A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also...

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Bibliographic Details
Published in:Applied mathematics letters 2021-11, Vol.121, p.107361, Article 107361
Main Authors: Khodabakhshi, Parisa, Willcox, Karen E., Gunzburger, Max
Format: Article
Language:English
Subjects:
MATHEMATICS AND COMPUTING
Monte Carlo Methods
Multifidelity methods
Nonlocal diffusion
Nonlocal models
Uncertainty quantification
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Summary:Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. We introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2021.107361