Prediction of aerodynamic flow fields using convolutional neural networks

By Yaser Afshar, Saakaar Bhatnagar, Shaowu Pan, Karthik Duraisamy, S. Kaushik. Computational Mechanics, 2019

631 citations recorded by the source corpus.

An approximation model based on convolutional neural networks (CNNs) is proposed for flow field predictions. The CNN is used to predict the velocity and pressure field in unseen flow conditions and geometries given the pixelated shape of the object. In particular, we consider Reynolds Averaged Navier–Stokes (RANS) flow solutions over airfoil shapes as training data. The CNN can automatically detect essential features with minimal human supervision and is shown to effectively estimate the velocity and pressure field orders of magnitude faster than the RANS solver, making it possible to study the impact of the airfoil shape and operating conditions on the aerodynamic forces and the flow field in near-real time. The use of specific convolution operations, parameter sharing, and gradient sharpening are shown to enhance the predictive capabilities of the CNN. We explore the network architecture and its effectiveness in predicting the flow field for different airfoil shapes, angles of attack, and Reynolds numbers.

Subfields: Aerospace Engineering, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ebd67537c800d52526b541c8dfb49d405436f696

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Citations in the corpus

Transformer for Partial Differential Equations' Operator Learning (2022, methodology): “The use of convolutional layers for structured grids (Khoo et al., 2021; Zhu & Zabaras, 2018; Bhatnagar et al., 2019; Pant et al., 2021), and graph layers for learning unstructured local relations in a system (de Avila Belbute-Peres et al., 2020; Iakovlev et al., 2021; Li & Farimani, 2022; Li et…”
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries (2022, neutral): “Among them, the graph neural networks have been studied for complex geometries [6, 7] Recently, a new class of data-driven models known as neural operators aim to directly learn the solution operator of the PDE in a mesh-invariant manner.”
Multipole Graph Neural Operator for Parametric Partial Differential Equations (2020, background): “The first parametrizes the solution operator as a deep convolutional neural network (CNN) between finite-dimensional Euclidean spaces Fθ : R → R [23, 49, 3, 9, 45].”
Neural Operator: Learning Maps Between Function Spaces (2021, positive): “It remedies the mesh-dependent nature of the approach in the papers (Guo et al., 2016; Zhu and Zabaras, 2018; Adler and Oktem, 2017; Bhatnagar et al., 2019) by producing a single set of network parameters that can be used with different discretizations.”
Machine Learning in Aerodynamic Shape Optimization (2022, methodology): “CNN has been used in aerospace engineering to predict flow fields by treating airfoil shapes as image inputs [255].”
PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain (2020, methodology): “Deterministic Navier-Stokes equations There has been growing interests in using CNNs to simulate/model fluid flows governed by Navier-Stokes equations, but most of them are formulated in a data-intensive supervised fashion [57, 74, 85].”
Multiwavelet-based Operator Learning for Differential Equations (2021, background): “The FNO model with higher values of k m has better performance due to more Fourier bases for representing the high-frequency signal, while MWT does better even with low modes in its A, B, C CNNs, highlighting the importance of using wavelet-based ﬁlters in the signal processing.”
Learning Mesh-Based Simulation with Graph Networks (2020, background): “High resolution simulations are often very slow, and learned models can provide faster predictions, reducing turnaround time for workflows in engineering and science [14, 6, 44, 18, 1].”
Message Passing Neural PDE Solvers (2022, methodology): “(4) Finite-dimensional operator methods (Raissi, 2018; Sirignano & Spiliopoulos, 2018; Bhatnagar et al., 2019; Guo et al., 2016; Zhu & Zabaras, 2018; Khoo et al., 2020), where dim(F) < ∞ are grid-dependent, so cannot generalize over geometry and sampling.”
Fourier Neural Operator for Parametric Partial Differential Equations (2020, background): “These approaches parameterize the solution operator as a deep convolutional neural network between ﬁnite-dimensional Euclidean spaces Guo et al. (2016); Zhu & Zabaras (2018); Adler & Oktem (2017); Bhatnagar et al. (2019); Khoo et al. (2017).”
Choose a Transformer: Fourier or Galerkin (2021, methodology): “Deep convolutional neural networks (DCNN) are widely applied to learn the solution maps with a fixed discretization size [1, 9, 40, 36, 35, 100, 86].”