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Classroom Contents
Tensor Train Algorithms for Stochastic PDE Problems - Sergey Dolgov, University of Bath
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- 1 Intro
- 2 Stochastic partial differential equation
- 3 (tailored) Bayesian inverse problem
- 4 Bayesian inversion - solution approaches
- 5 Separation of variables
- 6 2 variables: low-rank matrices
- 7 Cross approximation methods
- 8 Cross interpolation
- 9 Maximum Volume principle
- 10 Cross approximation alternating iteration
- 11 Cross approximation algorithm
- 12 Tensor Train (TT) decomposition
- 13 How to compute a TT decomposition?
- 14 TT for inverse PDE problems
- 15 TT for inverse problems
- 16 Conditional probability factorisation
- 17 Conditional distribution sampling method
- 18 TT-CD sampling
- 19 Even better samples: mapped QMC
- 20 Two-level control variate QMC-MCMC algorithm
- 21 Inverse diffusion equation
- 22 MCMC chain and accuracy of the density function
- 23 Computation of the posterior Qol
- 24 Shock absorber: problem setting
- 25 Shock absorber: quadrature error
- 26 Conclusion
