IGPP is pleased to invite you to join its Winter 2023 Seminar Series presentation featuring University of Kansas's Erik Van Vleck. Dr. Van Vleck's talk, "Dimension Reduction for Data Assimilation: Adaptive Meshing and Reduced Order Modeling" will be available March 7, 2023 via Zoom: https://ucsd.zoom.us/j/95717258185?pwd=ZXVjNG01alRyOTFqUWdVYkVyekxkdz09 Password: igpp
Time: 12:00 pm, Pacific Time
Location: Revelle conference room and Zoom
Abstract: The understanding of nonlinear, high dimensional flows, e.g., atmospheric and ocean flows, is critical to address the impacts of global climate change. Data Assimilation (DA) techniques combine physical models and observational data, often in a Bayesian framework, to predict the future state of the model and the uncertainty in this prediction. Inherent in these systems are noise (Gaussian and non-Gaussian), nonlinearity, and high dimensionality that pose challenges to making accurate predictions. We present some historical origins of DA in Numerical Weather Prediction and a survey of several modern DA techniques. We next discuss recent work on dimension reduction techniques (adaptive spatial meshes and reduced order modeling (ROM) techniques) and their impact on DA schemes. Adaptive moving spatial meshes are useful for solving physical models given by time-dependent partial differential equations by concentrating mesh points in portions of the spatial domain. We outline a framework to develop time- dependent reference meshes using the metric tensors that define the spatial meshes of the ensemble members. We propose a new, time-dependent spatial localization scheme based on
adaptive moving mesh techniques. We also explore how adaptive moving mesh techniques can control and inform the placement of mesh points to concentrate near the location of observations, reducing the error of observation interpolation. In addition, we consider ROM techniques that include Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), and Assimilation in the Unstable Subspace (AUS) for both model and data dimension reduction. Algorithms to take advantage of projected physical and data models may be combined with common DA techniques such as Ensemble Kalman Filter (EnKF) and Particle Filter (PF) variants with a focus on a projected optimal proposal particle filter. We illustrate the utility of our results using discontinuous Galerkin approximations of inviscid Burgers’ equations, the Lorenz 96 equations, and a Shallow water model.