Special Mathematics Lecture

Contact:
Serge Richard (richard@math.nagoya-u.ac.jp), Rm. 247 in Sci. Bldg. A

Introduction to data assimilation (Spring 2022)

Registration code : 0053621
Schedule : Wednesday (18.30 - 20.00) in room 207 of Science Building A and on Zoom

• Syllabus : pdf file

• Class dates :
  April 13, 20, 27
  May 11, 18, 25
  June 1, 8, 15, 22, 29
  July 6, 13, 20
  

• Program :
  1) Motivation
  2) Mathematical background
  3) Basic algorithms of data assimilation
  4) Variants and extensions of the Kalman filter
  

• Lecture notes :
  The cumulative notes
  

• Weekly summaries : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

• Additional material :
  Summary on random variable
  Presentation of Qiwen on Lorenz 63 model: pdf file, ppt file (with movie)
  Summary on filters
  Presentation of Qiwen on Lorenz 96 model: pdf file, ppt file
  

• Study sessions : Are organized on an individual basis by some students. For any information, contact Hiep, Qi, Vic, Tom.

• For the evaluation, you need to submit the solutions of some exercises and/or the proofs of some statements. These submissions can take place at any time during the semester. If you have any question, contact me or Qiwen Sun.

• Student's reports :
  A minimization problem, by Sirawich Saranakomkoop
  Proof of Woodbury Matrix Identity and the Kalman Update Formula, by Vic Austen
  Forecast: data driven, by Nguyen Minh Diep
  Best Linear Unbiased Estimator, by Ethan Dowley
  Marginal and conditional pdfs, and various exercises about the normal distribution, by Nguyen Hoang Hiep and Jotaro Kobayashi
  On Monte Carlo quadrature, by Taichi Kato
  The Kalman filter, by Hla Hany Mohamed Helmy Ahmed
  Monte Carlo method: an application for the determination of pi, by Miki Satoshi
  An example of Bayesian inference, by Peng Qi
  Another approach for the Kalman filter, by Nguyen Duc Thanh
  Several results with the normal distribution, by Malak Hamed Mokhtar
  Least squares, by Qiuling Low
  

• References:
  [ABN] Data Assimilation, methods, algorithms, and applications, by M. Asch, M. Bocquet, M. Nodet
  [Ev] Data Assimilation, the ensemble Kalman filter, by G. Evensen
  [HE] Introduction to hidden Semi-Markov models, by J. van der Hoek, R. Elliott
  [LSZ] Data Assimilation, a mathematical introduction, by K. Law, A. Stuart, K. Zygalakis
  [RC] Probabilistic Forecasting and Bayesian Data Assimilation, by S. Reich, C. Cotter
  [Roh] Multivariate localization methods for ensemble Kalman filtering, S. Roh et al.
  [Sa] Bayesian filtering and smoothing, by S. Sarkka
  [SRMT] Analysis of COVID-19 spread in Tokyo through an agent-based model with data assimilation, C. Sun, S. Richard, T. Miyoshi, N. Naohiro