A Diffusion-Contrastive Graph Neural Network with Virtual Nodes for Wind Nowcasting in Unobserved Regions

Abstract: Accurate weather nowcasting remains one of the central challenges in atmospheric science, with critical implications for climate resilience, energy security, and disaster preparedness. Since it is not feasible to deploy observation stations everywhere, some regions lack dense observational networks, resulting in unreliable short-term wind predictions across those unobserved areas. Here we present a deep graph self-supervised framework that extends nowcasting capability into such unobserved regions without requiring new sensors. Our approach introduces "virtual nodes" into a diffusion and contrastive-based graph neural network, enabling the model to learn wind condition (i.e., speed, direction and gusts) in places with no direct measurements. Using high-temporal resolution weather station data across the Netherlands, we demonstrate that this approach reduces nowcast mean absolute error (MAE) of wind speed, gusts, and direction in unobserved regions by more than 30% - 46% compared with interpolation and regression methods. By enabling localized nowcasts where no measurements exist, this method opens new pathways for renewable energy integration, agricultural planning, and early-warning systems in data-sparse regions.

• The paper presents ContraVirt, a novel diffusion-contrastive graph neural network that integrates virtual nodes to nowcast wind variables in unobserved regions.
• It employs both supervised regression and contrastive self-supervised learning to enhance spatiotemporal predictions, achieving significant error reductions over baselines.
• Ablation studies confirm that leveraging graph diffusion and virtual nodes stabilizes predictions, offering a promising solution for remote meteorological forecasting.

Diffusion-Contrastive Graph Neural Networks with Virtual Nodes: Wind Nowcasting in Unobserved Regions

Introduction

The core problem addressed in "A Diffusion-Contrastive Graph Neural Network with Virtual Nodes for Wind Nowcasting in Unobserved Regions" (2604.10328) is the reliable prediction of wind variables (speed, direction, gusts) in regions where no direct meteorological observations exist. Traditional nowcasting relies on dense sensor networks, but vast areas—offshore, rural, or remote—are undersampled due to economic and logistical constraints. Approaches such as spatial interpolation or data assimilation within NWP frameworks have persistent limitations in accurately capturing non-smooth meteorological transitions caused by complex atmospheric dynamics.

The paper introduces ContraVirt, a spatiotemporal graph neural network that integrates both real (observed) and virtual (unobserved) nodes, leveraging graph diffusion and contrastive self-supervised learning to accurately nowcast wind fields in these unobserved regions. The framework harnesses both physical-geographical intuition (Tobler’s First Law) and contemporary advances in GNNs, enabling effective message passing and robust embedding learning in the absence of labeled data at virtual nodes.

Figure 1: Station locations across the Netherlands and the spatiotemporal coverage of training/testing datasets; virtual nodes cover unobserved grid regions.

Methodology

Virtual Node Construction and Input Representation

ContraVirt discretizes the prediction domain into a regular grid, inserting virtual nodes at grid centers for cells without real meteorological stations. This hybrid graph enables full spatial coverage: real stations serve as ground-truth sources, while virtual nodes approximate features as weighted averages from three nearest real stations, with learnable embeddings employed for lagged variables, and additional geo- and node-type embeddings to aid generalization.

Graph Architecture and Diffusion

The base graph connects each node to its three nearest geographical neighbors. The core propagation mechanism uses a Personalized PageRank (PPR) diffusion, ensuring both local and global transfer of meteorological signals. Critically, diffusion weights are reparameterized to enhance propagation from real to virtual nodes (weight $\gamma > 1$) and suppress inter-virtual interactions ($\delta < 1$), promoting stable signal transmission from observed to unobserved regions without excessive redundancy or noise.

Figure 2: Model architecture—graph construction from real (blue) and virtual (red) nodes, with diffusion-based edges and bifurcated supervised/contrastive learning heads.

Joint Supervised and Contrastive Objectives

The learning scheme employs a dual loss:

• Supervised regression at real nodes for direct wind variable prediction.
• Self-supervised contrastive learning at virtual nodes via two strategies:
  • Augmented contrastive: Pairs each node with a masked version, pushing representations toward invariance under input perturbation.
  • Multi-step contrastive: Pairs each virtual node at time $t$ with its nearest real neighbor at $t+3$ (30 min ahead), enforcing spatiotemporal consistency.

Contrastive loss uses momentum contrast (MoCo) with a memory queue for diverse and stable negative sampling. The balance between supervised and contrastive terms is dynamically modulated based on a warm-up schedule and ongoing MAE, ensuring that the self-supervision becomes increasingly influential as the primary regression stabilizes.

