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Riemannian Manifold Hamiltonian Monte Carlo based subset simulation for reliability analysis in non-Gaussian space
https://orcid.org/0000-0003-4058-260X
https://orcid.org/0000-0003-4205-1829
Abstract This paper proposes a Riemannian Manifold Hamiltonian Monte Carlo based subset simulation (RMHMC-SS) method to overcome limitations of existing Monte Carlo approaches in solving reliability problems defined in highly-curved non-Gaussian spaces. RMHMC is based on the second-order geometric information of a probability space. Specifically, it generates an optimized path for Markov chain evolutions in a Hamiltonian constructed on the Riemannian manifold. Compared with the recently proposed Hamiltonian Monte Carlo based subset simulation (HMC-SS) approach, the RMHMC-SS approach shows better performance in handling highly-curved probability distributions. After a brief review of HMC-SS, the theory and implementation details of RMHMC-SS are presented. Finally, various reliability examples are studied to test and verify the proposed RMHMC-SS method.
Highlights Riemannian Manifold Hamiltonian Monte Carlo based subset simulation is developed. Second order geometric information is used for efficient MCMC evolution. The method is designed for reliability problems in highly-curved non-Gaussian space. The method is successfully demonstrated by applications to non-Gaussian problems.
Riemannian Manifold Hamiltonian Monte Carlo based subset simulation for reliability analysis in non-Gaussian space
https://orcid.org/0000-0003-4058-260X
https://orcid.org/0000-0003-4205-1829
Abstract This paper proposes a Riemannian Manifold Hamiltonian Monte Carlo based subset simulation (RMHMC-SS) method to overcome limitations of existing Monte Carlo approaches in solving reliability problems defined in highly-curved non-Gaussian spaces. RMHMC is based on the second-order geometric information of a probability space. Specifically, it generates an optimized path for Markov chain evolutions in a Hamiltonian constructed on the Riemannian manifold. Compared with the recently proposed Hamiltonian Monte Carlo based subset simulation (HMC-SS) approach, the RMHMC-SS approach shows better performance in handling highly-curved probability distributions. After a brief review of HMC-SS, the theory and implementation details of RMHMC-SS are presented. Finally, various reliability examples are studied to test and verify the proposed RMHMC-SS method.
Highlights Riemannian Manifold Hamiltonian Monte Carlo based subset simulation is developed. Second order geometric information is used for efficient MCMC evolution. The method is designed for reliability problems in highly-curved non-Gaussian space. The method is successfully demonstrated by applications to non-Gaussian problems.
Riemannian Manifold Hamiltonian Monte Carlo based subset simulation for reliability analysis in non-Gaussian space
https://orcid.org/0000-0003-4058-260X
https://orcid.org/0000-0003-4205-1829
Abstract This paper proposes a Riemannian Manifold Hamiltonian Monte Carlo based subset simulation (RMHMC-SS) method to overcome limitations of existing Monte Carlo approaches in solving reliability problems defined in highly-curved non-Gaussian spaces. RMHMC is based on the second-order geometric information of a probability space. Specifically, it generates an optimized path for Markov chain evolutions in a Hamiltonian constructed on the Riemannian manifold. Compared with the recently proposed Hamiltonian Monte Carlo based subset simulation (HMC-SS) approach, the RMHMC-SS approach shows better performance in handling highly-curved probability distributions. After a brief review of HMC-SS, the theory and implementation details of RMHMC-SS are presented. Finally, various reliability examples are studied to test and verify the proposed RMHMC-SS method.
Highlights Riemannian Manifold Hamiltonian Monte Carlo based subset simulation is developed. Second order geometric information is used for efficient MCMC evolution. The method is designed for reliability problems in highly-curved non-Gaussian space. The method is successfully demonstrated by applications to non-Gaussian problems.
Riemannian Manifold Hamiltonian Monte Carlo based subset simulation for reliability analysis in non-Gaussian space
Chen, Weiming (author) / Wang, Ziqi (author) / Broccardo, Marco (author) / Song, Junho (author)
Structural Safety ; 94
2021-08-05
Article (Journal)
Electronic Resource
English
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