Computationally and Memory Efficient Graph Neural Network for Emulating Storm Surge Inundation State Over Extended Geospatial Domains

Abstract Data‐driven emulation of storm surges has emerged as a valuable tool for supporting regional coastal risk assessment. Surrogate models for such applications are developed using data sets of surge predictions for synthetic storms across a large number of locations, corresponding to the nodes of the utilized numerical model used. Recent work has shown that for improving the accuracy of storm surge predictions, the development of classification surrogate models that explicitly predict the inundation state (i.e., wet or dry) of each node, is advantageous. The development of accurate classifiers requires addressing the sophisticated dependencies across the high‐dimensional output corresponding to the nodal responses. Graph‐based surrogate modeling approaches are particularly effective for this purpose, as they provide a structured framework to represent such complex dependencies. However, graph‐based approaches face challenges in scaling to high‐dimensional data, such as those encountered in this application. A novel and scalable Graph Neural Network (GNN) framework that integrates sparsity into the graph connectivity is introduced to address this. This framework relies on the construction of a graph structure using a cross‐observational similarity instead of the commonly used spatial correlation. To incorporate the storm features within the GNN, a mapping is introduced to project them to distinguishable features across individual nodes. An end‐to‐end calibration is established for this mapping, promoting a joint calibration along with the graph‐based classifier. To address computational limitations and enhance scalability for higher‐dimensional data sets, a soft‐clustering formulation is considered. The proposed framework outperforms alternative machine learning approaches while addressing the scalability challenges common to GNN applications.