Space Research Innovation Act This bill directs the National Aeronautics and Space Administration (NASA) to (1) establish a university-affiliated research center to facilitate NASA capabilities, and (2) use the research center to fund analyses and engineering support related to cis-lunar and deep-space missions and interplanetary research. The bill lists the following entities as eligible to participate in the research center: (1) an institution of higher education, (2) an operator of a federally funded research and development center, and (3) a nonprofit or not-for-profit research institution.