  Microstructural materials design is one of the most important applications of
inverse modeling in materials science. Generally speaking, there are two broad
modeling paradigms in scientific applications: forward and inverse. While the
forward modeling estimates the observations based on known parameters, the
inverse modeling attempts to infer the parameters given the observations.
Inverse problems are usually more critical as well as difficult in scientific
applications as they seek to explore the parameters that cannot be directly
observed. Inverse problems are used extensively in various scientific fields,
such as geophysics, healthcare and materials science. However, it is
challenging to solve inverse problems, because they usually need to learn a
one-to-many non-linear mapping, and also require significant computing time,
especially for high-dimensional parameter space. Further, inverse problems
become even more difficult to solve when the dimension of input (i.e.
observation) is much lower than that of output (i.e. parameters). In this work,
we propose a framework consisting of generative adversarial networks and
mixture density networks for inverse modeling, and it is evaluated on a
materials science dataset for microstructural materials design. Compared with
baseline methods, the results demonstrate that the proposed framework can
overcome the above-mentioned challenges and produce multiple promising
solutions in an efficient manner.
