# Towards Physics-informed Deep Learning for Turbulent Flow Prediction

arXiv: https://arxiv.org/abs/1911.08655 · HTML: https://mlsanity.com/paper/1911.08655/

## Key facts

- Cited by 204 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2019.

## Built on by (most cited first, 30 of 204)

- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
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- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Scalable Transformer for PDE Surrogate Modeling](https://mlsanity.com/paper/2305.17560/) (2023)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [Solving High-Dimensional PDEs with Latent Spectral Models](https://mlsanity.com/paper/2301.12664/) (2023)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions](https://mlsanity.com/paper/2212.07564/) (2022)
- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning](https://mlsanity.com/paper/2203.16797/) (2022)
- [Encoding physics to learn reaction-diffusion processes](https://mlsanity.com/paper/2106.04781/) (2021)
- [On the Connection Between MPNN and Graph Transformer](https://mlsanity.com/paper/2301.11956/) (2023)
- [Learning to correct spectral methods for simulating turbulent flows](https://mlsanity.com/paper/2207.00556/) (2022)
- [From Zero to Turbulence: Generative Modeling for 3D Flow Simulation](https://mlsanity.com/paper/2306.01776/) (2023)
- [STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2209.00225/) (2022)
- [Group Equivariant Fourier Neural Operators for Partial Differential Equations](https://mlsanity.com/paper/2306.05697/) (2023)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)

## Abstract (arXiv)

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spectral filters in a coupled model of Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), followed by a specialized U-net for prediction. Our approach, which we call turbulent-Flow Net (TF-Net), is grounded in a principled physics model, yet offers the flexibility of learned representations. We compare our model, TF-Net, with state-of-the-art baselines and observe significant reductions in error for predictions 60 frames ahead. Most importantly, our method predicts physical fields that obey desirable physical characteristics, such as conservation of mass, whilst faithfully emulating the turbulent kinetic energy field and spectrum, which are critical for accurate prediction of turbulent flows.