Design optimization of a scramjet under uncertainty using probabilistic learning on manifolds

•LES simulations with three different resolutions are used to generate a training dataset for scramjet combustion.•DMAP manifolds are learned from these simulations.•Over a million additional samples are generated on the manifold using a projected Itô equation.•The new samples are used to define and...

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Bibliographic Details
Published in:Journal of computational physics 2019-12, Vol.399, p.108930, Article 108930
Main Authors: Ghanem, R.G., Soize, C., Safta, C., Huan, X., Lacaze, G., Oefelein, J.C., Najm, H.N.
Format: Article
Language:English
Subjects:
Computational physics
Computer simulation
Constraints
Datasets
Design optimization
Differential equations
Diffusion maps
ENGINEERING
Engineering Sciences
Fluids mechanics
Large eddy simulation
Learning
Machine Learning
Mathematics
Mechanics
Optimization and Control
Optimization under uncertainty
Probability
Probability theory
Sampling on manifolds
Scattering
Scramjet simulations
Spatial resolution
Statistics
Supersonic combustion ramjet engines
Uncertainty quantification
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Summary:•LES simulations with three different resolutions are used to generate a training dataset for scramjet combustion.•DMAP manifolds are learned from these simulations.•Over a million additional samples are generated on the manifold using a projected Itô equation.•The new samples are used to define and solve a stochastic optimization problem using non-parametric regression. We demonstrate, on a scramjet combustion problem, a constrained probabilistic learning approach that augments physics-based datasets with realizations that adhere to underlying constraints and scatter. The constraints are captured and delineated through diffusion maps, while the scatter is captured and sampled through a projected stochastic differential equation. The objective function and constraints of the optimization problem are then efficiently framed as non-parametric conditional expectations. Different spatial resolutions of a large-eddy simulation filter are used to explore the robustness of the model to the training dataset and to gain insight into the significance of spatial resolution on optimal design.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2019.108930