Mathematics and numerics for data assimilation and state estimation, summer semester 2020

Content:

Bayesian inference; stochastic processes; the Fokker-Planck equation, discrete time, linear and nonlinear filtering algorithms, numerical methods for data assimilation.

Lecturers:

Lectures and ubungs: Hakon Hoel, office: C364, Kackertstr. 9, email: hoel AT uq.rwth-aachen.de

Course literature:

Main literature: "Filtering and Prediction: A Primer" by Fristedt, B, Jain, N. and Krylov, N., 1st ed. AMS (2007), and "Data assimilation" by Law, K., Stuart, A., & Zygalakis, K., 1st ed. Springer (2015).

Supplementary:

• "Probability: Theory and Examples" Durrett, R, Version 5 January 11, 2019. Downloadable from https://services.math.duke.edu/~rtd/PTE/PTE5_011119.pdf
• "Data Assimilation and Inverse Problems" by Sanz-Alonso D., Stuart, A. and Taeb, A., https://arxiv.org/abs/1810.06191.
• "Bayesian Filtering and Smoothing" Särkkä, S (2013).Cambridge University Press. Downloadable from: http://users.aalto.fi/~ssarkka/pub/cup_book_online_20131111.pdf
• "Probabilistic forecasting and Bayesian data assimilation" by Reich, S. and Cotter, C., 1st ed. Cambridge University Press (2015).
• "Applied Stochastic Analysis" by E, W., Li, T., Vanden-Eijnden, E., 1st ed. American Mathematical Society (2019).

Weekly lectures and ubungs:

Most weeks there will be 4 SWS lectures and 2 SWS ubungs (see plan below for exceptions).

Student presentation:

Bonus points equivalent to 0.1*MAX_EXAM score is awarded to those giving a (roughly) 20 minutes presentation on an important topic/paper in data assimilation at specified times in early July.

Suggested topics and papers (text marked in red are taken topics):

• "A new approach to linear filtering and prediction problems" Kalman, R. E. 1960b, Transactions of the ASME, Journal of Basic Engineering, 82(1), 35–45.
• Telecomunications (and hidden Markov modeling more generally): "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm" IEEE Transactions on Information Theory, Viterbi 1967
• Numerical weather prediction: "Atmospheric modeling, data assimilation and predictability" Kalnay.
• "Understanding GPS principles and applications" Kaplan 1996
• Oil reservoir state estimation: "Data Assimilation" Evensen and "An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation" Gu and Oliver.
• "The theory of dynamic programming" (Bulletin of the AMS, 1954) Bellman
• "Estimation with Applications to Tracking and Navigation" Bar-Shalom, Li and Kirubarajan.
• Data assimilation applied to spread of diseases. Suggestion: "Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study", Lekone and Finkenstädt.
• "Ensemble Kalman methods for inverse problems" Iglesias, Law and Stuart
• Data assimilation for the cardiovascular system (Sections 10 and 11 in): "The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications" Quateroni, Manzoni and Vergara.
• "On the convergence of the ensemble Kalman filter" Mandel, Cobb and Beezley.
• "On sequential Monte Carlo sampling methods for Bayesian filtering" Doucet, Godsill and Andrieu.
• "Multilevel Ensemble Kalman filtering" Hoel, Law and Tempone.
• Infinite dimensional Bayesian inference: "Inverse problems, a Bayesian perspective" Stuart.
• "Nonlinear Controllability and Observability" Hermann and Krener
• "Data assimilation: The Schrödinger perspective" Reich

Grading and credits:

Final oral exam 31/7 from 9AM to 5PM at Kackertstr. 9, room C301. Credits: 9 ECTS.

Weekly plan for lectures and ubungs (will be updated):

The plan will be updated during the semester.

Literature abbreviations: (Fristedt, Jain and Krylov) = FJK, (Law, Stuart and Zygalakis) = LSZ, (Sanz-Alsons, Stuart, Taeb) = SST, (S. Sarka) = Sar, (Reich and Cotter) = RC, (E, Li and Vanden-Eijnden) = ELV-E