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

arXiv: https://arxiv.org/abs/2305.11111 · HTML: https://mlsanity.com/paper/2305.11111/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 4 of 4)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [DPNNet-2.0 Part I: Finding hidden planets from simulated images of protoplanetary disk gaps](https://mlsanity.com/paper/2107.09086/) (2021)
- [PGNets: Planet mass prediction using convolutional neural networks for radio continuum observations of protoplanetary disks](https://mlsanity.com/paper/2111.15196/) (2021)

## Built on by (most cited first, 19 of 19)

- [A Mathematical Guide to Operator Learning](https://mlsanity.com/paper/2312.14688/) (2023)
- [Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustness](https://mlsanity.com/paper/2305.17289/) (2023)
- [Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation](https://mlsanity.com/paper/2404.12355/) (2024)
- [Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networks](https://mlsanity.com/paper/2402.15406/) (2024)
- [D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators](https://mlsanity.com/paper/2310.18888/) (2023)
- [MODNO: Multi Operator Learning With Distributed Neural Operators](https://mlsanity.com/paper/2404.02892/) (2024)
- [Active operator learning with predictive uncertainty quantification for partial differential equations](https://mlsanity.com/paper/2503.03178/) (2025)
- [Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestration](https://mlsanity.com/paper/2409.16572/) (2024)
- [BiLO: Bilevel Local Operator Learning for PDE Inverse Problems](https://mlsanity.com/paper/2404.17789/) (2024)
- [Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operators](https://mlsanity.com/paper/2410.24162/) (2024)
- [Cauchy Random Features for Operator Learning in Sobolev Space](https://mlsanity.com/paper/2503.00300/) (2025)
- [Disk2Planet: A Robust and Automated Machine Learning Tool for Parameter Inference in Disk-Planet Systems](https://mlsanity.com/paper/2409.17228/) (2024)
- [Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptation](https://mlsanity.com/paper/2507.17019/) (2025)
- [Operator Learning for Families of Finite-State Mean-Field Games](https://mlsanity.com/paper/2602.13169/) (2026)
- [Inverse Neural Operator for ODE Parameter Optimization](https://mlsanity.com/paper/2603.11854/) (2026)
- [GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries](https://mlsanity.com/paper/2509.24117/) (2025)
- [Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Models](https://mlsanity.com/paper/2604.06433/) (2026)
- [IV-Net: A neural network for elliptic PDEs with random and highly varying coefficients](https://mlsanity.com/paper/2605.24876/) (2026)
- [Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equations](https://mlsanity.com/paper/2608.27626/) (2026)

## Abstract (arXiv)

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 α, the disk aspect ratio h0, 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 urlhttps://github.com/smao-astro/PPDONet.