Spatial graphs are particular graphs for which the nodes are localized in space (e.g., public transport network, molecules, branching biological structures). In this work, we consider the problem of spatial graph reduction, that aims to find a smaller spatial graph (i.e., with less nodes) with the same overall structure as the initial one. In this context, performing the graph reduction while preserving the main topological features of the initial graph is particularly relevant, due to the additional spatial information. Thus, we propose a topological spatial graph coarsening approach based on a new framework that finds a trade-off between the graph reduction and the preservation of the topological characteristics. The coarsening is realized by collapsing short edges. In order to capture the topological information required to calibrate the reduction level, we adapt the construction of classical topological descriptors made for point clouds (the so-called persistent diagrams) to spatial graphs. This construction relies on the introduction of a new filtration called triangle-aware graph filtration. Our coarsening approach is parameter-free and we prove that it is equivariant under rotations, translations and scaling of the initial spatial graph. We evaluate the performances of our method on synthetic and real spatial graphs, and show that it significantly reduces the graph sizes while preserving the relevant topological information.

Graph transformers have demonstrated remarkable capability on complex spatio-temporal tasks, yet their depth is often limited by oversmoothing and weak long-range dependency modeling. To address these challenges, we introduce GRIT -LP, a graph transformer explicitly designed for polar ice-layer thickness estimation from polar radar imagery. Accurately estimating ice layer thickness is critical for understanding snow accumulation, reconstructing past climate patterns and reducing uncertainties in projections of future ice sheet evolution and sea level rise. GRIT -LP combines an inductive geometric graph learning framework with self-attention mechanism, and introduces two major innovations that jointly address challenges in modeling the spatio-temporal patterns of ice layers: a partitioned spatial graph construction strategy that forms overlapping, fully connected local neighborhoods to preserve spatial coherence and suppress noise from irrelevant long-range links, and a long-range skip connection mechanism within the transformer that improves information flow and mitigates oversmooth-ing in deeper attention layers. We conducted extensive experiments, demonstrating that GRIT -LP outperforms current state-of-the-art methods with a 24.92% improvement in root mean squared error. These results highlight the effectiveness of graph transformers in modeling spatiotemporal patterns by capturing both localized structural features and long-range dependencies across internal ice layers, and demonstrate their potential to advance data-driven understanding of cryospheric processes. Introduction Graph transformers have proven to be highly effective for modeling complex graph-structured data, with wide-range of applications in real-world scenarios, particularly those involving spatiotemporal patterns. Their ability to capture intricate relationships and dependencies makes them highly valuable in domains such as pedestrian trajectory prediction [1] and traffic prediction [2]. Despite their success, current graph transformer architectures face notable limitations, including overfitting and over-smoothing--a phenomenon where node features become indistinguishable as layers deepen [3]. Additionally, many existing graph transformers are relatively shallow, limiting their ability to effectively capture the complex, long-range dependencies that often emerge in real-world datasets.

Understanding the thickness and variability of internal ice layers in radar imagery is crucial for monitoring snow accumulation, assessing ice dynamics, and reducing uncertainties in climate models. Radar sensors, capable of penetrating ice, provide detailed radargram images of these internal layers. In this work, we present ST-GRIT, a spatio-temporal graph transformer for ice layer thickness, designed to process these radargrams and capture the spatiotemporal relationships between shallow and deep ice layers. ST-GRIT leverages an inductive geometric graph learning framework to extract local spatial features as feature embeddings and employs a series of temporal and spatial attention blocks separately to model long-range dependencies effectively in both dimensions. Experimental evaluation on radargram data from the Greenland ice sheet demonstrates that ST-GRIT consistently outperforms current state-of-the-art methods and other baseline graph neural networks by achieving lower root mean-squared error. These results highlight the advantages of self-attention mechanisms on graphs over pure graph neural networks, including the ability to handle noise, avoid oversmoothing, and capture long-range dependencies. Moreover, the use of separate spatial and temporal attention blocks allows for distinct and robust learning of spatial relationships and temporal patterns, providing a more comprehensive and effective approach.

Global Station Weather Forecasting (GSWF) is a key meteorological research area, critical to energy, aviation, and agriculture. Existing time series forecasting methods often ignore or unidirectionally model spatial correlation when conducting large-scale global station forecasting. This contradicts the intrinsic nature underlying observations of the global weather system, limiting forecast performance. To address this, we propose a novel Spatial Structured Attention Block in this paper. It partitions the spatial graph into a set of subgraphs and instantiates Intra-subgraph Attention to learn local spatial correlation within each subgraph, and aggregates nodes into subgraph representations for message passing among the subgraphs via Inter-subgraph Attention -- considering both spatial proximity and global correlation. Building on this block, we develop a multiscale spatiotemporal forecasting model S$^2$Transformer by progressively expanding subgraph scales. The resulting model is both scalable and able to produce structured spatial correlation, and meanwhile, it is easy to implement. The experimental results show that it can achieve performance improvements up to 16.8% over time series forecasting baselines at low running costs.

