Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges

Long-span roadway bridges present a significant computational challenge for structural analysis. Because vehicular loads are highly localized, traditional Finite Element Method (FEM) simulations are inefficient for tasks requiring repeated evaluations, such as generating influence surfaces or maintaining structural digital twins. This paper addresses the need for a surrogate model capable of capturing high-gradient, localized structural responses without the prohibitive cost of full-scale FEM simulations.

The authors introduce the Adaptive Distance-Aware Deep Operator Network (AD-DeepONet). Unlike standard operator learning models that attempt to map inputs to the entire structural domain, this framework employs a K-nearest neighbors (KNN) strategy to dynamically select an 'adaptive Schur domain'—a localized region surrounding the load application point. To improve the model's sensitivity to geometry, the trunk network is augmented with distance-aware features, including relative position vectors, normalized direction vectors, and Euclidean distance. Finally, the model uses a physics-based Schur complement formulation to reconstruct the full-field response from these localized predictions, ensuring the results remain consistent with the bridge's global equilibrium.

The proposed AD-DeepONet achieves FEM-level accuracy with relative errors consistently below 5%. In terms of computational efficiency, the framework provides a 60x speedup for total response evaluation (including full-field reconstruction) compared to traditional FEM. When excluding the post-processing reconstruction step, the inference speed is up to four orders of magnitude faster than conventional methods. The model was successfully validated on both a benchmark bridge and the real-world Mussafah Bridge, demonstrating its utility for rapid influence line and surface generation.