Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils

by   Khemraj Shukla, et al.

Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications. Here, we investigate the use of DeepONets to infer flow fields around unseen airfoils with the aim of shape optimization, an important design problem in aerodynamics that typically taxes computational resources heavily. We present results which display little to no degradation in prediction accuracy, while reducing the online optimization cost by orders of magnitude. We consider NACA airfoils as a test case for our proposed approach, as their shape can be easily defined by the four-digit parametrization. We successfully optimize the constrained NACA four-digit problem with respect to maximizing the lift-to-drag ratio and validate all results by comparing them to a high-order CFD solver. We find that DeepONets have low generalization error, making them ideal for generating solutions of unseen shapes. Specifically, pressure, density, and velocity fields are accurately inferred at a fraction of a second, hence enabling the use of general objective functions beyond the maximization of the lift-to-drag ratio considered in the current work.


page 11

page 14

page 16

page 18


Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks

An approximation model based on convolutional neural networks (CNNs) is ...

Deep neural networks for fast acquisition of aortic 3D pressure and velocity flow fields

Computational fluid dynamics (CFD) can be used to simulate vascular haem...

Geodesic analysis in Kendall's shape space with epidemiological applications

We analytically determine Jacobi fields and parallel transports and comp...

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

While it is widely known that neural networks are universal approximator...

Corrector Operator to Enhance Accuracy and Reliability of Neural Operator Surrogates of Nonlinear Variational Boundary-Value Problems

This work focuses on developing methods for approximating the solution o...

A hybrid Decoder-DeepONet operator regression framework for unaligned observation data

Deep neural operators (DNOs) have been utilized to approximate nonlinear...

Kronecker Attention Networks

Attention operators have been applied on both 1-D data like texts and hi...

Please sign up or login with your details

Forgot password? Click here to reset