Can CNNs Construct Highly Accurate Model Efficiently with Limited Training Samples for Hundreds-Dimensional Problems?

With the increase of the nonlinearity and dimension, it is difficult for the present popular metamodeling techniques to construct reliable metamodels. To address this problem, Convolutional Neural Network (CNN) is introduced to construct a highly accurate metamodel efficiently. Considering the inherent characteristics of the CNN, it is a potential modeling tool to handle highly nonlinear and dimensional problems (hundreds-dimensional problems) with the limited training samples. In order to evaluate the proposed CNN metamodel for hundreds-dimensional and strong nonlinear problems, CNN is compared with other metamodeling techniques. Furthermore, several high-dimensional analytical functions are also employed to test the CNN metamodel. Testing and comparisons confirm the efficiency and capability of the CNN metamodel for hundreds-dimensional and strong nonlinear problems. Moreover, the proposed CNN metamodel is also applied to IsoGeometric Analysis (IGA)-based optimization successfully.