  We present a novel physics-informed deep learning framework for solving
steady-state incompressible flow on multiple sets of irregular geometries by
incorporating two main elements: using a point-cloud based neural network to
capture geometric features of computational domains, and using the mean squared
residuals of the governing partial differential equations, boundary conditions,
and sparse observations as the loss function of the network to capture the
physics. While the solution of the continuity and Navier-Stokes equations is a
function of the geometry of the computational domain, current versions of
physics-informed neural networks have no mechanism to express this functionally
in their outputs, and thus are restricted to obtain the solutions only for one
computational domain with each training procedure. Using the proposed
framework, three new facilities become available. First, the governing
equations are solvable on a set of computational domains containing irregular
geometries with high variations with respect to each other but requiring
training only once. Second, after training the introduced framework on the set,
it is now able to predict the solutions on domains with unseen geometries from
seen and unseen categories as well. The former and the latter both lead to
savings in computational costs. Finally, all the advantages of the point-cloud
based neural network for irregular geometries, already used for supervised
learning, are transferred to the proposed physics-informed framework. The
effectiveness of our framework is shown through the method of manufactured
solutions and thermally-driven flow for forward and inverse problems.
