  Data-driven materials design often encounters challenges where systems
require or possess qualitative (categorical) information. Metal-organic
frameworks (MOFs) are an example of such material systems. The representation
of MOFs through different building blocks makes it a challenge for designers to
incorporate qualitative information into design optimization. Furthermore, the
large number of potential building blocks leads to a combinatorial challenge,
with millions of possible MOFs that could be explored through time consuming
physics-based approaches. In this work, we integrated Latent Variable Gaussian
Process (LVGP) and Multi-Objective Batch-Bayesian Optimization (MOBBO) to
identify top-performing MOFs adaptively, autonomously, and efficiently without
any human intervention. Our approach provides three main advantages: (i) no
specific physical descriptors are required and only building blocks that
construct the MOFs are used in global optimization through qualitative
representations, (ii) the method is application and property independent, and
(iii) the latent variable approach provides an interpretable model of
qualitative building blocks with physical justification. To demonstrate the
effectiveness of our method, we considered a design space with more than 47,000
MOF candidates. By searching only ~1% of the design space, LVGP-MOBBO was able
to identify all MOFs on the Pareto front and more than 97% of the 50
top-performing designs for the CO$_2$ working capacity and CO$_2$/N$_2$
selectivity properties. Finally, we compared our approach with the Random
Forest algorithm and demonstrated its efficiency, interpretability, and
robustness.
