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The paper presents a new efficient and robust method for rare event probability estimation for computational models of an engineering product or a process returning categorical information only, for example, either success or failure. For…
This paper presents the development of an algorithm, termed the Global-Local Hybrid Surrogate (GLHS), designed to efficiently compute the probability of rare failure events in complex systems. The primary goal is to enhance the accuracy of…
Failure probability estimation problem is an crucial task in engineering. In this work we consider this problem in the situation that the underlying computer models are extremely expensive, which often arises in the practice, and in this…
Structural reliability analysis is concerned with estimation of the probability of a critical event taking place, described by $P(g(\textbf{X}) \leq 0)$ for some $n$-dimensional random variable $\textbf{X}$ and some real-valued function…
Gaussian processes (GPs) are generally regarded as the gold standard surrogate model for emulating computationally expensive computer-based simulators. However, the problem of training GPs as accurately as possible with a minimum number of…
Accurate surrogate construction for PDE-driven high-dimensional rare-event simulation is challenging when performance evaluations are expensive. Since a globally accurate surrogate may require many high-fidelity evaluations, adaptive…
An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…
We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…
We tackle the problem of quantifying failure probabilities for expensive deterministic computer experiments with stochastic inputs under a fixed budget. The computational cost of the computer simulation prohibits direct Monte Carlo (MC) and…
Stochastic inverse problems are generally solved by some form of finite sampling of a space of uncertain parameters. For computationally expensive models, surrogate response surfaces are often employed to increase the number of samples used…
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
Reliability-based design optimization (RBDO) provides a rational and sound framework for finding the optimal design while taking uncertainties into ac-count. The main issue in implementing RBDO methods, particularly stochastic simu-lation…
This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…
Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…
Performance variability management is an active research area in high-performance computing (HPC). We focus on input/output (I/O) variability. To study the performance variability, computer scientists often use grid-based designs (GBDs) to…