Masayuki Yano, University of Toronto

Masayuki Yano is an associate professor in the Institute for Aerospace Studies at the University of Toronto. He obtained his bachelor's degree in Aerospace Engineering from Georgia Tech, Masters' degree in Computation for Design and Optimization from MIT, and PhD in Aerospace Computational Engineering from MIT. His research interests lie in the development and assessment of numerical methods for PDEs with emphasis on adaptive high-order methods, error estimation, model reduction, and data assimilation.

Projection-based model reduction for rapid and reliable solution of many-query aerodynamics problems

This talk presents our work on model reduction for parametrized aerodynamics problems. Many engineering tasks require the evaluation of quantities of interests, such as lift and drag, as a function of configuration parameters, such as flight condition (e.g., Mach number and angle of attack) and geometry parameters (e.g., airfoil shape). We present model reduction methods that accelerate the solution of PDEs by several orders of magnitude in many-query scenarios, such as database generation, uncertainty quantification, and optimization, while rigorously estimating and controlling the error in predictive settings. The acceleration is provided through offline-online computational decomposition: in the offline stage, we invoke the CFD solver for judiciously chosen configurations to build a reduced-order model (ROM) which approximates the parametrized PDE solution manifold; in the online stage, we invoke the ROM to provide rapid and reliable prediction for any parameter values. The key ingredients are the following: an adaptive high-order discontinuous Galerkin method, which provides stable and efficient solution of CFD problems; reduced basis spaces, which provide low-dimensional approximations of the parametric manifolds; the empirical quadrature procedure, which provides hyperreduction that enables rapid evaluation of the residual; the dual-weighted residual method, which provides effective error estimates for quantities of interest; and adaptive training algorithms, which train ROMs that meet the user-specified error tolerance in an automated manner. We demonstrate the framework for parametrized aerodynamics problems modeled by the compressible Euler and Reynolds-averaged Navier-Stokes equations, with applications to parameter sweep, uncertainty quantification, and data assimilation.