Tubenet: A Special Trumpetnet for Explicit Solutions to Inverse Problems

Abstract

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.