A Spike‐Based Graph Surrogate for Modeling Finite Element Structures

ABSTRACT The use of Artificial Intelligence (AI) in structural mechanics has grown substantially in the recent years, with diverse applications ranging from constitutive laws and Gauss‐point‐level enhancements to the complete replacement of classical Finite Element Methods (FEM) with surrogate models. In this context, Graph Neural Networks (GNNs) have emerged as a particularly effective class of surrogates, as their graph‐based formulation offers a natural representation of unstructured domains such as finite element meshes. In this study, we employ an attention‐based graph architecture as a surrogate model for fundamental finite element structures, predicting structural deformations and stress–strain field variables in elastic and viscoplastic regimes. The proposed approach leverages the attention mechanism to compute the hidden representations of each node in the mesh using a self‐attention strategy over its neighborhood. This enables the model to capture the physical and geometrical nonlinearities accurately. While conventional GNNs showcase strong predictive performance, their training and inference stages are associated with considerable energy consumption. To address this, we explore the integration of Spiking Neural Networks (SNNs) into the graph learning paradigm, motivated by their event‐driven computation and potential for energy‐efficient execution. Although SNNs are widely used in the graph learning domain for classification tasks, their binary nature often limits their applicability to regression problems due to information loss. To overcome this, we employ graded spikes to compute the attention coefficients for each node in the graph. The proposed spike‐based graph model is compared with its non‐spiking counterpart in terms of accuracy and computational characteristics across different datasets.