Learning structural response operators across varying geometries and loads with global and local geometry encoding

Abstract

Predicting mechanical responses across complex geometries and varying loading conditions is central to simulation-driven engineering, yet capturing the influence of geometric boundaries remains challenging for data-driven models. Here we propose a Load- and Geometry-adaptive Deep Operator Network (LG-DON) that integrates global geometric representations with local, boundary-aware information to predict structural responses. By distinguishing distances to different boundary categories rather than relying on the nearest boundary alone, the framework captures spatially varying geometric influences that conventional distance-based representations may overlook. Across benchmark problems involving diverse non-convex geometries, LG-DON reduces the mean relative L2 error from 12.17% for a modified MIONet baseline to 7.41%. Controlled ablation studies further demonstrate the advantages of category-resolved boundary distances and show that combining global and local geometric representations outperforms either representation alone in 15 of 18 evaluated configurations. These findings highlight the value of integrating complementary geometric information for accurate operator learning across complex structural domains.