In this paper, we propose a novel Spatial Balance Attention block for spatiotemporal forecasting. To strike a balance between obeying spatial proximity and capturing global correlation, we partition the spatial graph into a set of subgraphs and instantiate Intra-subgraph Attention to learn local spatial correlation within each subgraph; to capture the global spatial correlation, we further aggregate the nodes to produce subgraph representations and achieve message passing among the subgraphs via Inter-subgraph Attention. Building on the proposed Spatial Balance Attention block, we develop a multiscale spatiotemporal forecasting model by progressively increasing the subgraph scales. The resulting model is both scalable and able to produce structured spatial correlation, and meanwhile, it is easy to implement. We evaluate its efficacy and efficiency against the existing models on real-world spatiotemporal datasets from medium to large sizes. The experimental results show that it can achieve performance improvements up to 7.7% over the baseline methods at low running costs.

Gaining a deeper understanding of the thickness and variability of internal ice layers in Radar imagery is essential in monitoring the snow accumulation, better evaluating ice dynamics processes, and minimizing uncertainties in climate models. Radar sensors, capable of penetrating ice, capture detailed radargram images of internal ice layers. In this work, we introduce GRIT, graph transformer for ice layer thickness. GRIT integrates an inductive geometric graph learning framework with an attention mechanism, designed to map the relationships between shallow and deeper ice layers. Compared to baseline graph neural networks, GRIT demonstrates consistently lower prediction errors. These results highlight the attention mechanism's effectiveness in capturing temporal changes across ice layers, while the graph transformer combines the strengths of transformers for learning long-range dependencies with graph neural networks for capturing spatial patterns, enabling robust modeling of complex spatiotemporal dynamics.

Spatial-temporal data, fundamental to many intelligent applications, reveals dependencies indicating causal links between present measurements at specific locations and historical data at the same or other locations. Within this context, adaptive spatial-temporal graph neural networks (ASTGNNs) have emerged as valuable tools for modelling these dependencies, especially through a data-driven approach rather than pre-defined spatial graphs. While this approach offers higher accuracy, it presents increased computational demands. Addressing this challenge, this paper delves into the concept of localisation within ASTGNNs, introducing an innovative perspective that spatial dependencies should be dynamically evolving over time. We introduce \textit{DynAGS}, a localised ASTGNN framework aimed at maximising efficiency and accuracy in distributed deployment. This framework integrates dynamic localisation, time-evolving spatial graphs, and personalised localisation, all orchestrated around the Dynamic Graph Generator, a light-weighted central module leveraging cross attention. The central module can integrate historical information in a node-independent manner to enhance the feature representation of nodes at the current moment. This improved feature representation is then used to generate a dynamic sparse graph without the need for costly data exchanges, and it supports personalised localisation. Performance assessments across two core ASTGNN architectures and nine real-world datasets from various applications reveal that \textit{DynAGS} outshines current benchmarks, underscoring that the dynamic modelling of spatial dependencies can drastically improve model expressibility, flexibility, and system efficiency, especially in distributed settings.

In this paper, we present a novel method to significantly enhance the computational efficiency of Adaptive Spatial-Temporal Graph Neural Networks (ASTGNNs) by introducing the concept of the Graph Winning Ticket (GWT), derived from the Lottery Ticket Hypothesis (LTH). By adopting a pre-determined star topology as a GWT prior to training, we balance edge reduction with efficient information propagation, reducing computational demands while maintaining high model performance. Both the time and memory computational complexity of generating adaptive spatial-temporal graphs is significantly reduced from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$. Our approach streamlines the ASTGNN deployment by eliminating the need for exhaustive training, pruning, and retraining cycles, and demonstrates empirically across various datasets that it is possible to achieve comparable performance to full models with substantially lower computational costs. Specifically, our approach enables training ASTGNNs on the largest scale spatial-temporal dataset using a single A6000 equipped with 48 GB of memory, overcoming the out-of-memory issue encountered during original training and even achieving state-of-the-art performance. Furthermore, we delve into the effectiveness of the GWT from the perspective of spectral graph theory, providing substantial theoretical support. This advancement not only proves the existence of efficient sub-networks within ASTGNNs but also broadens the applicability of the LTH in resource-constrained settings, marking a significant step forward in the field of graph neural networks. Code is available at https://anonymous.4open.science/r/paper-1430.

Brain network analysis is vital for understanding the neural interactions regarding brain structures and functions, and identifying potential biomarkers for clinical phenotypes. However, widely used brain signals such as Blood Oxygen Level Dependent (BOLD) time series generated from functional Magnetic Resonance Imaging (fMRI) often manifest three challenges: (1) missing values, (2) irregular samples, and (3) sampling misalignment, due to instrumental limitations, impacting downstream brain network analysis and clinical outcome predictions. In this work, we propose a novel model called BrainODE to achieve continuous modeling of dynamic brain signals using Ordinary Differential Equations (ODE). By learning latent initial values and neural ODE functions from irregular time series, BrainODE effectively reconstructs brain signals at any time point, mitigating the aforementioned three data challenges of brain signals altogether. Comprehensive experimental results on real-world neuroimaging datasets demonstrate the superior performance of BrainODE and its capability of addressing the three data challenges.