Jianqing Zhu

Jianqing Zhu, Juncai He, Lian Zhang et al.

By investigating iterative methods for a constrained linear model, we propose a new class of fully connected V-cycle MgNet for long-term time series forecasting, which is one of the most difficult tasks in forecasting. MgNet is a CNN model that was proposed for image classification based on the multigrid (MG) methods for solving discretized partial differential equations (PDEs). We replace the convolutional operations with fully connected operations in the existing MgNet and then apply them to forecasting problems. Motivated by the V-cycle structure in MG, we further propose the FV-MgNet, a V-cycle version of the fully connected MgNet, to extract features hierarchically. By evaluating the performance of FV-MgNet on popular data sets and comparing it with state-of-the-art models, we show that the FV-MgNet achieves better results with less memory usage and faster inference speed. In addition, we develop ablation experiments to demonstrate that the structure of FV-MgNet is the best choice among the many variants.

Juncai He, Jinchao Xu, Lian Zhang et al.

We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN). From this viewpoint, we establish detailed connections between the traditional iterative schemes for linear systems and the architectures of the basic blocks of ResNet- and MgNet-type models. Using these connections, we present some modified ResNet models that compared with the original models have fewer parameters and yet can produce more accurate results, thereby demonstrating the validity of this constrained learning data-feature-mapping assumption. Based on this assumption, we further propose a general data-feature iterative scheme to show the rationality of MgNet. We also provide a systematic numerical study on MgNet to show its success and advantages in image classification problems and demonstrate its advantages in comparison with established networks.