Can CNNs Construct Highly Accurate Model Efficiently with Limited Training Samples?

It is well known that metamodel or surrogate modeling techniques have been widely applied in engineering problems due to their higher efficiency. However, with the increase of the linearity and dimensions, it is difficult for the present popular metamodeling techniques to construct reliable metamodel and apply to more and more complicated high dimensional problems. Recently, neural networks (NNs), especially deep neural networks (DNNs) have been widely recognized as feasible and effective tools for multidiscipline. Actually, some popular NNs, such as back propagation neural networks (BPNNs) can be regarded as a kind of metamodeling techniques. However, for high dimensional problems, it seems difficult for a BPNN to construct a metamodel. In this study, to construct the high accurate metamodel efficiently, another powerful NN, convolutional neural networks (CNNs) are introduced to construct metamodels. Considering the distinctive characteristic of the CNNs, the CNNs are considered to be a potential modeling tool to handle highly nonlinear and dimensional problems with the limited training samples.