Probabilistic inversion within a multiple-point statistics framework is stillcomputationally prohibitive for large-scale problems. To partly address this,we introduce and evaluate a new training-image based simulation and inversionapproach for complex geologic media. Our approach relies on a deep neuralnetwork of the spatial generative adversarial network (SGAN) type. Aftertraining using a training image (TI), our proposed SGAN can quickly generate 2Dand 3D unconditional realizations. A key feature of our SGAN is that it definesa (very) low-dimensional parameterization, thereby allowing for efficientprobabilistic (or deterministic) inversion using state-of-the-art Markov chainMonte Carlo (MCMC) methods. A series of 2D and 3D categorical TIs is first usedto analyze the performance of our SGAN for unconditional simulation. The speedat which realizations are generated makes it especially useful for simulatingover large grids and/or from a complex multi-categorical TI. Subsequently,synthetic inversion case studies involving 2D steady-state flow and 3Dtransient hydraulic tomography are used to illustrate the effectiveness of ourproposed SGAN-based probabilistic inversion. For the 2D case, the inversionrapidly explores the posterior model distribution. For the 3D case, theinversion recovers model realizations that fit the data close to the targetlevel and visually resemble the true model well. Future work will focus on theinclusion of direct conditioning data and application to continuous TIs.
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