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

• Published in: Journal of computational physics Vol. 399; p. 108930
• Main Authors: Ghanem, R.G., Soize, C., Safta, C., Huan, X., Lacaze, G., Oefelein, J.C., Najm, H.N.
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15.12.2019; Elsevier Science Ltd; Elsevier
• 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; Uncertainty quantification; Scramjet simulations; Diffusion maps; Optimization under uncertainty; Sampling on manifolds; Machine learning
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.108930

•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.