Adaptive Distance-Aware Trunk Deep Operator Learning for Long-Span Roadway Bridges
Authors: Bilal Ahmed, Diab W. Abueidda, Waleed El-Sekelly, Tarek Abdoun, Mostafa E. Mobasher
Organizations: Civil and Urban Engineering Department, New York University Abu Dhabi, United Arab Emirates · New York University Abu Dhabi, United Arab Emirates · Department of Structural Engineering, Mansoura University, Mansoura, Egypt
Long-span roadway bridges exhibit highly localized structural responses under vehicular loading, making repeated FE analysis computationally expensive for applications such as influence surface generation and structural digital twins. Existing SciML approaches struggle to accurately capture these localized responses. To address this challenge, this study proposes an adaptive-trunk DeepONet for localized structural response prediction in large-scale bridge systems. The framework dynamically constructs a load-dependent learning domain using a KNN strategy, allowing the network to focus on structural influence zones. The trunk network is further enhanced using distance-aware features that encode the geometric relationship between the load and structural nodes. A physics-based full-field reconstruction is incorporated through a stiffness-informed Schur complement formulation, enabling predictions at adaptive nodes to be extended to the entire structural domain. To enable scalable training, response data are generated using a reduced-order equivalent shell model that preserves the dominant global behavior while significantly reducing computational cost. The proposed framework is validated on both a benchmark bridge model and the real-world Mussafah Bridge. Results show that the method achieves FEM-level accuracy with relative errors below 5%, while reducing the total response evaluation time (including full-field reconstruction) by approximately 60x; excluding the post-processing reconstruction step, the AD-DeepONet inference is up to four orders of magnitude faster than FEM. In addition, the framework enables rapid generation of full-field responses, influence lines, and influence surfaces under arbitrary vehicular loading configurations, demonstrating strong potential for large-scale bridge analysis and digital twin applications.
This paper proposes a novel physics-guided spectral deep operator network, termed SpectONet, for solving Euler-Bernoulli beam (EBB) vibration problems. The proposed framework integrates the operator-learning capability of DeepONet with physics-informed constraints and Chebyshev-Gauss-Lobatto (CGL) sensor placement. Unlike conventional DeepONet frameworks, which commonly employ uniformly distributed sensors, SpectONet uses nonuniform spectral sensor locations with a higher concentration of points near the domain boundaries. This sampling strategy improves the finite-dimensional representation of boundary-sensitive structural responses while requiring only a limited number of branch-network inputs. The governing beam equation, together with the associated initial and boundary conditions, incorporated into the training objective to promote physically consistent and generalizable predictions. Numerical experiments on three synthetic EBB vibration problems and a real-world bridge vibration dataset demonstrate the effectiveness of the proposed framework. Comparisons with strong baselines such as, Vanilla DeepONet, PI-DeepONet, PINN, and CNN-UNet show that SpectONet consistently achieves lower prediction errors across all considered evaluation metrics. In particular, SpectONet achieves at least 64% improvement over the considered baseline models across the three synthetic problems and at least 37% for the real-world problems. These results demonstrate that SpectONet provides an accurate, computationally efficient, and physically consistent operator-learning framework for structural vibration analysis.
Finite Element Analysis (FEA) is widely used for transient mechanical simulations, but its high computational cost limits real-time and high-resolution applications. Deep learning surrogate models can reduce this cost; however, many existing approaches are restricted to steady-state prediction or cannot jointly predict Node- and Element-based Outputs (NEO) over time. The state-of-the-art DeepFEA framework has addressed these issues but remains limited to structured finite element (FE) meshes. To overcome this limitation, this study proposes DeepFEAv2, a deep learning surrogate framework that enables prediction of transient FEA simulations across different FE mesh topologies and element types. The main contributions of DeepFEAv2 are: (a) a module that uses the FE connectivity matrix to organize input features by element and arrange them into an input sequence guided by the mesh topology; (b) a novel neural network architecture designed to process the input sequence and jointly predict NEO over time; and (c) a FEA-informed optimization strategy for regularizing these NEO predictions. DeepFEAv2 was evaluated on structured and unstructured 3D linear elastic datasets, as well as on a pressure-driven aortic valve dataset. DeepFEAv2 achieved R^2 values up to 0.99 and normalized errors as low as 0.38%. Compared with DeepFEA, it achieved up to 38.0% relative increase in R^2 and up to 87.1% reduction in normalized error. DeepFEAv2 also performed inference up to three orders of magnitude faster than traditional FEA. These results demonstrate that DeepFEAv2 can efficiently model transient FEA simulations across increasingly complex FE settings, providing a scalable surrogate framework for transient FEA.
Georgios Triantafyllou, Panagiotis G. Kalozoumis, Dimitris K. Iakovidis
This work aims to develop a fast and physically consistent surrogate model for real-time structural health monitoring of fractured elastic domains. We propose a physics-informed DeepONet framework that predicts displacement fields from both boundary conditions and fracture geometry, using a dedicated encoding strategy for the latter and without relying on finite-element-generated training data. The traction-free condition on the fracture boundary is imposed weakly through a localized penalty term. The presented numerical example focuses on one representative fracture geometry, demonstrating the feasibility of the formulation and laying the groundwork for extensions to surrogate modeling across diverse fracture geometries.