Physics-informed semantic inpainting: Application to geostatistical modeling
This work addresses geostatistical modeling for geological inference, offering an incremental improvement by incorporating indirect measurements into an existing deep learning method.
The paper tackled the problem of inferring heterogeneous geological fields from limited direct and indirect measurements by proposing a physics-informed semantic inpainting framework using WGAN-GP, which improved inpainting performance by satisfying physical conservation laws in a 512-dimensional simulation.
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.