Topic
Sparse grid
About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.
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TL;DR: An application of the variance-based global sensitivity measures for evaluation of fault location algorithms to identify factors and their interactions that contribute to the fault locator output variability, based on the results of Sparse Grid Regression.
6 citations
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TL;DR: A novel, alternative, hierarchical approach, based on adaptive sparse grids quadrature, specifically using the same construction as multi-index stochastic collocation (MISC) coupled with Brownian bridge construction and Richardson extrapolation is designed, which demonstrates substantial computational gains with respect to the standard MC method.
Abstract: The rough Bergomi (rBergomi) model, introduced recently in [4], is a promising rough volatility model in quantitative finance. This new model exhibits consistent results with the empirical fact of implied volatility surfaces being essentially time-invariant. This model also has the ability to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, and due to the non-Markovian nature of the fractional driver, the prevalent option is to use Monte Carlo (MC) simulation for pricing. Despite recent advances in the MC method in this context, pricing under the rBergomi model is still a time-consuming task. To overcome this issue, we design a novel, alternative, hierarchical approach, based on adaptive sparse grids quadrature, specifically using the same construction as multi-index stochastic collocation (MISC) [21], coupled with Brownian bridge construction and Richardson extrapolation. By uncovering the available regularity, our hierarchical method demonstrates substantial computational gains with respect to the standard MC method, when reaching a sufficiently small error tolerance in the price estimates across different parameter constellations, even for very small values of the Hurst parameter. Our work opens a new research direction in this field, i.e. to investigate the performance of methods other than Monte Carlo for pricing and calibrating under the rBergomi model.
6 citations
TL;DR: By analyzing the results of several numerical and engineering examples, it is found that the novel proposed interpretation about the importance measures of the correlated input variables is reasonable, and the proposed methods for solving importance measures are efficient and accurate.
6 citations
01 Jan 2009
6 citations
TL;DR: In this article, a stochastic electrothermal problem featuring 12 bondwire-related uncertainties is considered, and the impact of the uncertain inputs on the temperature developed during the duty cycle of an IC is quantified.
Abstract: Summary
The temperature developed in bondwires of integrated circuits (ICs) is a possible source of malfunction and has to be taken into account during the design phase of an IC. Because of manufacturing tolerances, a bondwire's geometrical characteristics are uncertain parameters, and as such, their impact has to be examined with the use of uncertainty quantification methods. Considering a stochastic electrothermal problem featuring 12 bondwire-related uncertainties, we want to quantify the impact of the uncertain inputs onto the temperature developed during the duty cycle of an IC. For this reason, we apply the stochastic collocation method on sparse grids, which is considered the current state-of-the-art. We also implement an approach based on the recently introduced low-rank tensor decompositions, in particular the tensor train decomposition, which in theory promises to break the curse of dimensionality. A comparison of both methods is presented, with respect to accuracy and computational effort.
6 citations