# Physics-Informed Graph Neural Operator

With phasor measurement units installed at only a few generator buses and reporting intermittently, a physics-informed graph neural operator maps a measurement window directly to the rotor-angle and speed trajectories of all machines, including those without sensors, and trains without state labels. It imposes the swing equations as a hard constraint, or as a soft one with a learned correction that absorbs model error; on the 9-bus, Kundur, 39-bus and 118-bus systems it is the most accurate estimator that neither optimizes per scenario nor uses state labels, except on the 9-bus system at large model error, where a tuned Kalman smoother is better.

With phasor measurement units installed at only a few generator buses and reporting intermittently, a physics-informed graph neural operator maps a measurement window directly to the rotor-angle and speed trajectories of all machines, including those without sensors, and trains without state labels. It imposes the swing equations as a hard constraint, or as a soft one with a learned correction that absorbs model error; on the 9-bus, Kundur, 39-bus and 118-bus systems it is the most accurate estimator that neither optimizes per scenario nor uses state labels, except on the 9-bus system at large model error, where a tuned Kalman smoother is better.