Naheed Anjum Arafat

We propose SGS-GNN, a supervised graph sparsifier for Graph Neural Networks (GNNs) to improve predictive performance and reduce the cost of message passing by removing task-irrelevant edges. Existing unsupervised sparsifiers are not task-aware, while existing supervised sparsifiers suffer from significant memory overhead, poor sparsity control, and a lack of homophily/heterophily awareness. SGS-GNN addresses these limitations by adopting a feature- and structure-aware edge-probability encoder, a sparse subgraph sampler that strictly adheres to a global sparsity constraint, and a homophily-aware regularizer to improve prediction accuracy across homophilic and heterophilic graphs. A key scalability-enhancing feature of SGS-GNN is that it ensures encoder updates are computed by backpropagating through the sampled subgraph, and avoids retaining edge-level computation graphs for all edges via gradient checkpointing. A key efficiency-enhancing feature of SGS-GNN is that the edge-probability encoder is updated only when it outperforms a degree-based edge sampler, ensuring performance no worse than a strong unsupervised baseline. Experiments on 33 homophilic and heterophilic graphs show that SGS-GNN improves F1-scores by 4% relative to full training and up to 30% on heterophilic graphs. Furthermore, SGS-GNN outperforms state-of-the-art methods by 4–7% at similar sparsity levels while reducing peak memory usage by up to 3.9\texttimes.

Computational fluid dynamics (CFD) simulation is an irreplaceable modelling step in many engineering designs, but it is often computationally expensive. Some graph neural network (GNN)- based CFD methods have been proposed. However, the current methods inherit the weakness of traditional numerical simulators, as well as ignore the cell characteristics in the mesh used in the finite volume method, a common method in practical CFD applications. Specifically, the input nodes in these GNN methods have very limited information about any object immersed in the simulation domain and its surrounding environment. Also, the cell characteristics of the mesh such as cell volume, face surface area, and face centroid are not included in the message-passing operations in the GNN methods. To address these weaknesses, this work proposes two novel geometric representations: Shortest Vector (SV) and Directional Integrated Distance (DID). Extracted from the mesh, the SV and DID provide global geometry perspective to each input node, thus removing the need to collect this information through message-passing. This work also introduces the use of Finite Volume Features (FVF) in the graph convolutions as node and edge attributes, enabling its message-passing operations to adjust to different nodes. Finally, this work extends the use of residual training to improve flow field prediction for a GNN scenario with immersed object, when low resolution data is available. Experimental results on two datasets with five different state-of-the-art GNN methods for CFD indicate that SV, DID, FVF and residual training can effectively reduce the predictive error of current GNN-based methods by as much as 41%. Our codes and datasets are available at https://github.com/toggled/FvFGeo.

We propose neighborhood-based core decomposition: a novel way of decomposing hypergraphs into hierarchical neighborhood-cohesive subhypergraphs. Alternative approaches to decomposing hypergraphs, e.g., reduction to clique or bipartite graphs, are not meaningful in certain applications, the later also results in inefficient decomposition; while existing degree-based hypergraph decomposition does not distinguish nodes with different neighborhood sizes. Our case studies show that the proposed decomposition is more effective than degree and clique graph-based decompositions in disease intervention and in extracting provably approximate and application-wise meaningful densest subhypergraphs. We propose three algorithms: Peel, its efficient variant E-Peel, and a novel local algorithm: Local-core with parallel implementation. Our most efficient parallel algorithm Local-core(P) decomposes hypergraph with 27M nodes and 17M hyperedges in-memory within 91 seconds by adopting various optimizations. Finally, we develop a new hypergraph-core model, the (neighborhood, degree)-core by considering both neighborhood and degree constraints, design its decomposition algorithm Local-core+Peel, and demonstrate its superiority in spreading diffusion.