PPDONet: Deep Operator Networks for Fast Prediction of Steady-state Solutions in Disk–Planet Systems

Abstract

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, a class of neural networks capable of learning nonlinear operators to represent deterministic and stochastic differential equations. With PPDONet we map three scalar parameters in a disk–planet system—the Shakura–Sunyaev viscosity α , the disk aspect ratio h _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 https://github.com/smao-astro/PPDONet.

Keywords

• Protoplanetary disks
• Planetary-disk interactions
• Hydrodynamical simulations
• Neural networks
• Open source software