Physics-informed neural networks approach for one-dimensional beams

Resumo

Physics-informed neural network (PINN) is a machine learning technique where the physics of the problem is embedded into the loss function. The straightforward approach is to define the loss function using the problem governing differential equations and its boundary/initial conditions in a sort of collocation method. In general, the hyperparameters of neural networks for each problem at hands are defined via a grid search-like procedure, or simply by trial and error. In this paper, the application of PINNs is illustrated for one-dimensional beam problems, and the influence that the network weights initialization procedure has on the training is investigated. The code was built using SciANN, a Python package that uses TensorFlow and Keras for scientific computing and physics-informed deep learning employing artificial neural networks.