Deep and Physics-Informed Neural Networks as a Substitute for Finite Element Analysis

Today, an engineer's success is largely based on their skill at employing Finite Element Analysis (FEA), a standard engineering modeling tool to numerically assess the behavior of structures. So far, improvements in computational power and FEA element formulations have supported significant advancements in this field. FEA can be used to provide accurate and fast answers to many engineering problems. However, FEA models are still associated with prohibitive time costs when solving complex scenarios. Unlike traditional computer algorithms, Machine Learning, by minimizing pre-established loss functions, can ascertain patterns and make predictions without being explicitly programmed for a given task. This paper presents initial results on improving structural analysis tools by harnessing the power of Machine Learning algorithms, namely Deep Artificial Neural Networks (ANNs) and Physics-Informed Neural Networks (PINNs), with the final objective of substituting or accelerating FEA in accurately predicting the structural behavior within an engineering domain. It is found that ANNs can accurately predict the stress, strain, and displacement maps for a cantilevered rectangular plate under a concentrated load. ANNs demonstrate that, with a large training dataset, efficient and accurate predictions can be achieved although only for specific problems. These algorithms could be enhanced with the governing differential equations to improve convergence and speed. PINNs show that, despite being less efficient than FEA, the method shows more generalization potential than ANNs. Both results show the potential for machine learning algorithms to enhance traditional computational mechanics methods.