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

arXiv: https://arxiv.org/abs/2606.20015 · HTML: https://mlsanity.com/paper/2606.20015/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 16 of 16)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Learning Operators with Coupled Attention](https://mlsanity.com/paper/2201.01032/) (2022)
- [Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads](https://mlsanity.com/paper/2306.03645/) (2023)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Digital twin, physics-based model, and machine learning applied to damage detection in structures](https://mlsanity.com/paper/2005.14360/) (2020)
- [A multi-fidelity deep operator network (DeepONet) for fusing simulation and monitoring data: Application to real-time settlement prediction during tunnel construction](https://mlsanity.com/paper/2310.00057/) (2023)
- [Point-DeepONet: Predicting Nonlinear Fields on Non-Parametric Geometries under Variable Load Conditions](https://mlsanity.com/paper/2412.18362/) (2024)
- [Predictions of Transient Vector Solution Fields with Sequential Deep Operator Network](https://mlsanity.com/paper/2311.11500/) (2023)
- [Parameter estimation of structural dynamics with neural operators enabled surrogate modeling](https://mlsanity.com/paper/2410.11712/) (2024)
- [Damage identification for bridges using machine learning: Development and application to KW51 bridge](https://mlsanity.com/paper/2408.03002/) (2024)
- [Physics-informed Multiple-Input Operators for efficient dynamic response prediction of structures](https://mlsanity.com/paper/2505.07090/) (2025)

## Abstract (arXiv)

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.