Spatio-temporal copula-based graph neural networks for traffic forecasting

Traffic forecasting is a crucial aspect of modern Intelligent Transportation Systems (ITS) and the Internet of Vehicles (IoV), playing a vital role in improving the safety and efficiency of daily transportation activities. Despite the valuable contributions of traditional machine learning (ML) models and advanced deep learning (DL) techniques, there persist challenges in capturing the intricate spatial and temporal dependencies inherent in traffic flow. In response to these challenges, we present GRAPHITE, an innovative framework that combines Graph Neural Networks (GNNs) and Generative Adversarial Networks (GANs) to leverage generative reasoning for efficient traffic management. Our model seamlessly integrates historical traffic volume data collected by road sensors with local spatial information encoded through knowledge graphs (KGs) associated with each sensor. These KGs offer a structured representation of relationships between traffic sensors and points of interest (POIs) in their neighborhood, thereby enhancing the comprehension of the urban context and leading to more accurate traffic predictions. Extensive experiments conducted on diverse datasets underscore the efficacy of GRAPHITE. Notably, we achieved a maximum decrease in RMSE of 31.05% compared to GAN-GRU and a maximum increase in R2 of 8.15% compared to GAN-RNN, positioning GRAPHITE as a standout solution among the current state-of-the-art approaches. Our code is available at: https://github.com/MODAL-UNINA/GRAPHITE.

Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are usually guided by pre-defined kernels such as Laplacian matrix, adjacency matrix, or their variants. However, the adoptions of pre-defined kernels may restrain the generalities to different graphs: mismatch between graph and kernel would entail sub-optimal performance. For example, GNNs that focus on low-frequency information may not achieve satisfactory performance when high-frequency information is significant for the graphs, and vice versa. To solve this problem, in this paper, we propose a novel framework - i.e., namely Adaptive Kernel Graph Neural Network (AKGNN) - which learns to adapt to the optimal graph kernel in a unified manner at the first attempt. In the proposed AKGNN, we first design a data-driven graph kernel learning mechanism, which adaptively modulates the balance between all-pass and low-pass filters by modifying the maximal eigenvalue of the graph Laplacian. Through this process, AKGNN learns the optimal threshold between high and low frequency signals to relieve the generality problem. Later, we further reduce the number of parameters by a parameterization trick and enhance the expressive power by a global readout function. Extensive experiments are conducted on acknowledged benchmark datasets and promising results demonstrate the outstanding performance of our proposed AKGNN by comparison with state-of-the-art GNNs. The source code is publicly available at: https://github.com/jumxglhf/AKGNN.

Federated learning has been applied to various tasks in intelligent transportation systems to protect data privacy through decentralized training schemes. The majority of the state-of-the-art models in intelligent transportation systems (ITS) are graph neural networks (GNN)-based for spatial information learning. When applying federated learning to the ITS tasks with GNN-based models, the existing frameworks can only protect the data privacy; however, ignore the one of topological information of transportation networks. In this article, we propose a novel federated learning framework to tackle this problem. Specifically, we introduce a differential privacy-based adjacency matrix preserving approach for protecting the topological information. We also propose an adjacency matrix aggregation approach to allow local GNN-based models to access the global network for a better training effect. Furthermore, we propose a GNN-based model named attention-based spatial-temporal graph neural networks (ASTGNN) for traffic speed forecasting. We integrate the proposed federated learning framework and ASTGNN as FASTGNN for traffic speed forecasting. Extensive case studies on a real-world dataset demonstrate that FASTGNN can develop accurate forecasting under the privacy preservation constraint.

