IGPP is pleased to invite you to join its Spring 2022 Seminar Series presentation featuring Stanford University's Hannah Lu. Dr. Lu's talk, "Dynamic Mode Decomposition for Reduced-Order Modeling in Transport Phenomena" will be available via Zoom on Tuesday, April 12, 2022, starting at 12:00pm. Zoom: https://ucsd.zoom.us/j/96756414714?pwd=N2dTRi9MZDM4N0JBOEJYQ0E0UllSZz09. Password: DMD
Time: 12:00 pm, Pacific Time
Note: This meeting will be recorded. Please make sure that you are comfortable with this before registering.
Abstract: 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., Proper Orthogonal Decomposition) 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-informed 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-informed DMD based on hodograph transformation. This strategy is consistent with the spirit of physics-aware DMDs in that it retains information about shock dynamics. Several numerical tests are presented to demonstrate the accuracy and efficiency of the proposed methods.