Neural Operators for Cardiac Field Reconstruction from Simulated Magnetic Sensors

Learning physical state from remote sensors requires a model to invert a measurement process that can attenuate and spatially mix the underlying signal. We study this problem for cardiac magnetic sensing using 500 independent openCARP simulations on a controlled ventricular tissue sheet. A Biot-Savart forward calculation converts simulated electrophysiology into 301-frame magnetic sensor sequences, and Fourier neural operator (FNO) and DeepONet models reconstruct local activation time (LAT) and action potential duration (APD). On 75 grouped test simulations, FNO attains LAT and APD90 R² values of 0.954 and 0.960, while DeepONet attains 0.968 and 0.970. With the trained checkpoints frozen, we recompute the sensor observations at tissue distances of 35, 50, and 65 mm. DeepONet remains within 0.0013 of its nominal LAT and APD90 scores at every tested distance, whereas FNO loses 0.0737 LAT R² and 0.1082 APD90 R² at 65 mm. Additional region-level evaluation shows that accurate smooth fields do not guarantee reliable recovery of compact conduction abnormalities. The study provides a reproducible test bed for physical sensor inversion and identifies acquisition geometry and task-specific evaluation as distinct requirements for learned field reconstruction.