Graph Neural Networks (GNNs) have emerged as a powerful framework for processing irregular, complex systems such as social networks and knowledge graphs. However, the inherent structural complexity of graphs imposes significant memory and computational overhead. These challenges are exacerbated by the traditional von Neumann architecture, where physically separated memory and processing units lead to substantial data movement bottlenecks. Consequently, in-memory computing (IMC) paradigms—specifically those leveraging memristor crossbar arrays—have become increasingly vital. While extensive research has focused on utilizing memristor arrays as weight layers for neural network acceleration, the adjacency matrix—a fundamental component representing graph topology—remains largely unimplemented in hardware. In this work, we provide the first experimental demonstration of a GNN architecture where the adjacency matrix is physically realized using a memristor crossbar array, harnessing its massive parallel computing capabilities. By integrating this hardware-based adjacency matrix with software-defined layers, we successfully implement digital image processing and resolve complex combinatorial optimization problems. Our results exhibit significantly enhanced computational efficiency and underscore the potential of memristor arrays as core components in GNN acceleration. This physical implementation of the adjacency matrix expands the horizons of memristor-based neuromorphic computing systems, offering a scalable path toward high-performance machine learning and artificial intelligence hardware.

Traffic flow forecasting is essential for managing congestion, improving safety, and optimizing various transportation systems. However, it remains a prevailing challenge due to the stochastic nature of urban traffic and environmental factors. Better predictions require models capable of accommodating the traffic variability influenced by multiple dynamic and complex interdependent factors. In this work, we propose a Graph Neural Network (GNN) framework to address the stochasticity by leveraging adaptive adjacency matrices using log-normal distributions and Coefficient of Variation (CV) values to reflect real-world travel time variability. Additionally, weather factors such as temperature, wind speed, and precipitation adjust edge weights and enable GNN to capture evolving spatio-temporal dependencies across traffic stations. This enhancement over the static adjacency matrix allows the model to adapt effectively to traffic stochasticity and changing environmental conditions. Furthermore, we utilize the Adaptive Conformal Prediction (ACP) framework to provide reliable uncertainty quantification, achieving target coverage while maintaining acceptable prediction intervals. Experimental results demonstrate that the proposed model, in comparison with baseline methods, showed better prediction accuracy and uncertainty bounds. We, then, validate this method by constructing traffic scenarios in SUMO and applying Monte-Carlo simulation to derive a travel time distribution for a Vehicle Under Test (VUT) to reflect real-world variability. The simulated mean travel time of the VUT falls within the intervals defined by INRIX historical data, verifying the model’s robustness.

Graph neural networks (GNN) rely on graph operations that include neural network training for various graph related tasks. Recently, several attempts have been made to apply the GNNs to functional magnetic resonance image (fMRI) data. Despite recent progresses, a common limitation is its difficulty to explain the classification results in a neuroscientifically explainable way. Here, we develop a framework for analyzing the fMRI data using the Graph Isomorphism Network (GIN), which was recently proposed as a powerful GNN for graph classification. One of the important contributions of this paper is the observation that the GIN is a dual representation of convolutional neural network (CNN) in the graph space where the shift operation is defined using the adjacency matrix. This understanding enables us to exploit CNN-based saliency map techniques for the GNN, which we tailor to the proposed GIN with one-hot encoding, to visualize the important regions of the brain. We validate our proposed framework using large-scale resting-state fMRI (rs-fMRI) data for classifying the sex of the subject based on the graph structure of the brain. The experiment was consistent with our expectation such that the obtained saliency map show high correspondence with previous neuroimaging evidences related to sex differences.

Existing multivariate time series forecasting (MTSF) methods have begun to explore architectures built entirely upon Graph Neural Networks (GNNs). Directly connecting variables across different timestamps with a fully connected adjacency matrix introduces unnecessary noise and ignores the inherent temporal ordering between nodes. Besides this, the limited depth of Spatial graph convolutional layers restricts the ability of the model to capture long-term dependencies. We propose <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{S}^{\text{2}}$</tex>-<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{GNN}$</tex>, a multi-scale adaptive graph neural network method, which fusion spatial and spectral graph convolutions. An adaptive mechanism is used to capture the unidirectional relationship between nodes at different timestamps, which enables the construction of a graph structure that preserves the temporal order. Multi-order neighbor information and original node features are fused at each layer of spatial graph convolution to improve the local feature extraction capability of the spatial graph convolution. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{S}^{\text{2}}$</tex>-GNN introduces spectral graph convolution and applies singular value decomposition (SVD) in the frequency domain to decompose the adjacency matrix and implement spectral graph convolution, which enables the extraction of key structural information and provides a compact representation of global spatio-temporal dependencies. We conduct extensive experiments on 7 public datasets for time series forecasting. The experimental results show that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{S}^{\text{2}}$</tex>-GNN outperforms typical baseline models in time series forecasting tasks.

