The Mathematics of Climate and the Environment
IHP, Paris, September 9 - December 21 2019
Deadline for financial support: March 15th, 2019
Registration is free however mandatory: http://www.ihp.fr/en/CEB/T3-2019
Course III Schedule
Course II: Big data, data assimilation, and uncertainty quantification
28 Oct.–8 Nov. 2019
The course will take place in the amphitheater of the Institut Henry Poincaré
11 Rue Pierre et Marie Curie, 75005 Paris, France
(a) Data assimilation & climate science applications
M. Bocquet (ENPC) & D. Crisan (Imperial College London)
(b) Big data & uncertainty quantification
Omar Ghattas (U. Texas, Austin)
Schedule
Marc Bocquet
Monday, October 28, 10:30-12:30
Lecture 1. Elementary principles of geophysical data assimilation. The Bayesian standpoint. Classical methods of data assimilation: 3D-Var, the Kalman filter, 4D-Var.
Tuesday, October 29, 10:30-12:30
Lecture 2. The ensemble Kalman filter and its variants: mathematical and algorithmic aspects.
Thursday, October 31, 10:30-12:30
Lecture 3. Recent advances —hybrid and ensemble variational techniques. What should one expect from machine learning and deep learning.
Dan Crisan
Tuesday, November 5, 10:30am-12:30pm
Lecture 1. Data assimilation as a stochastic filtering problem. Framework. The signal and the observation process. Prior/Posterior distribution. The linear/Kalman filter.
Wednesday, November 6, 10:30am-12:30pm
Lecture 2. Solving data assimilation problems using particle filters. Mathematical and methodological considerations. The standard particle filter. Model reduction. Tempering. Jittering. Nudging.
Thursday, November 7, 10:30am-12:30pm
Lecture 3. Two case studies: 2D Euler and 2D Two-layer quasigeostrophic model. Algorithmic considerations: Choice of initial condition, number of particles, assimilation step, reduction parameter. Forecast reliability.
Omar Ghattas
Tuesday, November 5, 3-5pm
Lecture 1. Ill-posedness of inverse problems: Model problems, Tikhonov regularization, Morozov discrepancy, Bayesian formulation
Wednesday, November 6, 3-5pm
Lecture 2. The MAP estimate: large-scale optimization via inexact Newton-CG, adjoint-based gradients and Hessians via the Lagrangian formalism
Thursday, November 7, 3-5pm
Lecture 3. Laplace approximation of the posterior: Randomized eigensolvers, low-rank Hessian approximation, alternatives for highly data-informed problems
Friday, November 8, 10:30am-12:30pm
Lecture 4. Large-scale Bayesian inverse problem case study: Inference
of basal friction in flow of the Antarctic ice sheet from InSAR satellite data
Friday, November 8, 3-5pm
Lecture 5. Markov chain Monte Carlo: Metropolis-Hastings, preconditioned Crank-Nicolson and generalized pCN for infinite-dimensional posteriors
