Bayesian inversion of eikonal equations
We consider Bayesian inversion for eikonal equations subjected to the point source and Soner Boundary conditions. For every setting, we show Hadamard well-posedness rigorously by exploiting Lagrangian duality. In the isotropic setting, discretisation errors from finitely truncating the slowness e...
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| Format: | Thesis-Doctor of Philosophy |
| Language: | English |
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Nanyang Technological University
2024
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| Online Access: | https://hdl.handle.net/10356/172963 |
| _version_ | 1826119040087621632 |
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| author | Yeo, Zhan Fei |
| author2 | Hoang Viet Ha |
| author_facet | Hoang Viet Ha Yeo, Zhan Fei |
| author_sort | Yeo, Zhan Fei |
| collection | NTU |
| description | We consider Bayesian inversion for eikonal equations subjected to the point source and Soner Boundary conditions. For every setting, we show Hadamard well-posedness rigorously by exploiting Lagrangian duality.
In the isotropic setting, discretisation errors from finitely truncating the slowness expansion and approximating forward solutions via the Fast Marching Method (FMM) are derived in Hellinger distance for the uniform, loguniform, and lognormal prior cases. For star shaped priors, the induced error from taking approximations via the FMM is quantified. In the Riemannian anisotropy generalisation, the error induced by finite truncation of the metric expansion is derived for analogous uniform and lognormal priors. A modified FMM is employed to numerically approximate the posterior.
We develop complexity optimal Multilevel Markov Chain Monte Carlo (MLMCMC) to approximate posterior expectations. Numerical examples corroborate the optimality of MLMCMC and show that the algorithm is well capable of recovering the slowness from observation data. |
| first_indexed | 2024-10-01T04:53:31Z |
| format | Thesis-Doctor of Philosophy |
| id | ntu-10356/172963 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:53:31Z |
| publishDate | 2024 |
| publisher | Nanyang Technological University |
| record_format | dspace |
| spelling | ntu-10356/1729632024-02-01T09:53:44Z Bayesian inversion of eikonal equations Yeo, Zhan Fei Hoang Viet Ha School of Physical and Mathematical Sciences VHHOANG@ntu.edu.sg Science::Mathematics::Applied mathematics::Numerical analysis Engineering::Computer science and engineering::Mathematics of computing::Numerical analysis Science::Physics::Acoustics We consider Bayesian inversion for eikonal equations subjected to the point source and Soner Boundary conditions. For every setting, we show Hadamard well-posedness rigorously by exploiting Lagrangian duality. In the isotropic setting, discretisation errors from finitely truncating the slowness expansion and approximating forward solutions via the Fast Marching Method (FMM) are derived in Hellinger distance for the uniform, loguniform, and lognormal prior cases. For star shaped priors, the induced error from taking approximations via the FMM is quantified. In the Riemannian anisotropy generalisation, the error induced by finite truncation of the metric expansion is derived for analogous uniform and lognormal priors. A modified FMM is employed to numerically approximate the posterior. We develop complexity optimal Multilevel Markov Chain Monte Carlo (MLMCMC) to approximate posterior expectations. Numerical examples corroborate the optimality of MLMCMC and show that the algorithm is well capable of recovering the slowness from observation data. Doctor of Philosophy 2024-01-08T06:22:29Z 2024-01-08T06:22:29Z 2023 Thesis-Doctor of Philosophy Yeo, Z. F. (2023). Bayesian inversion of eikonal equations. Doctoral thesis, Nanyang Technological University, Singapore. https://hdl.handle.net/10356/172963 https://hdl.handle.net/10356/172963 10.32657/10356/172963 en Nanyang President's Graduate Scholarship (NPGS) This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). application/pdf Nanyang Technological University |
| spellingShingle | Science::Mathematics::Applied mathematics::Numerical analysis Engineering::Computer science and engineering::Mathematics of computing::Numerical analysis Science::Physics::Acoustics Yeo, Zhan Fei Bayesian inversion of eikonal equations |
| title | Bayesian inversion of eikonal equations |
| title_full | Bayesian inversion of eikonal equations |
| title_fullStr | Bayesian inversion of eikonal equations |
| title_full_unstemmed | Bayesian inversion of eikonal equations |
| title_short | Bayesian inversion of eikonal equations |
| title_sort | bayesian inversion of eikonal equations |
| topic | Science::Mathematics::Applied mathematics::Numerical analysis Engineering::Computer science and engineering::Mathematics of computing::Numerical analysis Science::Physics::Acoustics |
| url | https://hdl.handle.net/10356/172963 |
| work_keys_str_mv | AT yeozhanfei bayesianinversionofeikonalequations |