mlsanityData to 14 Oct 2026

A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling

arXiv 2506.07969 ↗First posted 9 Jun 2025cs.LG physics.flu-dyncited by 3

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Abstract (arXiv)

We consider the problem of modeling high-speed flows using machine learning methods. While most prior studies focus on low-speed fluid flows in which uniform time-stepping is practical, flows approaching and exceeding the speed of sound exhibit sudden changes such as shock waves. In such cases, it is essential to use adaptive time-stepping methods to allow a temporal resolution sufficient to resolve these phenomena while simultaneously balancing computational costs. Here, we propose a two-phase machine learning method, known as ShockCast, to model high-speed flows with adaptive time-stepping. In the first phase, we propose to employ a machine learning model to predict the timestep size. In the second phase, the predicted timestep is used as an input along with the current fluid fields to advance the system state by the predicted timestep. We explore several physically-motivated components for timestep prediction and introduce timestep conditioning strategies inspired by neural ODE and Mixture of Experts. We evaluate our methods by generating three supersonic flow datasets, available at https://huggingface.co/divelab. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 67 of its 110 references that are in the map. First posted on arXiv 9 Jun 2025.

Builds on

67 of 110 references.

References · 67

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  4. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  6. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
  7. 2018Neural Ordinary Differential Equationscited by 3,779
  8. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  9. 2022A ConvNet for the 2020scited by 3,579
  10. 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,509
  11. 2021Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsitycited by 3,073
  12. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
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  1. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 2,018
  2. 2021Alias-Free Generative Adversarial Networkscited by 1,184
  3. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  4. 2020Learning Mesh-Based Simulation with Graph Networkscited by 868
  5. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 776
  6. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 734
  7. 2021Machine learning accelerated computational fluid dynamicscited by 471
  8. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 427
  9. 2022Message Passing Neural PDE Solverscited by 386
  10. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 349
  11. 2021Choose a Transformer: Fourier or Galerkincited by 343
  12. 2017Stable Architectures for Deep Neural Networkscited by 341
  13. 2023ClimaX: A foundation model for weather and climatecited by 337
  14. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 336
  15. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 326
  16. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 303
  17. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 297
  18. 2022Transformer for Partial Differential Equations' Operator Learningcited by 283
  19. 2022On Neural Differential Equationscited by 268
  20. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 267
  21. 2021Factorized Fourier Neural Operatorscited by 249
  22. 2021Multiwavelet-based Operator Learning for Differential Equationscited by 234
  23. 2023Spherical Fourier Neural Operators: Learning Stable Dynamics on the Spherecited by 233
  24. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solverscited by 216
  25. 2023Convolutional Neural Operators for robust and accurate learning of PDEscited by 214
  26. 2017Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equationscited by 203
  27. 2024Poseidon: Efficient Foundation Models for PDEscited by 200
  28. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  29. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  30. 2023GenCast: Diffusion-based ensemble forecasting for medium-range weathercited by 177
  31. 2022Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecastcited by 166
  32. 2024DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Trainingcited by 151
  33. 2023Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systemscited by 121
  34. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 91
  35. 2022NOMAD: Nonlinear Manifold Decoders for Operator Learningcited by 83
  36. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 82
  37. 2023Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformerscited by 57
  38. 2022Real-time high-resolution CO2 geological storage prediction using nested Fourier neural operatorscited by 47

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Orbital Transformers for Predicting Wavefunctions in Time-Dependent Density Functional Theorycited by 0
  2. 2026Hybrid Neural World Modelscited by 0
  3. 2026AutoPDEBench: Benchmarking LLM Auto-Research for Neural PDE Solver Designcited by 0

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