Solving Plane Elasticity with an Ensemble of Physics-informed Neural Networks

Abstract

Elastic structures in solid mechanics are simulated with the use of a physics-informed multi-neural networks. The proposed computational approach is based on principles of artificial intelligence. A deep learning is performed through training the PINN model in order to fit the elasticity equations and associated boundary conditions at collocation points, without need of input-output data. An open source machine learning platform is used, based on Tensorflow, written in Python and Keras library, an application programming interface, intended for a deep learning. Artificial neural networks (ANNs) have led to revolutionary advances in the manufacturing industry. The main features of a neural network is an architecture which identifies the connections between layers and neurons, dataset which consists of training, validation and testing data, an optimization algorithm for minimizing the loss function and updating the weights and biases between the neurons.