arXiv subjects

Oindrila Kanjilal

Publications and source records attributed to Oindrila Kanjilal.

3 recordsLinked to original sources

arXiv2026

Engineering safe structures: recent advances in structural reliability modelling

This paper reviews advances over the last decade in the field of computational structural reliability modelling. The discussion is focused on problems of time-variant/time-invariant reliability at the component level. Three broad classes of problems are considered: (a) time-invariant reliability problems involving static problems, (b) problems of time-variant reliability analysis for deterministically parametered dynamical systems driven by random excitations, and (c) time-variant reliability analysis of randomly parametered dynamical systems subjected to random excitations. Four classes of approaches are discussed: (a) analytical methods based on first/second order reliability analyses (for time-invariant reliability analysis) and level crossing based approaches for time-variant reliability problems, (b) methods based on importance sampling strategies (including the Girsanov transformation based method for dynamical systems), (c) particle and trajectory splitting based methods, and (d) methods that employ machine learning based tools (primarily involving development of surrogate models and active learning strategies) in tackling reliability problems. The focus of the discussions is on methodological advances, and questions related to specific applications are not addressed. The review presents critical discussions on the relative merits of alternative approaches (in terms of computational efficiency, accuracy, scalability, treatment of rare events, ability to handle geometric complexities linked to failure surface, and suitability for high-dimensional problems) and identifies several directions for future research.

stat.ME↗

arXiv2026

Directional subset simulation method for reliability analysis

Estimating the probabilities of rare failure events is a key challenge in the reliability analysis of physical systems. Subset simulation (SS) is a very popular adaptive Monte Carlo method for this problem. In SS, the small failure probability is evaluated as a product of larger conditional probabilities by iteratively sampling a sequence of nested sub-domains of the parameter space, encompassing the target failure domain of interest, using Markov chain Monte Carlo methods. For failure domains with multiple modes, the Markov chain samples used to explore the intermediate levels of SS can be trapped in a confined region of the input parameter space, leading to inaccurate failure probability estimates. In this contribution, we propose the directional subset simulation (dSS) method for this problem, which uses concepts from directional sampling to informedly propagate samples towards failure. This is accomplished through a novel selection of the intermediate failure domains, which preserves samples in several directions in the parameter space in each intermediate level. The merits of the dSS method are illustrated through a selection of numerical examples.

stat.CO↗

arXiv2020

Integrals over Gaussians under Linear Domain Constraints

Integrals of linearly constrained multivariate Gaussian densities are a frequent problem in machine learning and statistics, arising in tasks like generalized linear models and Bayesian optimization. Yet they are notoriously hard to compute, and to further complicate matters, the numerical values of such integrals may be very small. We present an efficient black-box algorithm that exploits geometry for the estimation of integrals over a small, truncated Gaussian volume, and to simulate therefrom. Our algorithm uses the Holmes-Diaconis-Ross (HDR) method combined with an analytic version of elliptical slice sampling (ESS). Adapted to the linear setting, ESS allows for rejection-free sampling, because intersections of ellipses and domain boundaries have closed-form solutions. The key idea of HDR is to decompose the integral into easier-to-compute conditional probabilities by using a sequence of nested domains. Remarkably, it allows for direct computation of the logarithm of the integral value and thus enables the computation of extremely small probability masses. We demonstrate the effectiveness of our tailored combination of HDR and ESS on high-dimensional integrals and on entropy search for Bayesian optimization.

cs.LG↗