Cross-entropy-based importance sampling with failure-informed dimension reduction for rare event simulation

by   Felipe Uribe, et al.

The estimation of rare event or failure probabilities in high dimensions is of interest in many areas of science and technology. We consider problems where the rare event is expressed in terms of a computationally costly numerical model. Importance sampling with the cross-entropy method offers an efficient way to address such problems provided that a suitable parametric family of biasing densities is employed. Although some existing parametric distribution families are designed to perform efficiently in high dimensions, their applicability within the cross-entropy method is limited to problems with dimension of O(1e2). In this work, rather than directly building sampling densities in high dimensions, we focus on identifying the intrinsic low-dimensional structure of the rare event simulation problem. To this end, we exploit a connection between rare event simulation and Bayesian inverse problems. This allows us to adapt dimension reduction techniques from Bayesian inference to construct new, effectively low-dimensional, biasing distributions within the cross-entropy method. In particular, we employ the approach in [47], as it enables control of the error in the approximation of the optimal biasing distribution. We illustrate our method using two standard high-dimensional reliability benchmark problems and one structural mechanics application involving random fields.


page 1

page 2

page 3

page 4


Large deviation theory-based adaptive importance sampling for rare events in high dimensions

We propose a method for the accurate estimation of rare event or failure...

Certified Dimension Reduction for Bayesian Updating with the Cross-Entropy Method

In inverse problems, the parameters of a model are estimated based on ob...

Deep importance sampling using tensor-trains with application to a priori and a posteriori rare event estimation

We propose a deep importance sampling method that is suitable for estima...

Bayesian improved cross entropy method for network reliability assessment

We propose a modification of the improved cross entropy (iCE) method to ...

Cross-Entropy method: convergence issues for extended implementation

The cross-entropy method (CE) developed by R. Rubinstein is an elegant p...

Adapting Reduced Models in the Cross-Entropy Method

This paper deals with the estimation of rare event probabilities using i...

Cross-Entropy Based Importance Sampling for Stochastic Simulation Models

To efficiently evaluate system reliability based on Monte Carlo simulati...

Please sign up or login with your details

Forgot password? Click here to reset