Cardiac digital twins have shown promise to personalize treatments. However, there are multiple challenges to incorporate patient-specific information from non-invasive data. For instance, recovering the activation sequence in atria from the standard electrocardiogram (ECG) remains elusive. Recent studies have tackled this task on the ventricles, where the ECG signal is much stronger. This work presents a novel methodology to recover the atrial electrical activity with physics-informed neural networks. Instead of focusing on the activation times, we predict the direction of propagation of the electrical wave at each point with a neural network. Then, by solving a linear system for the Poisson equation, we recover the activation times that satisfy the anisotropic eikonal equation. The proposed methodology is compared with a methodology that predicts directly the electrical propagation and does not enforce the propagation model. We compare it to a traditional physics-informed neural network formulation, where the eikonal equation is only weakly imposed. We validate our methodology in a biatrial synthetic case using realistic lead fields for ECG calculation. We then learn the activation sequence from patient data, recovering a physiological activation pattern. We believe this is a first step toward digital twinning of the atria.