Amid growing expectations for the early realization of fusion energy, no theoretical framework yet exists that can accurately predict the performance and characteristics of future fusion devices. The uncertainties that hinder naive forecasting or extrapolation from experiential knowledge stem from the nonlinear nature of ultra‑high‑temperature plasmas and the systems that generate and sustain them. Understanding nonlinear phenomena is a grand challenge shared by complex systems (non‑integrable systems) such as weather, ecosystems, and the economy, and it represents a major frontier for the mathematical sciences.
In this project, plasma physics—as an experimental discipline (and, similarly, materials science for fusion‑reactor materials)—will collaborate with the mathematical sciences to generate new mathematical concepts and methodologies. This effort will be grounded in concrete problems and supported by abundant experimental data and numerical simulations.
Historically, plasma physics has given rise to numerous mathematical developments—related to solitons, chaos, singular perturbations, and hierarchical structures. Building on these traditions, and with an eye toward close collaboration with rapidly advancing AI and data science, this project will begin by formulating core challenges in the fusion domain in precise mathematical terms. Through redefinition of key concepts and disruptive innovation in methodology, the project will contribute to the early realization of fusion energy as well as improvements in performance and safety. In addition, the project will actively promote interdisciplinary networking among early‑career researchers participating in Moonshot Goal 10 (MS10), enabling them to discuss the future of their respective fields using mathematics as a common language, thereby contributing to the development of the next generation of talent.