mlsanityData to 14 Oct 2026

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

arXiv 2305.11111 ↗First posted 18 May 2023astro-ph.EP astro-ph.IM cs.LGcited by 19

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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.

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

4 of 22 references.

References · 4

  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  2. 2022A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networkscited by 236
  3. 2021DPNNet-2.0 Part I: Finding hidden planets from simulated images of protoplanetary disk gapscited by 7
  4. 2021PGNets: Planet mass prediction using convolutional neural networks for radio continuum observations of protoplanetary diskscited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 7; 2025: 4; 2026: 5.

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  1. 2023A Mathematical Guide to Operator Learningcited by 76
  2. 2023Fourier-DeepONet: Fourier-enhanced deep operator networks for full waveform inversion with improved accuracy, generalizability, and robustnesscited by 60
  3. 2024Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolationcited by 46
  4. 2024Conformalized-DeepONet: A Distribution-Free Framework for Uncertainty Quantification in Deep Operator Networkscited by 28
  5. 2023D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operatorscited by 18
  6. 2024MODNO: Multi Operator Learning With Distributed Neural Operatorscited by 14
  7. 2025Active operator learning with predictive uncertainty quantification for partial differential equationscited by 12
  8. 2024Efficient and generalizable nested Fourier-DeepONet for three-dimensional geological carbon sequestrationcited by 11
  9. 2024BiLO: Bilevel Local Operator Learning for PDE Inverse Problemscited by 8
  10. 2024Conformalized Prediction of Post-Fault Voltage Trajectories Using Pre-trained and Finetuned Attention-Driven Neural Operatorscited by 5
  11. 2025Cauchy Random Features for Operator Learning in Sobolev Spacecited by 5
  12. 2024Disk2Planet: A Robust and Automated Machine Learning Tool for Parameter Inference in Disk-Planet Systemscited by 3
7 more
  1. 2025Bayesian BiLO: Bilevel Local Operator Learning for Efficient Uncertainty Quantification of Bayesian PDE Inverse Problems with Low-Rank Adaptationcited by 2
  2. 2026Operator Learning for Families of Finite-State Mean-Field Gamescited by 2
  3. 2026Inverse Neural Operator for ODE Parameter Optimizationcited by 1
  4. 2025GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometriescited by 0
  5. 2026Operator Learning for Predicting Bulk Wave Parameters of Spectral Wave Modelscited by 0
  6. 2026IV-Net: A neural network for elliptic PDEs with random and highly varying coefficientscited by 0
  7. 2026Quantum SEDONet: Spectrally-Embedded Quantum Deep Operator Networks for Partial Differential Equationscited by 0