Experimental validation of a fast control-oriented, physics-informed surrogate model for plasma equilibrium reconstruction in the TCV tokamak

Magnetic equilibrium reconstruction provides the plasma state estimate required for real-time shape control in tokamaks. We present a fast, physics-informed neural network surrogate of the $\mathtt{\text{liuqe}}$ equilibrium reconstruction code \cite{liuqe1} for the TCV tokamak at EPFL, achieving inference times below 100~$\mathit{\mu }$s and enabling 10~kHz shape control. The model is trained on around 10,000 TCV discharges spanning the full operational range of plasma shapes. Its modular branch/trunk architecture decouples magnetic measurement encoding from spatial coordinate processing, enabling physics-informed regularization via automatic differentiation of the predicted flux map. The surrogate has been compiled and deployed on the TCV real-time control system, and validated both offline and in real time against the models $\mathtt{\text{liuqe-rt}}$ and $\mathtt{\text{lih}}$, showing comparable accuracy. Closed-loop performance assessed with the real-time software in-the-loop $\mathtt{\text{fge}}$ \cite{fge1} demonstrates control-equivalent behavior across multiple control strategies.