Dushhyanth Rajaram
(Advisor: Prof. Dimitri Mavris)

will defend a doctoral thesis entitled,

Methods for Construction of Surrogates For Computationally Expensive High-Dimensional Problems

Tuesday, October 13th at 11:00 a.m.

Meeting Link: https://bluejeans.com/472745898

Abstract
Maturation of computational models has increased reliance on numerical simulations for the analysis, and more importantly, design of complex engineered systems. The high accuracy and realism offered by simulation-based analysis often comes at a high computational cost especially in the many-query context, as such limiting its applicability in exploratory design studies. In the absence of inexpensive models that exploit physics-based simplifying assumptions, practitioners often resort to computationally cheap surrogate-based methods. However, several challenges arise when constructing surrogates for high-dimensional field outputs. Identifying and tackling these issues is the primary goal of this dissertation. The challenges posed by the following three key issues are investigated: 1) the need to handle large datasets under constrained computational resources, 2) the presence of a large number of inputs, 3) the need for accurate models under scarcity of data from expensive simulations with many inputs.

Pursuit of the first issue investigates the viability of randomization as a means to perform computationally efficient data compression while retaining sufficient accuracy to construct surrogate models for large field responses.  Accommodation of a large number of inputs is tackled through the formulation of a manifold optimization-based Gaussian Process (MO-GP) regression model that simultaneously finds a low-dimensional input subspace and trains a model in it using input-output pairs exclusively. To emulate field outputs using the Proper Orthogonal Decomposition (POD) and interpolation for analyses with a large number of inputs, the MO-GP model is leveraged to learn a map from the inputs to each POD coordinate. Finally, the use of a multifidelity extension to the MO-GP model in conjunction with a recently proposed manifold alignment-based model is proposed as a solution to improve predictive accuracy with insufficient high-fidelity data.

Findings show that: 1) randomization enables efficient construction of competitive predictive models under constrained computational resources, 2) the MO-GP model is effective in finding a low-dimensional input subspace for each POD coordinate and results in a good predictive model, and 3) an initial feasibility assessment of the multifidelity model on an airfoil flow emulation problem shows promise but warrants further investigation.

Committee

• Prof. Dimitri Mavris – School of Aerospace Engineering (Advisor and Committee Chair)

• Prof. Jechiel Jagoda – School of Aerospace Engineering
• Prof. Ümit V. Çatalyürek – School of Computational Science and Engineering
• Dr. Olivia Pinon Fischer – Senior Research Engineer, School of Aerospace Engineering
• Dr. Frederic Villeneuve – Principal Systems Lead, Blue Origin