Physics-informed neural networks for solving forward and inverse problems in complex beam systems
This addresses structural engineering problems by providing an efficient simulation method for beam systems, though it is incremental as it applies an existing PINN framework to a specific domain.
The paper tackled simulating complex beam systems using physics-informed neural networks (PINNs) to solve forward and inverse problems for Euler-Bernoulli and Timoshenko PDEs, achieving less than 1e-3 percent error in forward computations and robust parameter estimation with noisy data.
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.