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A fundamental problem in geophysical modeling is related to the identification and approximation of causal structures among physical processes. However, resolving the bidirectional mappings between physical parameters and model state variables (i.e., solving the forward and inverse problems) is challenging, especially when parameter dimensionality is high. Deep learning has opened a new door toward knowledge representation and complex pattern identification. In particular, the recently introduced generative adversarial networks (GANs) hold strong promises in learning cross-domain mappings for image translation. This study presents a state-parameter identification GAN (SPID-GAN) for simultaneously learning bidirectional mappings between a high-dimensional parameter space and the corresponding model state space. SPID-GAN is demonstrated using a series of representative problems from subsurface flow modeling. Results show that SPID-GAN achieves satisfactory performance in identifying the bidirectional state-parameter mappings, providing a new deep-learning-based, knowledge representation paradigm for a wide array of complex geophysical problems.

Plain Language Summary Development of physically based models requires two steps, mathematical abstraction (forward modeling) and parameter estimation (inverse modeling). A high-fidelity model requires high-quality parameter support. The need for identifying forward and reverse mappings (i.e., a function that associates element of one set to another) is thus ubiquitous in geophysical research. A significant challenge in geosciences is that geoparameters are spatially heterogeneous and high dimensional and yet can only be observed at limited locations. The conventional workflow, built on minimizing the model-observation mismatch at measurement locations, does not offer an efficient way for estimating the spatial structure of high-dimensional parameter fields. This work presents a deep-learning-based framework for identifying the state-parameter bidirectional mappings using the recently introduced generative adversarial networks (GANs). GANs have been shown to be adept at associating images from one domain to another. Its potential for discovering mappings in physically based models has not been demonstrated so far. This work shows that GAN can achieve high performance in learning bidirectional parameter-to-state mappings in physically based models, thus providing a new way of thinking and doing things in geosciences. The implication for additional applications in subsurface modeling is significant.