Physics-informed semantic inpainting: Application to geostatistical modeling

JOURNAL OF COMPUTATIONAL PHYSICS

卷:419

Article

Zheng, Qiang^1,2  Zeng, Lingzao¹  Karniadakis, George Em^2,3 

[1] Zhejiang Univ, Inst Soil & Water Resource & Environm Sci, Coll Environm & Resource Sci, Zhejiang Prov Key Lab Agr Resources & Environm, Hangzhou, Peoples R China

[2] Brown Univ, Div Appl Math, Providence, RI 02906 USA

[3] Pacific Northwest Natl Lab, Richland, WA 99352 USA

关键词: Physics-informed;    Semantic inpainting;    Generative adversarial network;    Geostatistical modeling;   

DOI  :  10.1016/j.jcp.2020.109676

来源: Elsevier

【 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free