Hamiltonian monte carlo-subset simulation (HMC-SS) methods for structural reliability analysis

In this study, we carefully analyze the most recent advancements in Hamiltonian Monte Carlo methods combined with Subset Simulation (HMC-SS) in the context of structural reliability analysis. The HMC method employs Hamiltonian dynamic to sample from a target probability distribution. In contrast to the standard Markov-Chain Monte Carlo methods (e.g., Gibbs or Metropolis-Hastings techniques), HMC alleviates the burn-in phase and the random walk behavior to achieve a more effective exploration of the target probability distribution. This turns out to be important in high-dimensional spaces (e.g., when the number of random variables is high), where the bulk of probability content concentrates in the so-called typical sets. The structure of the paper is as follows. We first briefly review the Subset Simulation and the general concepts of HMC. Following, in both standard Gaussian and non-Gaussian probability spaces, we present a series of complex structural reliability problems to test in practice the validity of the method. Finally, we conclude with a series of future developments and directions.