Towards Physics-informed Deep Learning for Turbulent Flow Prediction

By Rui Wang, Karthik Kashinath, Mustafa Mustafa, Adrian Albert, Rose Yu. Knowledge Discovery and Data Mining, 2019

451 citations recorded by the source corpus.

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, is grounded in a principled physics model, yet offers the flexibility of learned representations. We compare our model 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.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/989e681731eb27ac1e12b2d60c8612c6982fe8c7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

PDEBENCH: An Extensive Benchmark for Scientific Machine Learning (2022, methodology): “Methods include Physics-informed neural networks (PINNs) [47], Neural operators (NOs) [32, 26], treating ResNet as a PDE approximant [49], custom architectures for specific problems such as TFNet for turbulent fluid flows [61], and generic image-to-image regression models such as the U-Net [48].”
Physics-informed neural networks (PINNs) for fluid mechanics: a review (2021, background): “More relevant works on mechanics in general can be found in references: [53] for turbulent flow, [54] for phase-field fracture model, and [55] for inferring modulus in a nonhomogeneous material.”
Monarch: Expressive Structured Matrices for Efficient and Accurate Training (2022, background): “Furthermore, follow-up works (Liu & Zenke, 2020; Wang et al., 2020a; Tanaka et al., 2020) show that we can find tickets without any training labels.”
Factorized Fourier Neural Operators (2021, methodology): “They can even be based on existing simulation methods such as the operator designed by Wang et al. (2020) that uses learned ﬁlters in both Reynolds-averaged Navier-Stokes and Large Eddy Simulation before combining the predictions using U-Net.”
Learning Mesh-Based Simulation with Graph Networks (2020, background): “Conversely, the accuracy of predictions can be increased by including specialized knowledge about the system modelled in the form of loss terms [39, 21], or by physics-informed feature normalization [36].”
Neural Operator: Learning Maps Between Function Spaces (2021, background): “• TF-Net: A network designed for learning turbulent flows based on a combination of spatial and temporal convolutions Wang et al. (2020).”
Physics-Informed Neural Operator for Learning Partial Differential Equations (2021, unknown): “Recent advances in operator learning replace traditional convolutional neural networks and U-Nets from computer vision with operator-based models tailored to PDEs with greatly improved model expressiveness [31, 36, 41, 49, 10].”
Transformer for Partial Differential Equations' Operator Learning (2022, background): “Convolutional layers (Stachenfeld et al., 2022; Wang et al., 2020; Bhatnagar et al., 2019; Kochkov et al., 2021), kernels (Saha & Mukhopadhyay, 2021), and graph-based layers (de Avila Belbute-Peres et al., 2020; Iakovlev et al., 2021; Li & Farimani, 2022; Li et al., 2022) are some of the common…”