Affiliation：Kyoto University

Abstract：Recent advancements in numerical methods for solid mechanics have focused on the development of physics-informed neural networks (PINNs) and deep neural operators. These innovative approaches aim to address key challenges in solving governing partial differential equations (PDEs) while enhancing computational efficiency and predictive fidelity. This study presents two significant contributions: the Physics-Informed Neural Operator Solver (PINOS) and the Vehicle Bridge Interaction Neural Operator (VINO), both of which leverage machine learning techniques to improve structural analysis and monitoring.
The Physics-Informed Neural Operator Solver (PINOS) facilitates accurate and efficient simulations without the need for labeled datasets. It incorporates a neural operator backbone, geometry-decoded layers, and weak-form PDEs based on the principle of least work. Validation through various numerical simulations, including one-dimensional trusses and three-story building structures, reveals that PINOS achieves speedups ranging from 3 to 20 times compared to traditional finite element software. These results demonstrate the potential of PINOS to enhance solution approximations while significantly reducing computational costs.
The Vehicle-Bridge Interaction Neural Operator (VINO) focuses on structural design analysis and condition monitoring by learning the relationship between structural responses and damage from a bridge finite element model. As a surrogate model, VINO has demonstrated over 99% accuracy in predicting structural responses and a remarkable 2000-fold speedup in analysis. Additionally, it effectively detects, localizes, and quantifies bridge damages through experimental validation. Together, these advancements underscore the promising integration of PINNs and deep neural operators in structural engineering, paving the way for future research on complex geometrical structures and non-linear constitutive relationships.

Publication related to your research:
（Journal paper）

• C. Kaewnuratchadasorn, J. Wang, C.W. Kim, "Neural operator for structural simulation and bridge health monitoring", Computer-Aided Civil and Infrastructure Engineering, Vol.39, pp.872–890, 2024
• C. Kaewnuratchadasorn, J. Wang, C.W. Kim, "Physics-informed neural operator solver and super-resolution for solid mechanics", Computer-Aided Civil and Infrastructure Engineering, Vol.39, pp.3435–3451, 2024
• C. Kaewnuratchadasorn, J. Wang, C.W. Kim, X. Deng, "Geometry physics neural operator solver for solid mechanics", Computer-Aided Civil and Infrastructure Engineering, Vol.40, pp.1388–1404, 2025