Physics-informed neural networks (PINNs) offer a powerful framework for solving inverse problems in cardiac electrophysiology by embedding biophysical constraints into data-driven models. In this work, we present a set of methodologies that leverage PINNs to reconstruct key electrophysiological properties of the atria—fiber orientation, activation sequences, and phase maps—from sparse and indirect observations.
We begin by extending Fibernet, a PINN-based method to infer the anisotropic conduction properties and fiber orientations in the atria using electroanatomical mapping data. By training ensembles of neural networks, we quantify the uncertainty in fiber estimation and select the most plausible conduction patterns. Inputs are defined directly on the atrial surface, improving anatomical consistency. This updated approach reduces fiber orientation error across eight different atrial geometries and produces results in under seven minutes.
Next, we address the challenge of reconstructing atrial activation sequences from body-surface electrocardiograms (ECGs). Our method learns the local direction of electrical propagation using a neural network, and then solves a Poisson equation to recover activation times that satisfy the anisotropic Eikonal model. This two-step approach improves upon traditional PINN formulations and yields physiologically realistic activation maps in both synthetic and patient-specific cases.
Finally, we propose a novel formulation to reconstruct phase maps of periodic atrial activity—such as rotors or spirals—from sparse electrode recordings. By casting the complex Eikonal equation with the phase as the primary variable, we train a neural network to output a complex-valued function whose angle defines the phase. This enables accurate reconstruction of phase fields and identification of singularities with clinical relevance.
Together, these advances demonstrate the potential of PINNs to integrate sparse data and physical principles in solving inverse problems central to cardiac electrophysiology.