Jing Wang

Hairun Xie, Jing Wang, Miao Zhang

The modern aerodynamic optimization has a strong demand for parametric methods with high levels of intuitiveness, flexibility, and representative accuracy, which cannot be fully achieved through traditional airfoil parametric techniques. In this paper, two deep learning-based generative schemes are proposed to effectively capture the complexity of the design space while satisfying specific constraints. 1. Soft-constrained scheme: a Conditional Variational Autoencoder (CVAE)-based model to train geometric constraints as part of the network directly. 2. Hard-constrained scheme: a VAE-based model to generate diverse airfoils and an FFD-based technique to project the generated airfoils onto the given constraints. According to the statistical results, the reconstructed airfoils are both accurate and smooth, without any need for additional filters. The soft-constrained scheme generates airfoils that exhibit slight deviations from the expected geometric constraints, yet still converge to the reference airfoil in both geometry space and objective space with some degree of distribution bias. In contrast, the hard-constrained scheme produces airfoils with a wider range of geometric diversity while strictly adhering to the geometric constraints. The corresponding distribution in the objective space is also more diverse, with isotropic uniformity around the reference point and no significant bias. These proposed airfoil parametric methods can break through the boundaries of training data in the objective space, providing higher quality samples for random sampling and improving the efficiency of optimization design.

Yueru Chen, Yiting Shao, Jing Wang et al.

Inspired by the recently proposed successive subspace learning (SSL) principles, we develop a successive subspace graph transform (SSGT) to address point cloud attribute compression in this work. The octree geometry structure is utilized to partition the point cloud, where every node of the octree represents a point cloud subspace with a certain spatial size. We design a weighted graph with self-loop to describe the subspace and define a graph Fourier transform based on the normalized graph Laplacian. The transforms are applied to large point clouds from the leaf nodes to the root node of the octree recursively, while the represented subspace is expanded from the smallest one to the whole point cloud successively. It is shown by experimental results that the proposed SSGT method offers better R-D performances than the previous Region Adaptive Haar Transform (RAHT) method.

Jing Wang, Meng Wang, Xuegang Hu et al.

In this paper, we propose a non-convex formulation to recover the authentic structure from the corrupted real data. Typically, the specific structure is assumed to be low rank, which holds for a wide range of data, such as images and videos. Meanwhile, the corruption is assumed to be sparse. In the literature, such a problem is known as Robust Principal Component Analysis (RPCA), which usually recovers the low rank structure by approximating the rank function with a nuclear norm and penalizing the error by an $\ell_1$-norm. Although RPCA is a convex formulation and can be solved effectively, the introduced norms are not tight approximations, which may cause the solution to deviate from the authentic one. Therefore, we consider here a non-convex relaxation, consisting of a Schatten-$p$ norm and an $\ell_q$-norm that promote low rank and sparsity respectively. We derive a proximal iteratively reweighted algorithm (PIRA) to solve the problem. Our algorithm is based on an alternating direction method of multipliers, where in each iteration we linearize the underlying objective function that allows us to have a closed form solution. We demonstrate that solutions produced by the linearized approximation always converge and have a tighter approximation than the convex counterpart. Experimental results on benchmarks show encouraging results of our approach.