Figure 3: (a) Graph diffusion transforms spatial relationships and distributions; (b) dependence of each virtual node on surrounding real stations.

Experimental Design

Dataset and Ablation

The evaluation uses hourly 10-minute wind observations from 33 onshore weather stations across the Netherlands, mapped onto a $9\times9$ grid. Eight real stations are withheld as test targets, substituted by virtual nodes during training to rigorously examine generalization to unmonitored locations.

Baseline comparisons include classic interpolation (IDW, KNN), and time series regression (LR, AR) approaches, as well as ablated versions of ContraVirt omitting either contrastive modules, MoCo, or diffusion.

Training Protocol

Models are implemented in PyTorch, trained via AdamW for up to 200 epochs with early stopping and learning rate scheduling. Key hyperparameters are calibrated empirically for trade-offs between accuracy and computational overhead.

Results

Information Propagation and Node Dependence

Diffusion transforms an initially sparse neighbor graph into a dense network, with virtual nodes primarily aggregating diverse signals from multiple nearby real stations; no single station dominates, confirming effective multi-source integration and robustness against local anomalies.

Nowcasting Accuracy and Ablation Analysis

ContraVirt (Augmented MoCo) achieves the lowest errors: wind speed MAE of 1.48 m/s and gust MAE of 1.75 m/s—representing 40–46% reductions versus classical baselines. For wind direction, the best model achieves 29.5° MAE, a 26–29% improvement. Removing the contrastive or diffusion modules substantially degrades performance, with non-contrastive models' MAE rising to 33–46°, and classical methods yielding even higher errors.

Figure 4: Performance comparisons—(a) MAE/RMSE across models, (b) MAE versus forecast lead time, (c) spatial MAE across test stations.

Error growth over increasing forecast horizons is more contained in ContraVirt models; degradation is notably slower compared to ablations or classical baselines. Spatial assessment confirms uniformly improved error profiles—especially pronounced in coastal and northern stations, areas typically underserved by interpolation-based methods.

Seasonal and Case Study Evaluation

ContraVirt (Multi-step MoCo) demonstrates error stabilization across seasons, with the most significant improvements during autumn and winter. This aligns with increased atmospheric turbulence and storm activity in these periods, indicating the framework's capacity to model rapid meteorological transitions.

Figure 5: (a) Seasonal MAE as a function of lead time; (b) spatial and seasonal MAE maps across the Netherlands.

Case study analyses—directional roses, wind speed, and gust time series—show ContraVirt reproducing both mean and extreme events, outperforming baselines that tend to dampen direction variability and underestimate extremes.

Figure 6: (a) Wind-direction roses for four test stations in storm season; (b,c) time-series alignment between predictions and observations for wind speed and gust.

Contrastive Representation Dynamics

Contrastive learning is analyzed using distance metrics and low-dimensional projections. A 30% masking ratio in Augmented MoCo yields optimal separation between positive (aligned) and negative (unaligned) pairs. Temporal offsets for multi-step contrastive pairs indicate a 30-minute gap ($t$ vs. $t+3$) provides the strongest supervisory signal. t-SNE/UMAP plots visualize the convergence of positive pairs and enhanced discriminability of node embeddings.

Figure 7: (a,b) Evolution of positive/negative pair embedding distances; (c,d) t-SNE and UMAP projections showing tight contrastive clustering with training.

Implications and Future Directions

ContraVirt substantiates the potential of diffusion-contrastive GNNs for spatiotemporal extrapolation in domains suffering from data sparsity. From a practical standpoint, this reduces the dependency on dense sensor networks, directly impacting the viability of wind resource assessment, disaster response, and climate adaptation planning in remote or resource-limited regions. Methodologically, the integration of virtual nodes within a structured self-supervised setting points to a flexible strategy for any geospatial variable exhibiting spatial autocorrelation and physical coupling—potentially transferable to hydrological, air quality, or crop yield prediction.

Theoretically, the fidelity with which ContraVirt captures both mean behavior and extremes suggests scope for extending contrastive learning paradigms with physics-informed constraints, adaptive graph topology, or multimodal sensor fusion. Enhancements may also include explicit uncertainty quantification, augmentation with satellite or reanalysis data, or integration with generative graph models for probabilistic forecasting.

Conclusion

The diffusion-contrastive framework with virtual nodes delivers robust nowcasting accuracy in unobserved regions, overcoming the limitations of both interpolation and traditional supervised learning under data scarcity. This approach demonstrates a scalable, physically congruent solution for extending high-fidelity environmental forecasting to unmonitored domains, setting a precedent for further innovation in geospatial AI for atmospheric science and allied fields.