# PEST: Physics-Enhanced Swin Transformer for 3D Turbulence Simulation

arXiv: https://arxiv.org/abs/2602.10150 · HTML: https://mlsanity.com/paper/2602.10150/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 44 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [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)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations](https://mlsanity.com/paper/1709.00037/) (2017)
- [FreqMoE: Dynamic Frequency Enhancement for Neural PDE Solvers](https://mlsanity.com/paper/2505.06858/) (2025)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [Accelerate Coastal Ocean Circulation Model with AI Surrogate](https://mlsanity.com/paper/2410.14952/) (2024)

## Built on by (most cited first, 5 of 5)

- [FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation](https://mlsanity.com/paper/2604.17149/) (2026)
- [Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing](https://mlsanity.com/paper/2604.07366/) (2026)
- [Physics-Preserving Latent Compression for Zero-Shot Resolution Transfer in 3D Turbulence](https://mlsanity.com/paper/2606.21781/) (2026)
- [TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning](https://mlsanity.com/paper/2608.04222/) (2026)
- [Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave It](https://mlsanity.com/paper/2609.32864/) (2026)

## Abstract (arXiv)

Accurate simulation of turbulent flows is fundamental to scientific and engineering applications. Direct numerical simulation (DNS) offers the highest fidelity but is computationally prohibitive, while existing data-driven alternatives struggle with stable long-horizon rollouts, physical consistency, and faithful simulation of small-scale structures. These challenges are particularly acute in three-dimensional (3D) settings, where the cubic growth of spatial degrees of freedom dramatically amplifies computational cost, memory demand, and the difficulty of capturing multi-scale interactions. To address these challenges, we propose a Physics-Enhanced Swin Transformer (PEST) for 3D turbulence simulation. PEST leverages a window-based self-attention mechanism to effectively model localized PDE interactions while maintaining computational efficiency. We introduce a frequency-domain adaptive loss that explicitly emphasizes small-scale structures, enabling more faithful simulation of high-frequency dynamics. To improve physical consistency, we incorporate Navier--Stokes residual constraints and divergence-free regularization directly into the learning objective. Extensive experiments on two representative turbulent flow configurations demonstrate that PEST achieves accurate, physically consistent, and stable autoregressive long-term simulations, outperforming existing data-driven baselines.