Zhiyang Zhang

Jiarui Cao, Zhiyang Zhang, Heming Wang et al.

Nowadays, the nanostructure inverse problem is an attractive problem that helps researchers to understand the relationship between the properties and the structure of nanomaterials. This article focuses on the problem of using PDF to recover the nanostructure, which this article views as a conditional generation problem. This article propose a deep learning model CbLDM, Condition-based Latent Diffusion Model. Based on the original latent diffusion model, the sampling steps of the diffusion model are reduced and the sample generation efficiency is improved by using the conditional prior to estimate conditional posterior distribution, which is the approximated distribution of p(z|x). In addition, this article uses the Laplacian matrix instead of the distance matrix to recover the nanostructure, which can reduce the reconstruction error. Finally, this article compares CbLDM with existing models which were used to solve the nanostructure inverse problem, and find that CbLDM demonstrates significantly higher prediction accuracy than these models, which reflects the ability of CbLDM to solve the nanostructure inverse problem and the potential to cope with other continuous conditional generation tasks.

Zhiyang Zhang, Shihua Zhang

Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networks). Here, we think three factors in each layer of it including the initialization, the dictionary design and the number of iterations greatly affect the performance of ML-CSC. Inspired by these considerations, we propose two novel multi-layer models--residual convolutional sparse coding model (Res-CSC) and mixed-scale dense convolutional sparse coding model (MSD-CSC), which have close relationship with the residual neural network (ResNet) and mixed-scale (dilated) dense neural network (MSDNet), respectively. Mathematically, we derive the shortcut connection in ResNet as a special case of a new forward propagation rule on ML-CSC. We find a theoretical interpretation of the dilated convolution and dense connection in MSDNet by analyzing MSD-CSC, which gives a clear mathematical understanding about them. We implement the iterative soft thresholding algorithm (ISTA) and its fast version to solve Res-CSC and MSD-CSC, which can employ the unfolding operation for further improvements. At last, extensive numerical experiments and comparison with competing methods demonstrate their effectiveness using three typical datasets.