Different types of effective neural network structures have been developed, including the recurrent neural networks (RNNs), concurrent neural networks (CNNs), among others. The TrumpetNet was recently proposed by the leading author for creating two-way deepnets using physics-law-based models, such as finite element method (FEM) and smoothed FEM or S-FEM. The unique feature of the TrumpetNet is the effectiveness of both forward and inverse problems, by design a desired net architecture. Most importantly, solutions to inverse problems can be analytically derived in explicit formulae for the first time. This work presents a novel TubeNet designed for inverse problems, by designing a simple but special tubular architecture. The TubeNet is a simplified TrumpetNet, and hence it is found easier to apply. It uses the principal component analysis (PCA) to reduce the dimensionality of the “measurement” data, which allows one to select the desired number of major principal components to match with the number of neurons in a layer in the TubeNet. Intensive studies and analyses were conducted to examine the proposed TubeNet, using solid mechanics problem considering material property as parameters to be inversely identified. In this work, we successfully inversely identified up to eight parameters for idealized composite laminates, through explicit formulas, termed as direct-weights-inversion (DWI) approach, which is a chain of matrix inversions for the weight matrices of the network layers. The proposed TubeNet concept can fundamentally change the way in which inverse problems in various fields of studies are dealt with. It is a breakthrough in dealing with inverse problem that are inherently difficult to solve.

中文翻译：

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Tubenet：用于显式解决逆问题的特殊喇叭网

已经开发了不同类型的有效神经网络结构，包括循环神经网络 (RNN)、并发神经网络 (CNN) 等。TrumpetNet 最近由主要作者提出，用于使用基于物理定律的模型创建双向深度网络，例如有限元法 (FEM) 和平滑 FEM 或 S-FEM。TrumpetNet 的独特之处在于通过设计所需的网络架构来解决正向和逆向问题的有效性。最重要的是，逆问题的解决方案首次可以在显式公式中解析得出。这项工作通过设计一个简单但特殊的管状架构，提出了一种针对逆问题设计的新型 TubeNet。TubeNet 是一个简化的 TrumpetNet，因此更容易应用。它使用主成分分析 (PCA) 来降低“测量”数据的维数，这允许人们选择所需数量的主要主成分以与 TubeNet 中一层中的神经元数量相匹配。进行了深入的研究和分析以检查所提出的 TubeNet，使用考虑材料特性的固体力学问题作为要反向识别的参数。在这项工作中，我们通过称为直接权重反转 (DWI) 方法的显式公式成功地反向确定了理想复合层压板的多达八个参数，这是网络层权重矩阵的矩阵反转链。提出的 TubeNet 概念可以从根本上改变各个研究领域的逆问题的处理方式。