Maintaining the stability of magnetically confined plasma is a central challenge on the path toward practical nuclear fusion. When modelled by kinetic Vlasov–Poisson equations, the control problem is particularly difficult due to nonlinearity, sensitivity to initial conditions, and partial observability. Recent advances in AI have shown considerable promise for plasma control, yet the theoretical foundations and principled algorithmic methodologies remain underexplored.

In this talk, we discuss recent advances in machine learning for plasma control. Starting from an expert controller designed for a fully observed model, we develop algorithms that learn feedback policies operating solely on experimentally available measurements. We study both offline and online imitation learning algorithms, revealing new tradeoff between adaptivity and stability. Offline behavior cloning adapts to the complexity of the initial distribution, but inevitably suffers from exponential error compounding. Online algorithms, by contrast, can achieve long-term stability with only polynomial error compounding. Our theory highlights the advantages of learning-based control in adapting to unknown initial conditions while maintaining long-time stability. Empirical results on simulated plasma systems further validate the effectiveness of our methods in stabilizing plasma over long time horizons.

This work builds a bridge between statistical learning theory and the control of complex physical systems, and represents a step toward theoretically grounded, AI-assisted control strategies for fusion energy. Joint work with Xiaofan Xia and Qin Li.