useful. We propose GC-MoE, a graph-conditioned mixture of experts framework that assigns each node a personalized combination of frozen forecasting experts based on graph topology and the recent traffic input window. GC-MoE combines frozen pretrained spatio-temporal GNN experts with an input-aware, spatially contextualized router while training only a lightweight routing module. We also study a bounded graph-conditioned output refinement layer as an optional extension and include node-adaptive ST-LoRA adapters only as an ablation diagnostic. Across four standard benchmarks (PEMS04, PEMS07, METR-LA, and PEMS-BAY), GC-MoE improves MAE over a zero-parameter ensemble baseline, with competitive RMSE and MAPE, while training only ~17K parameters on top of 1.5M frozen expert weights. The implementation is available at https://github.com/Ahghaffari/gc_moe.

Accurate long-range prediction of geophysical systems is difficult due to strongly nonlinear dynamics, the high computational cost of full-physics simulations, and the error accumulation that arise when one-step autoregressive surrogates are rolled out over decades. Deep neural network can serve as efficient emulators, but most are trained only for next-step prediction and often drift or become unstable as the forecast horizon grows. We propose a multi-horizon graph neural network emulator that learns state-to-state transitions from a single current time to multiple future lead times within one unified model. The physical domain is represented as a graph, where nodes correspond to spatial locations with time-varying geophysical attributes and edges encode local spatial interactions. Given the current graph state, the model predicts the future evolution of key fields, ice thickness and ice velocities at all nodes, using a shared graph backbone with separate output branches for each target variable. To improve stability, the network predicts state increments relative to the current state, which are then added back to reconstruct future states. Training jointly optimizes all lead times with a unified regression objective, and inference uses a coarse-to-fine rollout that advances with larger jumps and selectively refines with shorter jumps to reduce drift and avoid redundant computation. Experiments on multi-decadal Pine Island Glacier simulations show that our approach achieves higher long-range accuracy and improved stability than both (i) an initial-state baseline that predicts each future time directly from the starting state and (ii) a standard single-step autoregressive rollout, producing a more reliable emulator for downstream climate and sea-level studies.

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. \emph{Temporal-first} approaches build per-node temporal embeddings and only afterward perform spatial aggregation, whereas \emph{Spatial-first} approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; effectively, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's \emph{past} trajectory. This paper introduces \textbf{SiST-GNN} (\textbf{Si}multaneous \textbf{S}patial-\textbf{T}emporal \textbf{GNN}), which fuses the two signals inside a single message-passing operation rather than chaining them. At each snapshot, we maintain a recurrent hidden state per node that summarises its history, pairs it with the node's current feature vector, and treats the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. We compare against fourteen link-prediction baselines under both the fixed-split and live-update evaluation regimes, and eleven baselines on node classification. Across the public benchmarks, SiST-GNN improves on the strongest prior method in link prediction by 1-18% in the fixed-split setting, and is the leading learned method on five of six datasets in the live-update setting, improving on the strongest prior method by 1-158% there. We additionally derive three dynamic node-classification tasks by discretizing the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by 7-23% and matches continuous-time (CTDG) methods that consume the raw events directly.

Anomaly detection in Industrial Internet of Things (IIoT) environments is essential to protect the Industrial Control Systems (ICS) and Cyber-Physical Systems (CPS) from occuring run time false data injection and other malicious attacks. The increasing complexity of sensor networks and interconnected control loops makes it difficult to identify anomalous behavior hidden within high-dimensional and time-dependent signals. To address these challenges, this article introduces Adaptive Spatio-Temporal Reinforcement Optimization ASTRO (ASTRO), a novel anomaly detection framework that pioneers the use of reinforcement learning for dynamic threshold optimization. By integrating a Deep Q-Network (DQN) with Graph Neural Networks (GNNs), temporal modelling and a Multi-Head Attention mechanism, ASTRO continuously adapts its decision boundaries to improve detection accuracy. The GNN component models the spatial relations among sensors, Temporal model captures time series dependencies and the attention layer highlights most informative time steps. The model generates continuous anomaly scores, which are transformed into binary decisions using an adaptive threshold, optimized via a Deep Q-Network (DQN). The ASTRO approach is evaluated on two real world industrial benchmarks: the Secure Water Treatment (SWaT) and Water Distribution (WADI) datasets. The proposed model achieves an exceptional performance on the SWaT with F1 score of 0.990. Moreover, on highly complex 127 end devices WADI dataset, it secures F1 score of 0.788, outperforming state-of-the-art baselines by nearly 14%. Results across multiple runs confirm consistent generalization and stability. These experiments demonstrate that the ASTRO framework is highly practical and scalable method for strengthening the large scale cyber physical infrastructures