ディープラーニングを用いたマルチスケール定常熱伝導解析

抄録

In recent years, deep learning using convolution neural network (CNN) has made great achievements in the field of image recognition. However, there are few applications of deep learning using convolution neural network in the field of numerical simulation. In this study, we propose a new multiscale analysis method, termed the “CNN-based DDM” which combines CNN with a multiscale technique, the domain decomposition method (DDM) In the DDM, we first divide an entire (global) domain into multiple local domains. We then analyze each local domain by a conventional numerical scheme, e.g., a standard finite difference method (FDM) solver, and obtain relation between dependent-variable values at outer grid points of the local domain. The global domain can be analyzed efficiently and rapidly using the relations of all the local domains. In the proposed “CNN-based DDM”, the CNN constructs the relation between variable values at outer grid points of each local domain based on the shape, size, and material property distribution of the local domain. We analyzed the linear steady state heat conduction fields with 2-dimentional non-periodic and heterogeneous thermal conductivity distribution using the proposed method, DDM and FDM, respectively. The proposed method calculated the temperature distribution almost equivalent to that calculated by FDM. We tested two types of CNNs. The smaller CNN conducted the local analysis more quickly than the standard FDM. From the above, it is suggested that the proposed method is useful for reducing the computational cost of the DDM.