Riemannian Manifold Hamiltonian Monte Carlo based subset simulation for reliability analysis in non-Gaussian space

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.