Reducing the Cost of Ensemble-Based Data Assimilation in Multiple-Query Scenarios through Covariance Augmentation

Abstract

We present and assess a method to reduce the computational cost of performing data assimilation (DA) for reacting flow in multiple-query scenarios, where we consider several scenarios with similar underlying dynamics. We focus on ensemble-based DA, in particular the ensemble Kalman filter (EnKF). The accuracy of the EnKF, which depends on the quality of the sample covariance, improves with the ensemble size, but so does its computational cost. To reduce the ensemble size while maintaining accurate covariance, we propose a data-driven approach to augment the covariance based on the statistical behavior learned from model evaluations. We assess our augmentation method using one-dimensional model problems and synthetic reacting flow cases. We show in all cases that ensemble size, and thus computational cost, may be reduced by a factor of three to four while maintaining accuracy.I am grateful to Professor Masayuki Yano and Professor Adam Steinberg for their supervision and mentorship over the past two years. I appreciate your endless enthusiasm, patience, and encouragement to play around with new methods and explore what might be possible. I especially appreciate the efforts you made to maintain all this despite the pandemic. My thesis would not be where it is without your guidance.I would like to thank Professor Peter Grant for support in side projects and extracurriculars, especially in letting me use the aero design lab. You didn't have to do that, and I appreciate so much that you did. I would also like to thank Professor Gabriele D'Eleuterio for the nice chats and advice every time I passed by his office. I'm looking forward to seeing you again when the university reopens. Ci vediamo presto! I would like to thank the other founding members of the Bob Ross Fan Club, Madeline Zhang and Caulan Rupke, for the trips to Booster Juice, the paint nights, and showing off all the cool things they're up to.I would like to thank my UTIAS friends who made my time there so enjoyable. Thanks so much to