Microelectronics Research for Energy Innovation Act or the Micro Act This bill directs the Department of Energy (DOE) to carry out a cross-cutting program of research, development, and demonstration of microelectronics relevant to the mission of DOE and in the service of the nation's global competitiveness in the field of microelectronics. In carrying out such program, DOE shall award financial assistance to eligible entities, such as national laboratories, to carry out research projects in, among other things, foundational science areas and methods for leveraging artificial intelligence. The Office of Science within DOE shall establish up to four Microelectronics Science Research Centers to conduct mission-driven research to address foundational challenges in the design, development, and fabrication of microelectronics and to facilitate the translation of research results to industry. The Office of Science, in coordination with the Office of Technology Transitions, shall implement partnerships with industry groups to facilitate the translation and transfer of research results produced by the centers.