  In this paper, we propose an active learning method for an inverse problem
that aims to find an input that achieves a desired structured-output. The
proposed method provides new acquisition functions for minimizing the error
between the desired structured-output and the prediction of a Gaussian process
model, by effectively incorporating the correlation between multiple outputs of
the underlying multi-valued black box output functions. The effectiveness of
the proposed method is verified by applying it to two synthetic shape search
problem and real data. In the real data experiment, we tackle the input
parameter search which achieves the desired crystal growth rate in silicon
carbide (SiC) crystal growth modeling, that is a problem of materials
informatics.
