Combining artificial neural networks with finite element methods to predict the structural response of the proximal femur

The finite element method (FEM) is a highly popular discretization numerical technique in computational mechanics. However, nowadays, numerical applications are becoming increasingly complex. Thus, traditional solving techniques generally demand a larger computational capacity and show higher computational costs. Machine learning techniques can be combined with the FEM to reduce the computational cost associated with the numerical analysis, being applied as surrogate solvers or as a predictive tool. This work presents a brief introduction to feed forward neural networks, a machine learning techinque, using MATLAB with a first benchmark example of a classification problem, the "two moons" problem, with the objective of introducing the most important concepts. This first example allowed to understand the basic machine artificial learning with neural networks (NN) MATLAB tools. Then, a second problem was analysed with the objective of showing the potential of combining FEM with artificial NN for a biomechanical application. It was observed that the artificial NN allow to predict displacements and stresses with a high level of accuracy and, simultaneously, save a significant computational time. Surprisingly, feature analysis through connection weights approach on the input variables showed that the neural network was capable of detecting the physical importance of the variables for each problem. The most significant disadvantage of artificial NN is the necessity of acquiring large amounts of data and prepare such data for training and testing, which is time consuming