  Electroanatomical maps are a key tool in the diagnosis and treatment of
atrial fibrillation. Current approaches focus on the activation times recorded.
However, more information can be extracted from the available data. The fibers
in cardiac tissue conduct the electrical wave faster, and their direction could
be inferred from activation times. In this work, we employ a recently developed
approach, called physics informed neural networks, to learn the fiber
orientations from electroanatomical maps, taking into account the physics of
the electrical wave propagation. In particular, we train the neural network to
weakly satisfy the anisotropic eikonal equation and to predict the measured
activation times. We use a local basis for the anisotropic conductivity tensor,
which encodes the fiber orientation. The methodology is tested both in a
synthetic example and for patient data. Our approach shows good agreement in
both cases and it outperforms a state of the art method in the patient data.
The results show a first step towards learning the fiber orientations from
electroanatomical maps with physics-informed neural networks.
