Physics-informed neural networks for solving forward and inverse problems in complex beam systems
Abstract
This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler-Bernoulli and Timoshenko partial differential equations (PDEs) are solved using nondimensional equations with the physics-informed loss function. Higher-order complex beam PDEs are efficiently solved for forward problems to compute the transverse displacements and cross-sectional rotations with less than 1e-3 percent error. Furthermore, inverse problems are robustly solved to determine the unknown dimensionless model parameters and applied force in the entire space-time domain, even in the case of noisy data. The results suggest that PINNs are a promising strategy for solving problems in engineering structures and machines involving beam systems.
Cite
@article{arxiv.2303.01055,
title = {Physics-informed neural networks for solving forward and inverse problems in complex beam systems},
author = {Taniya Kapoor and Hongrui Wang and Alfredo Nunez and Rolf Dollevoet},
journal= {arXiv preprint arXiv:2303.01055},
year = {2023}
}