Since it is difficult to understand or predict research trends, we proposed methodologies for understanding and predicting research trends in the sciences, focusing on the structures of grants in the Japan Society for the Promotion of Science (JSPS), a Japanese funding agency. Grant applications are suitable for predicting research trends because these are research plans for the future, different from papers, which report research outcomes in the past. We investigated research trends in science focusing on research histories identified in grant application data of JSPS. Then we proposed a model for predicting research trends, assuming that breakthrough research encourages researchers to change from their current research field to an entirely new research field. Using breakthrough research, we aim to obtain higher precision in the prediction results. In our experimental results, we found that research fields in Informatics correlate well with actual scientific research trends. We also demonstrated that our prediction models are effective in actively interacting research areas, which include Informatics and Social Sciences.