Tensor Train Algorithms for Stochastic PDE Problems - Sergey Dolgov, University of Bath

Tensor Train Algorithms for Stochastic PDE Problems - Sergey Dolgov, University of Bath

Alan Turing Institute via YouTube Direct link

Inverse diffusion equation

21 of 26

21 of 26

Inverse diffusion equation

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Tensor Train Algorithms for Stochastic PDE Problems - Sergey Dolgov, University of Bath

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

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