This paper proposes a physics-informed graph neural operator for power system dynamic state estimation. From a sparse, intermittent measurement window at a few generator buses, the operator estimates the rotor-angle and speed trajectories of all machines, unmeasured ones included, in one forward pass. A graph-attention encoder processes the measurements, and the swing equations are imposed as a hard constraint or as a soft one with a learned correction that absorbs model errors. It is trained on simulated measurements, without state labels. With several phasor measurement units, masked training hides one from the input but keeps it in the loss. On four transmission systems, simulations show that the operator is the most accurate estimator that neither optimizes per scenario nor uses state labels, except on the smallest system at large model errors, where tuned Kalman smoothers are better. Networks trained on simulated states are more accurate on the two smallest systems but not on the 118-bus system, where the operator is faster and more accurate than hard-constrained moving-horizon estimation. Under model errors, it matches or outperforms an optimization-based benchmark at a fraction of its cost. The results hold for a detailed machine model with exact parameters seen only through voltage phasors.

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