Abstract A neural network enhanced system containing a subsystem with one or multiple neural networks is proposed. Instead of defining the loss function as the direct output of a neural network model, the proposed method uses the system output, which can be measured from experiments, to define the loss function. The loss function is contributed by the outputs from one or multiple neural network models through a subsystem. As a result, the direct output of the ANN model is not required to be measurable from experiments. A set of new back-propagation equations have been derived for this system. Two examples are given using the proposed system: learning the nonlinear in-plane shear constitutive law and learning the failure initiation criterion of fiber-reinforced composites (FRC). The neural network models in both examples are trained at the lamina level using the measurable experimental responses of laminates. The results obtained from the learned neural network models agree well with the corresponding analytical solutions. The proposed method can be used to train neural network models in a subsystem when only the input and output of the system is measurable.

中文翻译：

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一种使用间接可测量数据学习复合材料非线性本构律和失效起始准则的神经网络增强系统

摘要 提出了一种包含一个或多个神经网络子系统的神经网络增强系统。所提出的方法不是将损失函数定义为神经网络模型的直接输出，而是使用可以从实验中测量的系统输出来定义损失函数。损失函数由一个或多个神经网络模型通过子系统的输出贡献。因此，不需要从实验中测量 ANN 模型的直接输出。已经为该系统导出了一组新的反向传播方程。使用所提出的系统给出了两个示例：学习非线性平面内剪切本构律和学习纤维增强复合材料 (FRC) 的失效起始准则。两个示例中的神经网络模型都使用层压板的可测量实验响应在层压板级别进行训练。从学习到的神经网络模型获得的结果与相应的解析解非常吻合。当只有系统的输入和输出是可测量的时，所提出的方法可用于在子系统中训练神经网络模型。