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).
Artificial Intelligence-Based Multiscale Temporal Modeling for Anomaly Detection in Cloud Services
University of Southern California（南加州大学）；Carnegie Mellon University（卡内基梅隆大学）；Northeastern University（东北大学）；Rice University（莱斯大学）；Trine University（特里恩大学）
Discovering Multiscale Deep Formulas in Complex Systems via Neural-Guided Lambda Calculus
National Engineering Laboratory for Big Data Analytics（大数据分析国家工程实验室）；Xi’an Jiaotong University（西安交通大学）；School of Mathematics and Statistics（数学与统计学学院）；School of Computer Science and Technology, Faculty of Electronic and Information Engineering（计算机科学与技术学院，电子与信息工程学院）
Artificial intelligence for partial differential equations in computational mechanics: A review
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China（清华大学工程力学系）；Simulation Technology, Institute of Photonics, Leibniz University Hannover, Hannover 30167, Germany（汉诺威莱布尼茨大学光子研究所仿真技术部）；Drilling Mechanical Department, CNPC Engineering Technology RD Company Limited, Beijing 102206, China（中石油工程科技研发有限公司钻探机械部）；School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, QLD 4000, Australia（昆士兰科技大学机械、医疗与加工工程学院）；ARC Industrial Transformation Training Centre—Joint Biomechanics, Queensland University of Technology, Brisbane, QLD 4000, Australia（昆士兰科技大学 ARC 工业转型培训中心—联合生物力学）
