Hamiltonian Monte Carlo for Reliability Analysis
Prof. Hector Jensen
Hamiltonian Monte Carlo, which is based on Hamiltonian dynamics, is a powerful computational technique for sampling from complex distributions. In this sampling technique, each new candidate state is generated according to the trajectory of an auxiliary dynamical system, which is then accepted or rejected based on the traditional Metropolis-Hastings rule. In this framework, this presentation provides an overview of Hamiltonian Monte Carlo, including its theoretical background, algorithmic implementation, practical considerations for its application in the context of complex reliability analyses, and its integration with advanced simulation techniques.
The procedure has shown effective in reducing the correlation of samples with respect to traditional random walk approaches in a variety of applications, which can be beneficial for reliability analysis, including reliability of stochastic dynamical systems. Generally, Hamiltonian Monte Carlo methods alleviate the random-walk behavior to achieve more effective and consistent exploration of the probability space compared to standard random-walk-based Markov chain Monte Carlo methods. A number of numerical examples are presented to illustrate the capabilities and performance of Hamiltonian Monte Carlo. Overall, Hamiltonian Monte Carlo is a valuable tool for reliability analysis.
Hector Jensen is a Professor of Civil Engineering at the Santa Maria Technical University, Valparaiso, Chile, and Professor of Mechanical Engineering at the Catholic University of Chile, Santiago, Chile. He is a Mathematician Civil Engineer from the University of Chile and he received his PhD in Applied Mechanics from the California Institute of Technology (CALTECH), Pasadena, USA. His research interests include Computational Stochastic Mechanics, Advanced Simulation Methods, Robust and Reliability-Based Optimization, Risk and Sensitivity Analysis, Fuzzy Analysis, Finite Element Analysis, Dynamic Sub-structuring, and Bayesian Model Updating. He has been visiting professor in several American and European universities, including University of California at Los Angeles (UCLA), California Institute of Technology (CALTECH), University of Michigan (UM), University of Innsbruck, etc. He has published numerous journal and conference papers, as well as book chapters in areas of his expertise. In addition, a book that deals with the application of reduced-order models to complex simulation-based problems has been published by Springer in 2019 (Sub-Structure Coupling for Dynamic Analysis: Application to Complex Simulation-Based Problems Involving Uncertainty). He is preparing a new book related to the Reliability, Sensitivity and Optimization of Linear Structural Systems under Stochastic Gaussian Excitation based on Advanced Simulation Techniques. He has been invited to give lectures, keynotes, semi-plenary and plenary lectures in a number of universities and international conferences. He is member of the editorial board of several journals and he has been guest editor of different Journals, including Computers and Structures and Mechanical Systems and Signal Processing. He is also member of the scientific committee of many international conferences and reviewer of different journals. In 2018 he was selected by the Recruitment Program of High-end Foreign Experts of the State Administration of Foreign Affairs of the People’s Republic of China.