Physics-informed semantic inpainting：应用于地质统计建模
Physics-informed semantic inpainting: Application to geostatistical modeling
摘要：
地质统计学建模的一个基本问题是基于有限的测量数据和一些先验空间统计数据来推断非均匀地质场。语义修复是一种使用深度生成模型进行图像处理的技术，最近已被应用于此目的，证明了其在处理复杂空间模式方面的有效性。然而，原始的语义修复框架仅包含来自直接测量的信息，而在地质统计学中，间接测量通常是丰富的。为了克服这一限制，我们提出了一个物理信息语义修复框架，采用Wasserstein生成对抗网络与梯度惩罚（WGAN-GP），并通过利用潜在的物理定律联合结合直接和间接测量。我们对一个512维的高维问题的仿真结果表明，与仅使用直接测量相比，在新方法中，物理守恒定律得到满足，并有助于提高修复性能。
英文摘要：
A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness in dealing with complex spatial patterns. However, the original semantic inpainting framework incorporates only information from direct measurements, while in geostatistics indirect measurements are often plentiful. To overcome this limitation, here we propose a physics-informed semantic inpainting framework, employing the Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and jointly incorporating the direct and indirect measurements by exploiting the underlying physical laws. Our simulation results for a high-dimensional problem with 512 dimensions show that in the new method, the physical conservation laws are satisfied and contribute in enhancing the inpainting performance compared to using only the direct measurements.
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