  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.
