INNOVATIVE COMPUTATIONAL TECHNOLOGIES FOR CHALLENGINGENGINEERING PROBLEMS
Charbel Farhat1,2,3, Phil Avery1, Adrien Bos2 and Todd Chapman1
1
Department of Aeronautics and Astronautics
2
Department of Mechanical Engineering
3
Institute for Computational and Mathematical Engineering
Stanford University, Stanford, CA 94305, USA
Christian Soize
Laboratoire Modelisation et Simulation Multi Echelle
MSME UMR 8208 CNRS
Universite Paris-Est, 5 bd Descartes, 77454 Marne-la-Vallee, France
Grand Challenge problems in Aeronautical, Astronautical, Automotive and Naval Engineering
abound. Examples include problems pertaining to advanced technology concepts for N+3 subsonicand supersonic commercial transport aircraft, advanced spacecraft propulsion systems foraccessing space more routinely, light-weight supersonic inflatable aerodynamic decelerators for
robotic missions to Mars, optimal design under uncertainties, and autonomous systems withdecision making capabilities. Addressing these problems requires, in addition to flight tests, at-seatests, and other experiments, multiscale computational models and algorithms. It also necessitates
the development of advanced solution methods that can operate in practical amounts of CPU time,
while getting informed by observational data in a manner that can manage uncertainties andquantify them during predictions. By far however, the biggest challenge is to break the stalemate
position in which all but a select group of industries are as far as embracing high-fidelity
computational models, due to the usual concerns about their reliability and computational cost. To
this effect, this lecture will present some new directions and capabilities that are needed for rising
to these challenges. They include, among others, parametric, nonlinear, Stochastic, Hyperreduced,
Projection-based Reduced-Order Models (SHPROMS) that can extract from numerical orexperimental data fundamental information or knowledge that otherwise they do not capture, inorder to quantify uncertainties and enable real-time predictive simulations. Such capabilities arepotentially a game changer for computational design and optimization, embedded computing,model predictive control, and most importantly, dynamic data-driven applications systems.
Specifically, the lecture will begin with a progress report on the real-time solution of complex,
parametric engineering problems in aeronautics, automotive, and naval engineering using
HPROMs. Then, it will present a nonparametric probabilistic approach for modeling model form
uncertainties in a nonlinear HPROM and quantifying uncertainties in its associated highdimensional counterpart. This approach features three ideas: substituting the deterministic
Reduced-Order Basis (ROB) underlying an HPROM with a stochastic counterpart that depends ona small number of hyperparameters; constructing the probability measure of the stochastic ROB
on a subset of a compact Stiefel manifold in order to preserve linear independence and thesatisfaction of the boundary conditions; and solving a reduced-order statistical inverse problem todetermine the hyperparameters. These innovative ideas will be demonstrated in this lecture throughthe solution of several realistic problems in computational analysis and design.