PPDONet: Deep Operator Networks for Fast Prediction of Steady-State
  Solutions in Disk-Planet Systems
Shunyuan Mao Ruobing Dong Lu Lu Kwang Moo Yi Sifan Wang Paris Perdikaris
We develop a tool, which we name Protoplanetary Disk Operator Network
(PPDONet), that can predict the solution of disk-planet interactions in
protoplanetary disks in real-time. We base our tool on Deep Operator Networks
(DeepONets), a class of neural networks capable of learning non-linear
operators to represent deterministic and stochastic differential equations.
With PPDONet we map three scalar parameters in a disk-planet system -- the
Shakura \& Sunyaev viscosity $\alpha$, the disk aspect ratio $h_\mathrm{0}$,
and the planet-star mass ratio $q$ -- to steady-state solutions of the disk
surface density, radial velocity, and azimuthal velocity. We demonstrate the
accuracy of the PPDONet solutions using a comprehensive set of tests. Our tool
is able to predict the outcome of disk-planet interaction for one system in
less than a second on a laptop. A public implementation of PPDONet is available
at \url{https://github.com/smao-astro/PPDONet}.