iS‐GNN: Interpolation of Crustal Stress Maps Using a Graph Neural Network Model

Abstract

Estimating the orientation of the maximum horizontal stress (SHmax) from sparse and unevenly distributed geophysical observations remains a persistent challenge in tectonic and geomechanical stress studies. Classical interpolation methods often neglect the multiscale tectonic–geological heterogeneity of the crust, leading to biased estimates and excessive smoothing across structural boundaries. Although deep learning architectures such as Graph Neural Networks (GNNs) are well suited to learning from sparse and irregularly distributed data, they do not inherently account for data axiality. As a result, GNN interpolations may produce discontinuities when applied to the interpolation of angular quantities over regular grids, unless the periodic structure of the variable is explicitly incorporated into the model design. In this study, we propose a symmetry‐aware Graph Neural Network, termed iS–GNN, to interpolate SHmax orientations across arbitrary regular spatial grids while explicitly accounting for their inherent periodicity. The model encodes azimuthal values through trigonometric transformations to preserve axial symmetry and constructs a geodesy‐informed graph incorporating both spatial proximity and geological attributes. It is trained inductively on the World Stress Map data structure using a masked subgraph reconstruction strategy inspired by spatiotemporal kriging, enabling robust generalization to locations with unobserved stress measurements as well as to regular grid nodes. The results highlight the capability of GNN‐based frameworks to generate geophysically consistent stress‐field interpolations in regions where data coverage is sparse or uneven.