PhD Proposal by Nikhil Iyengar

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Nikhil Iyengar
(Advisor: Prof. Dimitri Mavris)

will propose a doctoral thesis entitled,

Uncertainty Propagation in High-dimensional Fields Using Reduced Order Modeling


Thursday, May 12 at 2:00 p.m.

in the
Collaborative Visualization Environment (CoVE)

Weber Space Science and Technology Building (SST II)



Physics-based models have become integral to the design and analysis of aircraft, with novel concepts requiring possibly millions of simulations prior to certification. Today, both in the United States and across the world, there is a growing interest in re-introducing commercial supersonic transport aircraft (SST), whose design relies extensively on such physics-based models. There has been especially significant research on modeling the aerodynamic field around SSTs, which is characterized by the presence of strong shocks and nonlinearities. The design of supersonic aircraft cannot rely solely on scalar or integrated quantities of interest, such as lift coefficient; rather, it is necessary to have access to the distribution of aerodynamic states (such as the pressure field) to accurately shape the aircraft and guide down-stream disciplinary analyses. High-fidelity Computational Fluid Dynamics (CFD) simulations closely match experimental data and can provide the aerodynamic state around a body, but each simulation can take hours or days to output a solution. For multi-query problems, which require repeated evaluation of the expensive simulation, this cost becomes computationally intractable. Uncertainty quantification is an important example of a multi-query problem seen during SST design. This is because several studies have cautioned that uncertainties in atmospheric and operating conditions can result in an SST that meets the performance requirements at some conditions but becomes infeasible at other conditions. Surrogate models have been identified as a key enabler for leveraging high-fidelity numerical simulations earlier in the design process because they are non-intrusive, data-driven, and cheap to evaluate. However, there exist several challenges when creating surrogate models for high-dimensional, uncertain field outputs with shocks that this thesis tackles.

In particular, this study explores the use of generalized Polynomial Chaos (gPC) in combination with both linear and nonlinear dimensionality reduction methods to create Reduced Order Models (ROM) that enable uncertainty quantification in high-dimensional fields with nonlinear structures. Although both gPC and ROM are well established in their respective communities, their combined usage, especially for high-dimensional fields outputs, is relatively unexplored. The specific research objectives of this proposal are: 1) to compare the performance of nonlinear dimensionality reduction methods when combined with polynomial chaos expansion to the linear POD-PCE benchmark method, 2) to assess the improvements in ROMs by combining the PCE method with a Kriging model, 3) to explore the use of the proposed methodology in predicting the sonic boom pressure signature for a supersonic aircraft with variations in atmospheric and operating conditions. This research will not only provide novel insight into the performance of PCE models in high-dimensional aerodynamic problems, but also enable uncertainty quantification in fields with complex flow structures necessary for the robust design of novel aircraft.



  • Prof. Dimitri Mavris – School of Aerospace Engineering (Advisor)
  • Prof. Graeme Kennedy – School of Aerospace Engineering
  • Prof. Lakshmi Sankar – School of Aerospace Engineering
  • Dr. Dushhyanth Rajaram – School of Aerospace Engineering


  • Workflow Status: Published
  • Created By: Tatianna Richardson
  • Created: 05/03/2022
  • Modified By: Tatianna Richardson
  • Modified: 05/03/2022


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