A robust solution of a statistical inverse problem in multiscale
computational mechanics using an artificial neural network
- URL: http://arxiv.org/abs/2011.11761v2
- Date: Thu, 11 Feb 2021 14:36:36 GMT
- Title: A robust solution of a statistical inverse problem in multiscale
computational mechanics using an artificial neural network
- Authors: Florent Pled (MSME), Christophe Desceliers (MSME), Tianyu Zhang (MSME)
- Abstract summary: This work addresses the inverse identification of apparent elastic properties of random heterogeneous materials using machine learning based on artificial neural networks.
The proposed neural network-based identification method requires the construction of a database from which an artificial neural network can be trained.
The performances of the trained artificial neural networks are analyzed in terms of mean squared error, linear regression fit and probability distribution.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This work addresses the inverse identification of apparent elastic properties
of random heterogeneous materials using machine learning based on artificial
neural networks. The proposed neural network-based identification method
requires the construction of a database from which an artificial neural network
can be trained to learn the nonlinear relationship between the hyperparameters
of a prior stochastic model of the random compliance field and some relevant
quantities of interest of an ad hoc multiscale computational model. An initial
database made up with input and target data is first generated from the
computational model, from which a processed database is deduced by conditioning
the input data with respect to the target data using the nonparametric
statistics. Two-and three-layer feedforward artificial neural networks are then
trained from each of the initial and processed databases to construct an
algebraic representation of the nonlinear mapping between the hyperparameters
(network outputs) and the quantities of interest (network inputs). The
performances of the trained artificial neural networks are analyzed in terms of
mean squared error, linear regression fit and probability distribution between
network outputs and targets for both databases. An ad hoc probabilistic model
of the input random vector is finally proposed in order to take into account
uncertainties on the network input and to perform a robustness analysis of the
network output with respect to the input uncertainties level. The capability of
the proposed neural network-based identification method to efficiently solve
the underlying statistical inverse problem is illustrated through two numerical
examples developed within the framework of 2D plane stress linear elasticity,
namely a first validation example on synthetic data obtained through
computational simulations and a second application example on real experimental
data obtained through a physical experiment monitored by digital image
correlation on a real heterogeneous biological material (beef cortical bone).
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