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.

References in corpus (6)

• Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
• Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
• Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling
• Physics Guided Machine Learning Methods for Hydrology

Cited by in corpus (6)

• Applications of Scientific Machine Learning for the Analysis of Functionally Graded Porous Beams
• Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plants
• Magnetic Hysteresis Modeling with Neural Operators
• Physics-Informed Neural Networks for Nonlocal Beam Eigenvalue Problems
• Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networks
• Toward using explainable data-driven surrogate models for treating performance-based seismic design as an inverse engineering problem