DDPS | Registration-based model reduction of parameterized advection-dominated PDEs
Talk Abstract We propose a model reduction procedure for rapid and reliable solution of parameterized advection-dominated problems. This class of problems is challenging for model reduction techniques due to the presence of nonlinear terms in the equations and also due to the presence of parameter-dependent discontinuities that cannot be adequately represented through linear approximation spaces. Our approach relies on three building blocks: (i) a general (i.e., independent of the underlying equation) registration procedure to align local features in a fixed reference domain, to ultimately improve the linear compressibility of the solution manifold; (ii) an hyper-reduced least-squares Petrov-Galerkin (LSPG) reduced-order model, to estimate the mapped solution; and (iii) a multi-fidelity strategy to reduce offline training costs. We present numerical results for a two-dimensional inviscid flow past a bump (Euler equations) and for a one-dimensional shallow water system, to show the potential of the method. Joint work with Dr. Lei Zhang (Inria Bordeaux). Speaker Biography Tommaso Taddei is a junior research scientist at Inria Bordeaux. He is also a member of the Institute of Mathematics in Bordeaux (IMB). His research focuses on model reduction methods for parameterized PDEs and data assimilation methods with applications in continuum mechanics. Before joining Inria in 2018, he was a post-doctoral associate in the group of Professor Yvon Maday at Laboratoire Jacques-Louis Lions, and a PhD student in the group of Professor Anthony Patera in the Department of Mechanical Engineering at MIT. LLNL-VIDEO-821770
Talk Abstract We propose a model reduction procedure for rapid and reliable solution of parameterized advection-dominated problems. This class of problems is challenging for model reduction techniques due to the presence of nonlinear terms in the equations and also due to the presence of parameter-dependent discontinuities that cannot be adequately represented through linear approximation spaces. Our approach relies on three building blocks: (i) a general (i.e., independent of the underlying equation) registration procedure to align local features in a fixed reference domain, to ultimately improve the linear compressibility of the solution manifold; (ii) an hyper-reduced least-squares Petrov-Galerkin (LSPG) reduced-order model, to estimate the mapped solution; and (iii) a multi-fidelity strategy to reduce offline training costs. We present numerical results for a two-dimensional inviscid flow past a bump (Euler equations) and for a one-dimensional shallow water system, to show the potential of the method. Joint work with Dr. Lei Zhang (Inria Bordeaux). Speaker Biography Tommaso Taddei is a junior research scientist at Inria Bordeaux. He is also a member of the Institute of Mathematics in Bordeaux (IMB). His research focuses on model reduction methods for parameterized PDEs and data assimilation methods with applications in continuum mechanics. Before joining Inria in 2018, he was a post-doctoral associate in the group of Professor Yvon Maday at Laboratoire Jacques-Louis Lions, and a PhD student in the group of Professor Anthony Patera in the Department of Mechanical Engineering at MIT. LLNL-VIDEO-821770