GRINN: A Physics-Informed Neural Network for solving hydrodynamic
  systems in the presence of self-gravity
Sayantan Auddy Ramit Dey Neal J. Turner Shantanu Basu
Modeling self-gravitating gas flows is essential to answering many
fundamental questions in astrophysics. This spans many topics including
planet-forming disks, star-forming clouds, galaxy formation, and the
development of large-scale structures in the Universe. However, the nonlinear
interaction between gravity and fluid dynamics offers a formidable challenge to
solving the resulting time-dependent partial differential equations (PDEs) in
three dimensions (3D). By leveraging the universal approximation capabilities
of a neural network within a mesh-free framework, physics informed neural
networks (PINNs) offer a new way of addressing this challenge. We introduce the
gravity-informed neural network (GRINN), a PINN-based code, to simulate 3D
self-gravitating hydrodynamic systems. Here, we specifically study
gravitational instability and wave propagation in an isothermal gas. Our
results match a linear analytic solution to within 1\% in the linear regime and
a conventional grid code solution to within 5\% as the disturbance grows into
the nonlinear regime. We find that the computation time of the GRINN does not
scale with the number of dimensions. This is in contrast to the scaling of the
grid-based code for the hydrodynamic and self-gravity calculations as the
number of dimensions is increased. Our results show that the GRINN computation
time is longer than the grid code in one- and two- dimensional calculations but
is an order of magnitude lesser than the grid code in 3D with similar accuracy.
Physics-informed neural networks like GRINN thus show promise for advancing our
ability to model 3D astrophysical flows.