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Fourth Year PhD Student
Energy Resources Engineering Department
Monday, April 4, 2022
12:15 PM - 1:15 PM
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models (ROMs) of complex dynamical systems. Despite its popularity, DMD and other singular-value decomposition (SVD) based techniques (e.g., POD) struggle to formulate accurate ROMs for advection-dominated problems because of the nature of SVD-based methods. We investigate this shortcoming of conventional POD and DMD methods formulated within the Eulerian framework. Then we propose a Lagrangian-based DMD method to overcome this so-called translational problem. Our approach is consistent with the spirit of physics-aware DMD since it accounts for the evolution of characteristic lines. Furthermore, we address the limitation of Lagrangian DMD in hyperbolic problems with shocks and propose a physics-aware DMD based on hodograph transformation. This strategy is consistent with the spirit of physics-aware DMDs in that it retains information about shock dynamics. We also derive a theoretical error estimator for DMD extrapolation of numerical solutions, which allows one to monitor and control the errors associated with DMD-based ROMs approximating the physics-based models. Our analysis demonstrates the importance of a proper selection of observables, as predicted by the Koopman operator theory. That, in turn, facilitates the design of efficient algorithms for multi-scale/multi-physics simulations, e.g., by using ROMs as a surrogate to accelerate expensive Markov Chain Monte Carlo sampling used in inverse problems.
Hannah Lu is a fourth year PhD student in Energy Resources Engineering Department of Stanford University, advised by Daniel M. Tartakovsky. Her research interests lie in the field of scientific computing, reduced order modeling, uncertainty quantification and machine learning in applications of environmental fluid mechanics. She received EDGE Doctoral Fellowship, Frank G. Miller Fellowship Award and Henry J. Ramey, Jr. Fellowship Award from Stanford, Student Travel Award from SIAM Conference on UQ, and NSF Fellowship from MMLDT-CSET Conference.