A Domain Decomposition–Based CNN-DNN Architecture for Model Parallel Training Applied to Image Recognition Problems

SIAM Journal on Scientific Computing, Volume 46, Issue 5, Page C557-C582, October 2024.
Abstract. Deep neural networks (DNNs) and, in particular, convolutional neural networks (CNNs) have brought significant advances in a wide range of modern computer application problems. However, the increasing availability of large numbers of datasets and the increasing available computational power of modern computers have led to steady growth in the complexity and size of DNN and CNN models, respectively, and thus, to longer training times. Hence, various methods and attempts have been developed to accelerate and parallelize the training of complex network architectures. In this work, a novel CNN-DNN architecture is proposed that naturally supports a model parallel training strategy and that is loosely inspired by two-level domain decomposition methods (DDMs). First, local CNN models, that is, subnetworks, are defined that operate on overlapping or nonoverlapping parts of the input data, for example, subimages. The subnetworks can be trained completely in parallel and independently of each other. Each subnetwork then outputs a local decision for the given machine learning problem which is exclusively based on the respective local input data. Subsequently, in a second step, an additional DNN model is trained which evaluates the local decisions of the local subnetworks and generates a final, global decision. With respect to the analogy to DDMs, the DNN models can be loosely interpreted as a coarse problem and hence, the new approach can be interpreted as a two-level domain decomposition. In this paper, we apply the proposed architecture to image classification problems using CNNs. Experimental results for different two-dimensional image classification problems are provided, as well as a face recognition problem and a classification problem for three-dimensional computed tomography (CT) scans. Therefore, classical Residual Network (ResNet) and VGG architectures are considered. More modern architectures, such as, e.g., MobileNet2, are left for future work. The results show that the proposed approach can significantly accelerate the required training time compared to the global model and, additionally, can also help to improve the accuracy of the underlying classification problem.