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).

中文翻译：

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使用人工神经网络求解多尺度计算力学中的统计逆问题

摘要 这项工作使用基于人工神经网络的机器学习解决了随机异质材料表观弹性特性的逆识别问题。所提出的基于神经网络的识别方法需要构建一个数据库，从中可以训练人工神经网络来学习随机柔顺场的先验随机模型的超参数与广告的一些相关感兴趣量之间的非线性关系hoc 多尺度计算模型。由输入数据和目标数据组成的初始数据库首先从计算模型中生成，通过使用非参数统计相对于目标数据调节输入数据，从中推断出处理后的数据库。然后从每个初始和处理的数据库中训练两层和三层前馈人工神经网络，以构建超参数（网络输出）和感兴趣量（网络输入）之间非线性映射的代数表示。从均方误差、线性回归拟合以及两个数据库的网络输出和目标之间的概率分布方面分析了经过训练的人工神经网络的性能。最后提出了输入随机向量的特殊概率模型，以考虑网络输入的不确定性，并针对输入的不确定性水平对网络输出进行鲁棒性分析。