The procedure of drug-target interaction prediction (DTI) stands as a vital process during drug discovery because it helps reveal which drug substances interact with which biological targets including proteins and receptors. For example, the interactions themselves are too complex to be predictively modelled using single type biological or chemical data; they likewise are so large and varied that approaches traditionally used to predict these interactions are not powerful enough. We use this paper to look at how graph neural networks (GNNs) are used to model molecular structures and predict drug target. GNNs guard their strength in modelling molecular structures because they master the process of detecting atomic and bond relationships thus producing precise molecular representations. The authors evaluate convolutional neural networks (CNNs) and recurrent neural networks (RNNs) alongside GNNs for their use in DTI prediction. The system accepts molecular graphs as its starting data to calculate the predicted interaction probability between drugs and their target proteins. Progressive experimentation has proven the model effectiveness which enables it to reduce drug candidates for experimental verification. The drug discovery process can reach improved efficiency in DTI prediction and accelerate therapeutic development according to results from machine learning (ML) particular GNNs.

Traffic flow forecasting is an essential task of an intelligent transportation system (ITS), closely related to intelligent transportation management and resource scheduling. Dynamic spatial-temporal dependencies in traffic data make traffic flow forecasting to be a challenging task. Most existing research cannot model dynamic spatial and temporal correlations to achieve well-forecasting performance. The multi-head self-attention mechanism is a valuable method to capture dynamic spatial-temporal correlations, and combining it with graph convolutional networks is a promising solution. Therefore, we propose a multi-head self-attention spatiotemporal graph convolutional network (MSASGCN) model. It can effectively capture local correlations and potential global correlations of spatial structures, can handle dynamic evolution of the road network, and, in the time dimension, can effectively capture dynamic temporal correlations. Experiments on two real datasets verify the stability of our proposed model, obtaining a better prediction performance than the baseline algorithms. The correlation metrics get significantly reduced compared with traditional time series prediction methods and deep learning methods without using graph neural networks, according to MAE and RMSE results. Compared with advanced traffic flow forecasting methods, our model also has a performance improvement and a more stable prediction performance. We also discuss some problems and challenges in traffic forecasting.

Optimizing graph neural network architectures for schizophrenia spectrum disorder prediction using evolutionary algorithms

The topology of fMRI-based networks defines the performance of a graph neural network for the classification of patients with major depressive disorder

Practical applications of graph neural networks (GNNs) in transportation are still a niche field. There exists a significant overlap between the potential of GNNs and the issues in strategic transport modelling. However, it is not clear whether GNN surrogates can overcome (some of) the prevalent issues. Investigation of such a surrogate will show their advantages and the disadvantages, especially throwing light on their potential to replace complex transport modelling approaches in the future, such as the agent‐based models. In this direction, as a pioneer work, this paper studies the plausibility of developing a GNN surrogate for the classical four‐step approach, one of the established strategic transport modelling approaches. A formal definition of the surrogate is presented, and an augmented data generation procedure is introduced. The network of the Greater Munich metropolitan region is used for the necessary data generation. The experimental results show that GNNs have the potential to act as transport planning surrogates and the deeper GNNs perform better than their shallow counterparts. Nevertheless, as expected, they suffer performance degradation with an increase in network size. Future research should dive deeper into formulating new GNN approaches, which are able to generalize to arbitrary large networks.

