[1] Spatially distributed hydrologic models are increasingly being used to study and predict soil moisture flow, groundwater recharge, surface runoff, and river discharge. The usefulness and applicability of such complex models is increasingly held back by the potentially many hundreds (thousands) of parameters that require calibration against some historical record of data. The current generation of search and optimization algorithms is typically not powerful enough to deal with a very large number of variables and summarize parameter and predictive uncertainty. We have previously presented a general-purpose Markov chain Monte Carlo (MCMC) algorithm for Bayesian inference of the posterior probability density function of hydrologic model parameters. This method, entitled differential evolution adaptive Metropolis (DREAM), runs multiple different Markov chains in parallel and uses a discrete proposal distribution to evolve the sampler to the posterior distribution. The DREAM approach maintains detailed balance and shows excellent performance on complex, multimodal search problems. Here we present our latest algorithmic developments and introduce MT-DREAM (ZS) , which combines the strengths of multiple-try sampling, snooker updating, and sampling from an archive of past states. This new code is especially designed to solve high-dimensional search problems and receives particularly spectacular performance improvement over other adaptive MCMC approaches when using distributed computing. Four different case studies with increasing dimensionality up to 241 parameters are used to illustrate the advantages of MT-DREAM (ZS) .Citation: Laloy, E., and J. A. Vrugt (2012), High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing, Water Resour. Res., 48, W01526,

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.

[1] This study reports on two strategies for accelerating posterior inference of a highly parameterized and CPU-demanding groundwater flow model. Our method builds on previous stochastic collocation approaches, e.g., Marzouk and Xiu (2009) and Marzouk and Najm (2009), and uses generalized polynomial chaos (gPC) theory and dimensionality reduction to emulate the output of a large-scale groundwater flow model. The resulting surrogate model is CPU efficient and serves to explore the posterior distribution at a much lower computational cost using two-stage MCMC simulation. The case study reported in this paper demonstrates a two to five times speed-up in sampling efficiency.

Abstract. Recently, deep learning (DL) has emerged as a revolutionary and versatile tool transforming industry applications and generating new and improved capabilities for scientific discovery and model building. The adoption of DL in hydrology has so far been gradual, but the field is now ripe for breakthroughs. This paper suggests that DL-based methods can open up a complementary avenue toward knowledge discovery in hydrologic sciences. In the new avenue, machine-learning algorithms present competing hypotheses that are consistent with data. Interrogative methods are then invoked to interpret DL models for scientists to further evaluate. However, hydrology presents many challenges for DL methods, such as data limitations, heterogeneity and co-evolution, and the general inexperience of the hydrologic field with DL. The roadmap toward DL-powered scientific advances will require the coordinated effort from a large community involving scientists and citizens. Integrating process-based models with DL models will help alleviate data limitations. The sharing of data and baseline models will improve the efficiency of the community as a whole. Open competitions could serve as the organizing events to greatly propel growth and nurture data science education in hydrology, which demands a grassroots collaboration. The area of hydrologic DL presents numerous research opportunities that could, in turn, stimulate advances in machine learning as well.