A data-driven identification method based on neural networks for solving statistical inverse problems in computational mechanics

International audiencehis work presents a data-driven machine learning framework for the solution of statistical inverse problems in multiscale computational solid mechanics. The proposed identification method is based on the design of an artificial neural network [Haykin, 1994, Demuth et al., 2014] in order to learn the nonlinear mapping between the hyperparameters of a prior stochastic model of the random compliance field [Soize, 2006] and dedicated quantities of interest of an ad hoc multiscale computational model. An initial database containing input and target data is first generated using the multiscale computational model. A processed database is then constructed by conditioning the input data with respect to the target data using classical kernel smoothing techniques in nonparametric statistics [Bowman and Azzalini, 1997] in order to derive an efficient trained neural network for identification purposes. Multilayer feedforward neural networks are then trained from each of the two databases and optimized by considering different network configurations in order to construct a fine-tuned surrogate model of the nonlinear relationship between the hyperparameters (network outputs) and the quantities of interest (network inputs). The performances of the trained neural networks are evaluated in terms of mean squared error, linear regression fit and probability distribution between network outputs and targets for both databases. The (best) trained neural network can then directly be used to identify the output hyperparameters given input observed quantities of interest with no call to the computational model. The efficiency of the neural network-based identification method is illustrated through two numerical examples developed within the framework of 2D plane stress linear elasticity. The proposed method is first validated on synthetic data obtained through numerical simulations and then applied to real experimental data obtained through mechanical tests monitored by digital image correlation on a real heterogeneous biological material (beef cortical bone)