mlsanityData to 7 Oct 2026

RheOFormer: A generative transformer model for simulation of complex fluids and flows

arXiv 2510.01365 ↗First posted 1 Oct 2025cs.LG physics.flu-dyncited by 2

Not on the map. Why?

Abstract (arXiv)

The ability to model mechanics of soft materials under flowing conditions is key in designing and engineering processes and materials with targeted properties. This generally requires solution of internal stress tensor, related to the deformation tensor through nonlinear and history-dependent constitutive models. Traditional numerical methods for non-Newtonian fluid dynamics often suffer from prohibitive computational demands and poor scalability to new problem instances. Developments in data-driven methods have mitigated some limitations but still require retraining across varied physical conditions. In this work, we introduce Rheological Operator Transformer (RheOFormer), a generative operator learning method leveraging self-attention to efficiently learn different spatial interactions and features of complex fluid flows. We benchmark RheOFormer across a range of different viscometric and non-viscometric flows with different types of viscoelastic and elastoviscoplastic mechanics in complex domains against ground truth solutions. Our results demonstrate that RheOFormer can accurately learn both scalar and tensorial nonlinear mechanics of different complex fluids and predict the spatio-temporal evolution of their flows, even when trained on limited datasets. Its strong generalization capabilities and computational efficiency establish RheOFormer as a robust neural surrogate for accelerating predictive complex fluid simulations, advancing data-driven experimentation, and enabling real-time process optimization across a wide range of applications.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 39 of its 84 references that are in the map. First posted on arXiv 1 Oct 2025.

Builds on

39 of 84 references.

References · 39

  1. 2017Attention Is All You Needcited by 59,932
  2. 2017Graph Attention Networkscited by 8,854
  3. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,530
  4. 2014Sequence to Sequence Learning with Neural Networkscited by 2,974
  5. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  6. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  7. 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
  8. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  9. 2015Effective Approaches to Attention-based Neural Machine Translationcited by 1,024
  10. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  11. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  12. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
27 more
  1. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  2. 2014Neural Turing Machinescited by 630
  3. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  4. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  5. 2021Machine learning accelerated computational fluid dynamicscited by 461
  6. 2015Attention-Based Models for Speech Recognitioncited by 400
  7. 2019Machine Learning for Fluid Mechanicscited by 380
  8. 2022Message Passing Neural PDE Solverscited by 368
  9. 2020Multipole Graph Neural Operator for Parametric Partial Differential Equationscited by 343
  10. 2021Choose a Transformer: Fourier or Galerkincited by 333
  11. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  12. 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
  13. 2020On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networkscited by 279
  14. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  15. 2023Neural Operators for Accelerating Scientific Simulations and Designcited by 218
  16. 2018Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantificationcited by 199
  17. 2019Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networkscited by 144
  18. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  19. 2020Transformers for Modeling Physical Systemscited by 105
  20. 2022Learning Operators with Coupled Attentioncited by 88
  21. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
  22. 2019Jointly Learning to Align and Translate with Transformer Modelscited by 75
  23. 2018Deep Dynamical Modeling and Control of Unsteady Fluid Flowscited by 67
  24. 2020Graph Convolutional Neural Networks for Body Force Predictioncited by 16
  25. 2024Masked Autoencoders are PDE Learnerscited by 11
  26. 2022Scientific Machine Learning for Modeling and Simulating Complex Fluidscited by 7
  27. 2024A physics-informed transformer neural operator for learning generalized solutions of initial boundary value problemscited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Hierarchical Multi-Fidelity Learning for Predicting Three-Dimensional Flame Wrinkling and Turbulent Burning Velocitycited by 0
  2. 2026Attention mechanism for scalable mesh-based neural surrogates of free-surface fluidscited by 0