Analogies have been central to creative problem-solving throughout the history of science and technology. As the number of scientific papers continues to increase exponentially, there is a growing opportunity for finding diverse solutions to existing problems. However, realizing this potential requires the development of a means for searching through a large corpus that goes beyond surface matches and simple keywords. Here we contribute the first end-to-end system for analogical search on scientific papers and evaluate its effectiveness with scientists' own problems. Using a human-in-the-loop AI system as a probe we find that our system facilitates creative ideation, and that ideation success is mediated by an intermediate level of matching on the problem abstraction (i.e., high versus low). We also demonstrate a fully automated AI search engine that achieves a similar accuracy with the human-in-the-loop system. We conclude with design implications for enabling automated analogical inspiration engines to accelerate scientific innovation.