Fast parameterization of planar domains for isogeometric analysis via generalization of deep neural network

Abstract

One prominent step in isogeometric analysis (IGA) is known as domain parameterization, that is, finding a parametric spline representation for a computational domain. Typically, domain parameterization is divided into two separate steps: identifying an appropriate boundary correspondence and then parameterizing the interior region. However, this separation significantly degrades the quality of the parameterization. To attain high-quality parameterization, it is necessary to optimize both the boundary correspondence and the interior mapping simultaneously, referred to as integral parameterization. In a prior research, an integral parameterization approach for planar domains based on neural networks was introduced. One limitation of this approach is that the neural network has no ability of generalization, that is, a network has to be trained to obtain a parameterization for each specific computational domain. In this article, we propose an efficient enhancement over this work, and we train a network which has the capacity of generalization—once the network is trained, a parameterization can be immediately obtained for each specific computational via evaluating the network. The new network greatly speeds up the parameterization process by two orders of magnitudes. We evaluate the performance of the new network on the MPEG data set and a self-design data set, and experimental results demonstrate the superiority of our algorithm compared to state-of-the-art parameterization methods.