  Continuous reconstructions of periodic phenomena provide powerful tools to
understand, predict and model natural situations and engineering problems. In
line with the recent method called Physics-Informed Neural Networks (PINN)
where a multi layer perceptron directly approximates any physical quantity as a
symbolic function of time and space coordinates, we present an extension,
namely ModalPINN, that encodes the approximation of a limited number of Fourier
mode shapes. In addition to the added interpretability, this representation
performs up to two orders of magnitude more precisely for a similar number of
degrees of freedom and training time in some cases as illustrated through the
test case of laminar shedding of vortices over a cylinder. This added
simplicity proves to be robust in regards to flow reconstruction using only a
limited number of sensors with asymmetric data that simulates an experimental
configuration, even when a Gaussian noise or a random delay is added, imitating
imperfect and sparse information.
