# Long-horizon prediction of three-dimensional wall-bounded turbulence with CTA-Swin-UNet and resolvent analysis

arXiv: https://arxiv.org/abs/2605.17888 · HTML: https://mlsanity.com/paper/2605.17888/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 68 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers](https://mlsanity.com/paper/2308.05732/) (2023)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows](https://mlsanity.com/paper/2007.00936/) (2020)
- [SwinLSTM:Improving Spatiotemporal Prediction Accuracy using Swin Transformer and LSTM](https://mlsanity.com/paper/2308.09891/) (2023)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [A Perspective on Machine Learning Methods in Turbulence Modelling](https://mlsanity.com/paper/2010.12226/) (2020)
- [BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics](https://mlsanity.com/paper/2501.18972/) (2025)
- [Learning from Predictions: Fusing Training and Autoregressive Inference for Long-Term Spatiotemporal Forecasts](https://mlsanity.com/paper/2302.11101/) (2023)
- [Reduced-order modeling of unsteady fluid flow using neural network ensembles](https://mlsanity.com/paper/2402.05372/) (2024)
- [Implicit factorized transformer approach to fast prediction of turbulent channel flows](https://mlsanity.com/paper/2412.18840/) (2024)
- [Vision-Informed Flow Image Super-Resolution with Quaternion Spatial Modeling and Dynamic Flow Convolution](https://mlsanity.com/paper/2401.15913/) (2024)

## Abstract (arXiv)

Long-horizon prediction of three-dimensional (3D) wall-bounded turbulence with machine-learning methods remains a challenging task, due to the rapid accumulation of autoregressive errors and the substantially computational cost. To address these challenges, we present a hybrid machine-learning framework, in which a channel-time-attention Swin-UNet (CTA-Swin-UNet) and a multi-time-scale fusion correction (MTFC) strategy are developed to predict the turbulent flow fields in a wall-parallel plane, with affordable computational cost. Then, 3D flow fields are reconstructed via a resolvent-based spectral linear stochastic estimation (SLSE), rooting from the predicted planar flow. Results show that the CTA-Swin-UNet outperforms the baseline models (LSTM, FNO and traditional Swin-UNet) in both single-step prediction and autoregressive rollouts, indicating the effectiveness of introducing the CTA module into the Swin-UNet architecture. At the same temporal interval, the CTA-Swin-UNet remains stable for approximately 150 rollout steps, while the baseline models fail within 20 to 50 rollout steps. After introducing the MTFC strategy, a longer horizon upto 300 steps is achieved. Using the resolvent-based SLSE reconstruction further recovers the 3D flow structures and energy spectral distributions from the predicted planar inputs, which demonstrates that the proposed framework provides an effective and computationally efficient approach for long-horizon autoregressive prediction of 3D wall-bounded turbulence.