Generative adversarial networks for multi-fidelity matrix completion with massive missing entries

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Multi-fidelity matrices refer to a pair of data matrices, whose entries are the measurements of a specific physical quantity at different fidelity levels w.r.t. two environment variables arranged as the row and the column of matrices, respectively. Although a high-fidelity (HF) matrix can provide an accurate description of the physical quantity, it usually has a number of missing entries because of high acquisition cost. In contrast, its low-fidelity (LF) counterpart is complete but the accuracy of its entries cannot meet the actual requirement. Multi-fidelity matrix completion (MMC) aims to complete the missing entries of the HF matrix by fusing the LF matrix and the available entries of the HF matrix. In this paper, we develop a generative adversarial network for multi-fidelity matrix completion (GAN-MMC), which is composed of a generator and a discriminator. The generator input is the LF matrix and its output is the approximation of the complete HF matrix. The discriminator identifies whether the HF approximation completed by the generator accords with the real HF data distribution. A matrix data augmentation method is proposed to enrich the samples for training GAN-MMC. Moreover, a correlation coefficient-based term is also imposed into the generative loss in order to make the generator capture the relatedness information between the available HF entries and the corresponding LF entries. The numerical experiments show that the proposed model can effectively complete the HF matrix with massive missing entries.