# Physics-informed semantic inpainting: Application to geostatistical modeling

arXiv: https://arxiv.org/abs/1909.09459 · HTML: https://mlsanity.com/paper/1909.09459/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2019.

## Built on by (most cited first, 15 of 15)

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- [Physical Knowledge Enhanced Deep Neural Network for Sea Surface Temperature Prediction](https://mlsanity.com/paper/2304.09376/) (2023)
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- [Generative modeling of spatio-temporal weather patterns with extreme event conditioning](https://mlsanity.com/paper/2104.12469/) (2021)
- [Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics](https://mlsanity.com/paper/2402.17913/) (2024)
- [Physics-Informed Deep Learning: A Promising Technique for System Reliability Assessment](https://mlsanity.com/paper/2108.10828/) (2021)
- [Magnetic Field Prediction Using Generative Adversarial Networks](https://mlsanity.com/paper/2203.07897/) (2022)
- [Simulated Data Generation Through Algorithmic Force Coefficient Estimation for AI-Based Robotic Projectile Launch Modeling](https://mlsanity.com/paper/2105.12833/) (2021)
- [CarbonNet: How Computer Vision Plays a Role in Climate Change? Application: Learning Geomechanics from Subsurface Geometry of CCS to Mitigate Global Warming](https://mlsanity.com/paper/2403.06025/) (2024)
- [Scalable physics-informed deep generative model for solving forward and inverse stochastic differential equations](https://mlsanity.com/paper/2503.18012/) (2025)
- [Extended Physics Informed Neural Network for Hyperbolic Two-Phase Flow in Porous Media](https://mlsanity.com/paper/2511.13734/) (2025)

## Abstract (arXiv)

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.