Graphon models provide a flexible nonparametric framework for estimating latent connectivity probabilities in networks, enabling a range of downstream applications such as link prediction and data augmentation. However, accurate graphon estimation typically requires a large graph, whereas in practice, one often only observes a small-sized network. One approach to addressing this issue is to adopt a transfer learning framework, which aims to improve estimation in a small target graph by leveraging structural information from a larger, related source graph. In this paper, we propose a novel method, namely GTRANS, a transfer learning framework that integrates neighborhood smoothing and Gromov-Wasserstein optimal transport to align and transfer structural patterns between graphs. To prevent negative transfer, GTRANS includes an adaptive debiasing mechanism that identifies and corrects for target-specific deviations via residual smoothing. We provide theoretical guarantees on the stability of the estimated alignment matrix and demonstrate the effectiveness of GTRANS in improving the accuracy of target graph estimation through extensive synthetic and real data experiments. These improvements translate directly to enhanced performance in downstream applications, such as the graph classification task and the link prediction task.

Spatiotemporal time series nowcasting should preserve temporal and spatial dynamics in the sense that generated new sequences from models respect the covariance relationship from history. Conventional feature extractors are built with deep convolutional neural networks (CNN). However, CNN models have limits to image-like applications where data can be formed with high-dimensional arrays. In contrast, applications in social networks, road traffic, physics, and chemical property prediction where data features can be organized with nodes and edges of graphs. Transformer architecture is an emerging method for predictive models, bringing high accuracy and efficiency due to attention mechanism design. This paper proposes a spatiotemporal model, namely GTrans, that transforms data features into graph embeddings and predicts temporal dynamics with a transformer model. According to our experiments, we demonstrate that GTrans can model spatial and temporal dynamics and nowcasts extreme events for datasets. Furthermore, in all the experiments, GTrans can achieve the highest F1 and F2 scores in binary-class prediction tests than the baseline models.