Computer simulations have revolutionized materials discovery, allowing scientists to test thousands of possibilities digitally before conducting expensive laboratory experiments, which accelerates innovation while dramatically reducing costs. There are critical national challenges that require advanced materials that perform under extreme conditions. Examples include next-generation computer chips essential for AI and quantum computing, and nuclear energy infrastructure materials that can withstand extreme radiation and heat in reactors. This project develops new mathematical tools and simulation methods enabling more efficient, accurate, and reliable materials modeling, accelerating breakthroughs in national nanotechnologies, clean energy systems, and resilient infrastructure. In addition, the project strengthens the U.S. scientific workforce by training students in advanced mathematical techniques that span multiple disciplines. Through international collaboration with the University of Warwick in the UK, both graduate and undergraduate students will engage in hands-on research experiences, inspiring them to pursue careers in science, technology, engineering, and mathematics. Overall, this project bridges mathematics, engineering, and computing to address real-world challenges in designing advanced materials, while supporting federal priorities in technological leadership, energy security, infrastructure resilience, and fostering the next generation's STEM talent pipeline.