人工神经网络(Artificial Neural Network,即ANN),它从信息处理角度对人脑神经元网络进行抽象,建立某种简单模型,按不同的连接方式组成不同的网络。在工程与学术界也常直接简称为神经网络或类神经网络。神经网络是一种运算模型,由大量的节点(或称神经元)之间相互联接构成。每个节点代表一种特定的输出函数,称为激励函数(activation function)。每两个节点间的连接都代表一个对于通过该连接信号的加权值,称之为权重,这相当于人工神经网络的记忆。网络的输出则依网络的连接方式,权重值和激励函数的不同而不同。而网络自身通常都是对自然界某种算法或者函数的逼近,也可能是对一种逻辑策略的表达。

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人工神经网络与其他学科领域联系日益紧密,人们通过对人工神经网络层结构的探索和改进来解决各个领域的问题。根据人工神经网络相关文献进行分析,综述了人工神经网络算法以及网络模型结构的发展史,根据神经网络的发展介绍了人工神经网络相关概念,其中主要涉及到多层感知器、反向传播神经网络、卷积神经网络以及递归神经网络,描述了卷积神经网络发展当中出现的部分卷积神经网络模型和递归神经网络中常用的相关网络结构,分别综述了各个人工神经网络算法在相关领域的应用情况,总结了人工神经网络的未来发展方向。

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Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. Traditionally, these surrogates have been trained using datasets which map strain inputs to stress outputs directly. Data-driven constitutive models for elastic and inelastic materials have commonly been developed based on artificial neural networks (ANNs), which recently enabled the incorporation of physical laws in the construction of these models. However, ANNs do not offer convergence guarantees and are reliant on user-specified parameters. In contrast to ANNs, Gaussian process regression (GPR) is based on nonparametric modeling principles as well as on fundamental statistical knowledge and hence allows for strict convergence guarantees. GPR however has the major disadvantage that it scales poorly as datasets get large. In this work we present a physics-informed data-driven constitutive modeling approach for isostropic and anisotropic materials based on probabilistic machine learning that can be used in the big data context. The trained GPR surrogates are able to respect physical principles such as material frame indifference, material symmetry, thermodynamic consistency, stress-free undeformed configuration, and the local balance of angular momentum. Furthermore, this paper presents the first sampling approach that directly generates space-filling points in the invariant space corresponding to bounded domain of the gradient deformation tensor. Overall, the presented approach is tested on synthetic data from isotropic and anisotropic constitutive laws and shows surprising accuracy even far beyond the limits of the training domain, indicating that the resulting surrogates can efficiently generalize as they incorporate knowledge about the underlying physics.

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