Physics-Informed Representation Learning for Electrocardiograms

Electrocardiograms (ECGs) are central to cardiac screening and diagnosis. Recent advances in self-supervised learning have enabled the development of generalizable ECG representations from large-scale unlabeled recordings. However, incorporating the physical structure of multi-lead ECG acquisition into self-supervised representation learning remains relatively underexplored. Each lead observes cardiac electrical activity from a distinct viewpoint determined by its positioning. The resulting signals exhibit structured dependencies across both lead and time dimensions. Building on these physical priors, we propose $\Phi \$-ECG,aPhysics-InformedECGself-supervisedrepresentationlearningframework.$\Phi$-ECG encodes three-dimensional lead directions using real spherical harmonic basis functions, explicitly incorporating acquisition into lead representations. We further introduce structured lead–time masking that samples visible leads separately from the limb and precordial groups and applies a shared temporal mask across them. By limiting reconstruction shortcuts arising from inter-lead redundancy and withholding simultaneous observations at masked time positions, this design encourages the model to jointly exploit complementary lead observations and temporal context for reconstruction. We evaluate $\Phi \$-ECGacrossECGdiseaseclassification,echocardiographicphenotypeprediction,reduced-leadtransfer,andmulti-leadreconstruction.Acrossthesesettings,$\Phi$-ECG consistently improves over strong self-supervised baselines, demonstrating robust generalization across diverse downstream tasks and evaluation settings. These results highlight the value of incorporating physically grounded priors into self-supervised ECG representation learning. The code will be released upon acceptance.