Eric Laloy

TL;DR: MT‐DREAM(ZS), which combines the strengths of multiple‐try sampling, snooker updating, and sampling from an archive of past states is introduced, which is especially designed to solve high‐dimensional search problems and receives particularly spectacular performance improvement over other adaptive MCMC approaches when using distributed computing.

Abstract: 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.

TL;DR: In this paper, the authors report on two strategies for accelerating posterior inference of a highly parameterized and CPU-demanding groundwater flow model using generalized polynomial chaos (gPC) theory and dimensionality reduction.

TL;DR: This paper suggests that DL-based methods can open up a complementary avenue toward knowledge discovery in hydrologic sciences, and suggests that integrating process-based models with DL models will help alleviate data limitations.

TL;DR: This work uses a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media and finds that the dimensionality reduction (DR) approach outperforms principle component analysis (PCA), optimization-PCA, and discrete cosine transform (DCT) DR techniques for unconditional geostatistical simulation of a channelized prior model.