论文标题
使用人工神经网络在多尺度计算力学中统计反问题的强大解决方案
A robust solution of a statistical inverse problem in multiscale computational mechanics using an artificial neural network
论文作者
论文摘要
这项工作解决了基于人工神经网络的机器学习的随机异质材料的明显弹性特性的逆鉴定。提出的基于神经网络的识别方法需要构建数据库，可以从中培训人工神经网络，以了解随机合规性领域的先前随机模型的超参数和一些相关量的多数兴趣之间的非线性关系。最初是由输入和目标数据组成的初始数据库，首先是从计算模型中生成的，通过该模型，通过使用非参数统计信息来调节输入数据，从中得出了处理后的数据库。然后，从每个初始和处理的数据库中训练两层和三层馈电的人工神经网络，以构建超参数（网络输出）和感兴趣的数量（网络输入）之间非线性映射的代数表示。分析了训练有素的人工神经网络的性能，分析了两个数据库的均衡误差，线性回归拟合和网络输出和目标之间的概率分布。最终提出了输入随机向量的临时概率模型，以考虑网络输入上的不确定性，并对输入不确定性级别对网络输出进行稳健性分析。通过在2D平面应力线性弹性的框架内开发的两个数值示例，即通过计算模拟获得的合成数据示例，通过计算材料（通过数字实验的第二个应用程序）在数字实验数据中获得的合成数据，通过数字型示例（通过数字图像Correles获得的第二个验证）来说明，提出的基于神经网络识别方法有效解决潜在的统计逆问题的能力有效地解决了基本统计逆问题。骨头）。
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).
