基于梯度惩罚 Wasserstein 生成对抗网络的数字岩心重建

文章针对三维 Wasserstein 生成对抗网络（Wasserstein generative adversarial networks，WGAN）重建数字岩心的梯度不稳定问题，提出一种基于带梯度惩罚的 Wasserstein 生成对抗网络（Wasserstein generative adversarial networks with gradient penalty，WGAN-GP）三维数字岩心重建算法。首先利用卷积神经网络构建生成网络学习真实样本的分布，然后再构建判别网络以区分重建样本和真实样本。由于 WGAN 的权值裁剪导致权重分散不均匀，WGAN-GP 增加了梯度惩罚项，使得梯度分布更加均匀并加快网络收敛速度，让训练更加稳定。实验通过孔隙度、比表面积和欧拉特性的对比表明，相比于 WGAN 算法，WGAN-GP 三维数字岩心重建算法能更加有效地重现岩石的三维孔隙结构特征。

In view of the problem of gradient instability in the reconstruction of 3D digital cores based on Wasserstein generative adversarial networks (WGAN), this paper proposes a Wasserstein generative adversarial networks with gradient penalty (WGAN-GP) algorithm. A convolutional network is used to build a generative network to learn the distribution of the real samples, and then a discriminative network is built to distinguish the reconstructed samples from the real samples. As the weight cropping of WGAN leads to uneven weight dispersion, WGAN-GP adds a gradient penalty term to make the gradient distribution more uniform and speed up the convergence of the network, allowing for more stable training. A comparison of porosity, specific surface area and Euler characteristics shows that the WGAN-GP reconstruction algorithm is more effective in reproducing the 3D pore structure characteristics of rocks than the WGAN reconstruction algorithm.