Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds

Abstract

The computational burden of Large-eddy Simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer samples. Such procedures, if successful, would greatly enhance the predictability of models in the sense of improving exploration and characterization of uncertainty due to model error and input dependencies, all while being constrained by the size of the associated statistical samples. In this paper, we show how a recently developed procedure for probabilistic learning on manifolds can serve to improve the predictability in a probabilistic framework of a scramjet simulation. The estimates of the probability density functions of the quantities of interest are improved together with estimates of the statistics of their maxima. We also demonstrate how the improved statistical model adds critical insight to the performance of the model.

Progress in Scramjet Design Optimization Under Uncertainty Using Simulations of the HIFiRE Direct Connect Rig

“…Research for scramjet with uncertainty quantification (UQ) has been gaining traction in recent years [4][5][6][7][8][9][10][11]. Notably, several of these papers have demonstrated the maturing computational methods, as well as standing difficulties, for performing UQ assessment to large-eddy simulations (LES).…”

SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials

“…Once an objective function is defined, a suitable machine learning strategy must be selected such that the supervised machine learning produces a mapping that maps input(s) to output(s) while maximizing the performance metrics defined by an objective (loss) function. This mapping can be generated by classical approaches, such as response surface [22], support vector machine [23], probabilistic learning [24], and neural network [25][26][27]. While different parametrizations of objective functions will affect the training procedure of all different types of supervised machine learning, our numerical experiments will be focusing on the deep neural network , one of the most common technique to generate generic constitutive laws in recent years.…”

Entropy-based closure for probabilistic learning on manifolds

“…Consequently, err PCA (ν) ≤ 10 −6 . Concerning the nonparametric estimate (see (3)), the values of the parameters defined by equation (8) are s = 0.615, s = 0.525, and s/s = 0.853. The use of equations (14) and (15) yields ε opt = 60 and m opt = 10.…”