  Materials discovery is often compared to the challenge of finding a needle in
a haystack. While much work has focused on accurately predicting the properties
of candidate materials with machine learning (ML), which amounts to evaluating
whether a given candidate is a piece of straw or a needle, less attention has
been paid to a critical question: Are we searching in the right haystack? We
refer to the haystack as the design space for a particular materials discovery
problem (i.e. the set of possible candidate materials to synthesize), and thus
frame this question as one of design space selection. In this paper, we
introduce two metrics, the Predicted Fraction of Improved Candidates (PFIC),
and the Cumulative Maximum Likelihood of Improvement (CMLI), which we
demonstrate can identify discovery-rich and discovery-poor design spaces,
respectively. Using CMLI and PFIC together to identify optimal design spaces
can significantly accelerate ML-driven materials discovery.
