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

Abstract

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–Bernoulli and Timoshenko
theories, 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

% 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.