A Novel Inverse Procedure Via Creating TubeNet with Constraint Autoencoder for Feature-Space Dimension-Reduction

Abstract

TubeNet has the simplest possible tubular configuration with the uniform number of neurons in all layers and enables explicit inversion. To create a TubeNet, dimension-reduction is a prerequisite for the inverse problems so that the numbers of neurons in the input and output layerscan be made the same. This study introduces a novel procedure to construct inverse TubeNets. The proposed procedure has three major sequential steps. (1) An autoencoder will be used to extract the necessary number of features from a large number of features in a high-dimensional space; (2) Constraints will be imposed to the autoencoder guided by the concepts of the principal component analysis (PCA), so that the extracted features possess the important orthogonality; (3) An L2 regularizer is proposed to adequately impose these constraints on the off-diagonal entries in the weight matrix of the autoencoder, ensuring quality orthogonality. The benchmark problems of inverse identification of material constants of composite laminated plates are used to evaluate the effect of the present TubeNet procedure with the constraint autoencoder, standard autoencoder and PCA, implemented in TubeNet. The study shows that the present constrained autoencoder can effectively overcome the shortcomings of PCA and standard autoencoder, and offers an effective way for dimension-reduction for inverse TubeNet.