Hamiltonian Monte Carlo methods for Subset Simulation in reliability analysis

This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for reliability analysis. The HMC method relies on a deterministic mechanism inspired by Hamiltonian dynamics to propose samples following a target probability distribution. The method alleviates the random walk behavior to achieve a more effective and consistent exploration of the probability space compared to standard Gibbs or Metropolis-Hastings techniques. After a brief review of the basic concepts of HMC method and its computational details, two algorithms are proposed to facilitate the application of HMC method to Subset Simulation in reliability analysis. Next, the behavior of the two HMC algorithms is illustrated using simple probability distribution models. Finally, the accuracy and efficiency of Subset Simulation employing the two HMC algorithms are tested using various reliability examples in both Gaussian and non-Gaussian spaces.