  Incompressible fluid flow around a cylinder is one of the classical problems
in fluid-dynamics with strong relevance with many real-world engineering
problems, for example, design of offshore structures or design of a pin-fin
heat exchanger. Thus learning a high-accuracy surrogate for this problem can
demonstrate the efficacy of a novel machine learning approach. In this work, we
propose a physics-informed neural network (PINN) architecture for learning the
relationship between simulation output and the underlying geometry and boundary
conditions. In addition to using a physics-based regularization term, the
proposed approach also exploits the underlying physics to learn a set of
Fourier features, i.e. frequency and phase offset parameters, and then use them
for predicting flow velocity and pressure over the spatio-temporal domain. We
demonstrate this approach by predicting simulation results over out of range
time interval and for novel design conditions. Our results show that
incorporation of Fourier features improves the generalization performance over
both temporal domain and design space.
