Physics-Informed Neural Networks for Solving Forward and Inverse Problems in Complex Beam Systems

This article 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&#x2013;Bernoulli and Timoshenko theories, where the double beams are connected with a Winkler foundation. In particular, forward and inverse problems for the Euler&#x2013;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 <inline-formula> <tex-math notation="LaTeX">$1e-3$</tex-math> </inline-formula>% error. Furthermore, inverse problems are robustly solved to determine the unknown dimensionless model parameters and applied force in the entire space&#x2013;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.