Machine Learning in Structural Engineering: Physics-Informed Neural Networks for Beam Problems

The objective of this paper is to provide an accessible introduction to the fundamental principles of physics-informed neural networks (PINNs), to facilitate aspiring researchers to start the journey in this field with minimal coding efforts. A series of structural analysis examples of one-dimensional beams are used to illustrate how the code can be structured. Deflections and cross-section rotations are obtained in a data-driven solution approach, while a data-driven discovery framework is developed to find the beam buckling loads. Regarding the former, the statics of the Timoshenko beam and a geometrically nonlinear case study are investigated, while the discovery framework is used to obtain the buckling load of Euler–Bernoulli beams. The results of PINN simulations are consistent with the reference solutions, with an error of the order of [Formula: see text] for each one of the different error measures.