Learning Optimal Aerodynamic Designs

The University of Texas at Austin Oden Institute for

Computational Engineering & SciencesOmar Ghattas, Karen Willcox,

Anirban Chaudhuri, Tom O’Leary-Roseberry

University of Michigan MDO Lab, Dept of Aerospace Engineering

Joaquim Martins, Xiaosong Du

ARPA-E DIFFERENTIATE Program

CFD-based aerodynamic design optimization

● CFD-based design optimization is a powerful technology that has revolutionized the efficient design of aerodynamic systems, including aircraft, ground vehicles, marine vessels, and energy generation via wind, water, and gas turbines

● CFD-based design optimization is challenging due to the need for: ○ Days of computing time to do a single 3D design optimization ○ HPC resources○ Sophisticated algorithms for adjoints, differentiable and robust

shape parameterization and mesh generation, PDE-constrained optimization, robust flow solvers

Our solution: Deep learning of CFD design optimization

● Use deep neural network to learn aerodynamic design optimization

● Specifically, learn the map from design requirements to optimal aerodynamic design with high accuracy (>95%)

● The neural network is executed at interactive speeds (millisecond)● Fast decision-making for tradespace exploration: Conceptual

design phase greatly accelerated● Supplement expert knowledge: No need to set up and run an

expensive CFD optimization every time you change performance requirements

Train DNN with MACH-Aero CFD design optimization framework

Developed at University of Michigan MDO Lab (Joaquim Martins, PI)

MACH-Aero framework

Example: design optimization of CRM wing benchmark

Wave drag is eliminated; total drag reduced by 8.5%

AeroLearn: A data-parsimonious deep neural network trained by MACH-Aero

● Train a DNN to learn the map… ○ From design requirements (lift & moment bounds, geometric constraints such as

thickness, environmental parameters such as Mach & Re, across flight envelope) ...○ … To optimal shape

● This results in a neural network with high-dimensional inputs & outputs (100s to 1000s)● Training a predictive network with black-box ML techniques would require 104--106 CFD

optimizations -- completely intractable! ● Our solution: AeroLearn

○ Sensitivity-based projections to find low-dimensional manifolds for inputs & outputs○ Multifidelity neural networks by enriching expensive high-fidelity data with cheaper

low-fidelity data● Result: Neural network that has high generalization accuracy (99.8% for drag, 99% for

geometry) for few training data (100s), executing at interactive speeds (milliseconds)

AeroLearn vs. CFD-based design optimization runtime:2D airfoil case with 4 inputs and 20 outputs

Mesh MACH-Aero design optimization time AeroLearn design optimization time

medium 1555 seconds 0.0005 seconds

fine 7732 seconds 0.0005 seconds

Design requirement inputs

Optimal design variable outputs

Generalization error vs. number of training data

99% accuracy in optimal shape, 99.8% accuracy in objective function (drag) with just ~100 training data

Rapid exploration of design requirement space

Summary and invitation to partner with us● CFD-based aerodynamic design optimization is a powerful technology, but is

often inaccessible to many who could benefit from it, due to the need for HPC resources, sophisticated algorithms and solvers, and advanced expertise.

● We have developed AeroLearn -- parsimonious deep neural networks that learn aerodynamic design by training on MACH-Aero optimizations

● AeroLearn networks are capable of very high accuracy in predicting the optimal shape and objective function with a limited number of training data

● Once trained, AeroLearn networks can explore the design requirement space to generate optimal designs at interactive (< millisecond) speeds

● We are looking for partners to commercialize this technology● Please stop by our booth and chat with us, or else email:

● Omar Ghattas (omar@oden.utexas.edu)