Budget-limited distribution learning in multifidelity problems

05/10/2021
by   Yiming Xu, et al.
0

Multifidelity methods are widely used for statistical estimation of quantities of interest (QoIs) in uncertainty quantification using simulation codes of differing costs and accuracies. Many methods approximate numerical-valued statistics that represent only limited information of the QoIs. In this paper, we introduce a semi-parametric approach that aims to effectively describe the distribution of a scalar-valued QoI in the multifidelity setup. Under a linear model hypothesis, we propose an exploration-exploitation strategy to reconstruct the full distribution of a scalar-valued QoI using samples from a subset of low-fidelity regressors. We derive an informative asymptotic bound for the mean 1-Wasserstein distance between the estimator and the true distribution, and use it to adaptively allocate computational budget for parametric estimation and non-parametric reconstruction. Assuming the linear model is correct, we prove that such a procedure is consistent, and converges to the optimal policy (and hence optimal computational budget allocation) under an upper bound criterion as the budget goes to infinity. A major advantage of our approach compared to several other multifidelity methods is that it is automatic, and its implementation does not require a hierarchical model setup, cross-model information, or a priori known model statistics. Numerical experiments are provided in the end to support our theoretical analysis.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/29/2021

A bandit-learning approach to multifidelity approximation

Multifidelity approximation is an important technique in scientific comp...
10/19/2020

Reweighting samples under covariate shift using a Wasserstein distance criterion

Considering two random variables with different laws to which we only ha...
10/26/2021

Uncertainty quantification in a mechanical submodel driven by a Wasserstein-GAN

The analysis of parametric and non-parametric uncertainties of very larg...
12/19/2021

Wasserstein Generative Learning of Conditional Distribution

Conditional distribution is a fundamental quantity for describing the re...
08/06/2014

Empirical non-parametric estimation of the Fisher Information

The Fisher information matrix (FIM) is a foundational concept in statist...
04/27/2020

Parametric unfolding. Method and restrictions

Parametric unfolding of a true distribution distorted due to finite reso...
04/24/2019

Efficient Simulation Budget Allocation for Subset Selection Using Regression Metamodels

This research considers the ranking and selection (R&S) problem of selec...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.