@article{beddarwiesing2024weisfeiler,
  abstract = {Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler–Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence. Moreover, the proof of the approximation capability is mostly constructive and allows us to deduce hints on the architecture of GNNs that can achieve the desired approximation.},
  author = {Beddar-Wiesing, Silvia and D'Inverno, Alessio and Graziani, Caterina and Lachi, Veronica and Moallemy-Oureh, Alice and Scarselli, Franco and Thomas, Josephine},
  doi = {10.1016/j.neunet.2024.106213},
  interhash = {2f32fbb1387911744c61e5895b224cbc},
  intrahash = {d2777197f992700161caeaa302801fb8},
  journal = {Neural Networks},
  pages = 106213,
  publisher = {Elsevier},
  title = {Weisfeiler–Lehman goes dynamic: An analysis of the expressive power of Graph Neural Networks for attributed and dynamic graphs},
  url = {https://www.sciencedirect.com/science/article/pii/S0893608024001370},
  volume = 173,
  year = 2024
}

@inproceedings{huang2023spatio,
  abstract = {RUL prediction plays a crucial role in the health management of industrial systems. Given the increasing complexity of systems, data-driven predictive models have attracted significant research interest. Upon reviewing the existing literature, it appears that many studies either do not fully integrate both spatial and temporal features or employ only a single attention mechanism. Furthermore, there seems to be inconsistency in the choice of data normalization methods, particularly concerning operating conditions, which might influence predictive performance. To bridge these observations, this study presents the Spatio-Temporal Attention Graph Neural Network. Our model combines graph neural networks and temporal convolutional neural networks for spatial and temporal feature extraction, respectively. The cascade of these extractors, combined with multihead attention mechanisms for both spatio-temporal dimensions, aims to improve predictive precision and refine model explainability. Comprehensive experiments were conducted on the CMAPSS dataset to evaluate the impact of unified versus clustering normalization. The findings suggest that our model performs state-of-the-art results using only the unified normalization. Additionally, when dealing with datasets with multiple operating conditions, cluster normalization enhances the performance of our proposed model by up to 27%.},
  author = {Huang, Zhixin and He, Yujiang and Sick, Bernhard},
  booktitle = {Computational Science and Computational Intelligence (CSCI)},
  interhash = {d2c044e372780d668eb0140a724454e0},
  intrahash = {ad927931297c4668fb4cda3fa215b717},
  note = {(accepted)},
  publisher = {IEEE},
  title = {Spatio-Temporal Attention Graph Neural Network for Remaining Useful Life Prediction},
  year = 2023
}

@article{thomas2023graph,
  abstract = {Graphs are ubiquitous in nature and can therefore serve as models for many practical but also
theoretical problems. For this purpose, they can be defined as many different types which
suitably reflect the individual contexts of the represented problem. To address cutting-edge
problems based on graph data, the research field of Graph Neural Networks (GNNs) has
emerged. Despite the field’s youth and the speed at which new models are developed, many
recent surveys have been published to keep track of them. Nevertheless, it has not yet
been gathered which GNN can process what kind of graph types. In this survey, we give a
detailed overview of already existing GNNs and, unlike previous surveys, categorize them
according to their ability to handle different graph types and properties. We consider GNNs
operating on static and dynamic graphs of different structural constitutions, with or without
node or edge attributes. Moreover, we distinguish between GNN models for discrete-time or
continuous-time dynamic graphs and group the models according to their architecture. We
find that there are still graph types that are not or only rarely covered by existing GNN
models. We point out where models are missing and give potential reasons for their absence.},
  author = {Thomas, Josephine and Moallemy-Oureh, Alice and Beddar-Wiesing, Silvia and Holzhüter, Clara},
  interhash = {229b2eb23d7fdfdf16d3c6d813e4c106},
  intrahash = {853c98d29b7c266e48e1cabd45dc5854},
  journal = {Transactions on Machine Learning Research},
  title = {Graph Neural Networks Designed for Different Graph Types: A Survey},
  url = {https://openreview.net/pdf?id=h4BYtZ79uy},
  year = 2023
}