Graph Neural Networks (GNN) have recently gained popularity in the forecasting domain due to their ability to model complex spatial and temporal patterns in tasks such as traffic forecasting and region-based demand forecasting. Most of these methods require a predefined graph as input, whereas in real-life multivariate time series problems, a well-predefined dependency graph rarely exists. This requirement makes it harder for GNNs to be utilised widely for multivariate forecasting problems in other domains such as retail or energy. In this paper, we propose a hybrid approach combining neural networks and statistical structure learning models to self-learn the dependencies and construct a dynamically changing dependency graph from multivariate data aiming to enable the use of GNNs for multivariate forecasting even when a well-defined graph does not exist. The statistical structure modeling in conjunction with neural networks provides a well-principled and efficient approach by bringing in causal semantics to determine dependencies among the series. Finally, we demonstrate significantly improved performance using our proposed approach on real-world benchmark datasets without a pre-defined dependency graph.

Real-time simulation and the integration of digital twins necessitate the development of computationally efficient surrogate models for contemporary food drying systems, in which complex physical processes must interact dynamically with virtual representations. Traditional modeling approaches for food drying are subject to notable limitations: empirical models often lack physical fidelity, whereas high-fidelity computational fluid dynamics (CFD) simulations require the resolution of tightly coupled heat and mass transfer processes among vapor, liquid water, and air phases within unsaturated porous media, rendering them computationally prohibitive for real-time applications. This work proposes a region-aware graph neural network (GNN) surrogate model for food drying simulation by leveraging mesh-based and region-specific representations of the drying process. The proposed GNN architecture, inspired by MeshGraphNet with specialized masked message passing, handles the heterogeneous domains and sharp discontinuities characteristic of coupled heat and mass transfer in food drying. The GNN model was trained on a limited dataset comprising 28 CFD simulations of hot-air drying of a potato slice under varying ambient conditions, generated using a CFD framework validated against numerical results from the literature and laboratory-scale experimental data. Despite this small training set, the model delivers predictive performance for operating conditions beyond those seen during training. Single-step predictions achieved RMSE values of 0.17 °C for temperature ( T ), 0.26% for relative humidity ( RH ), and 0.0028 for liquid saturation ( S w ). Comparative analysis with standard message passing revealed a threefold reduction in interfacial absolute error (0.003 vs. 0.008) and elimination of nonphysical field propagation across domain boundaries. The model maintained performance on the training domain edges, with moisture ratio curves achieving R 2 > 0.97 for 10-step rollouts (R 2 = 0.989 interior domain; R 2 = 0.979 edge domain) while preserving the characteristic S-shaped drying curves in longer autonomous simulations (R 2 = 0.784 and 0.873 for full rollouts of the interior and edge-of-domain test cases, respectively). This framework is applicable to real-time process control, design optimization, and digital twin implementations in food manufacturing. • Integrated a region-aware GNN into a digital twin for potato drying. • Achieved high accuracy with minimal data in heat and mass transfer prediction. • Region-aware message passing ensured physical consistency across domains. • Model adapted to changes in temperature and geometry with low prediction error. • Fast predictions enable real-time control and food process optimization

The emergence of deep learning has not only brought great changes in the field of image recognition, but also achieved excellent node classification performance in graph neural networks. However, the existing graph neural network framework often uses methods based on spatial domain or spectral domain to capture network structure features. This process captures the local structural characteristics of graph data, and the convolution process has a large amount of calculation. It is necessary to use multi-channel or deep neural network structure to achieve the goal of modeling the high-order structural characteristics of the network. Therefore, this paper proposes a linear graph neural network framework [Linear Graph Neural Network (LGNN)] with superior performance. The model first preprocesses the input graph, and uses symmetric normalization and feature normalization to remove deviations in the structure and features. Then, by designing a high-order adjacency matrix propagation mechanism, LGNN enables nodes to iteratively aggregate and learn the feature information of high-order neighbors. After obtaining the node representation of the network structure, LGNN uses a simple linear mapping to maintain computational efficiency and obtain the final node representation. The experimental results show that the performance of the LGNN algorithm in some tasks is slightly worse than that of the existing mainstream graph neural network algorithms, but it shows or exceeds the machine learning performance of the existing algorithms in most graph neural network performance evaluation tasks, especially on sparse networks.