Training‐Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network
By Eric Laloy, Romain Hérault, Diederik Jacques, Niklas Linde. 2017
345 citations recorded by the source corpus.
Probabilistic inversion within a multiple‐point statistics framework is often computationally prohibitive for high‐dimensional problems. To partly address this, we introduce and evaluate a new training‐image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generative adversarial network (GAN) type. After training using a training image (TI), our proposed spatial GAN (SGAN) can quickly generate 2‐D and 3‐D unconditional realizations. A key characteristic of our SGAN is that it defines a (very) low‐dimensional parameterization, thereby allowing for efficient probabilistic inversion using state‐of‐the‐art Markov chain Monte Carlo (MCMC) methods. In addition, available direct conditioning data can be incorporated within the inversion. Several 2‐D and 3‐D categorical TIs are first used to analyze the performance of our SGAN for unconditional geostatistical simulation. Training our deep network can take several hours. After training, realizations containing a few millions of pixels/voxels can be produced in a matter of seconds. This makes it especially useful for simulating many thousands of realizations (e.g., for MCMC inversion) as the relative cost of the training per realization diminishes with the considered number of realizations. Synthetic inversion case studies involving 2‐D steady state flow and 3‐D transient hydraulic tomography with and without direct conditioning data are used to illustrate the effectiveness of our proposed SGAN‐based inversion. For the 2‐D case, the inversion rapidly explores the posterior model distribution. For the 3‐D case, the inversion recovers model realizations that fit the data close to the target level and visually resemble the true model well.
Subfields: Geochemistry and Petrology, Ocean Engineering
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geochemistry and Petrology
In Ocean Engineering
Citations in the corpus
- Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data (2019, methodology): “Samples are obtained by cropping 64× 64 patches from one large training image [72] of size 2500 × 2500, or 32 × 32 patches from the resized 1250 × 1250 image (resized with nearest neighborhood).”
- Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, neutral): “The third input field dataset considered is channelized field [74], defined with binary values 0.”
- Deep Convolutional Encoder‐Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media (2018, methodology): “…in many communities such as computer vision [Badrinarayanan et al., 2017; He et al., 2016], dimensionality reduction [Chan and Elsheikh, 2017; Laloy et al., 2017, 2018], and surrogate modeling [Tripathy and Bilionis, 2018; Zhu and Zabaras, 2018] due to their robustness and generalization…”
- A Transdisciplinary Review of Deep Learning Research and Its Relevance for Water Resources Scientists (2017, methodology): “Then, the same authors switched to a SHEN 8573 spatial GAN to capture the complex spatial data distributions (Laloy et al., 2018).”