A bandit-learning approach to multifidelity approximation

Xu, Yiming; Keshavarzzadeh, Vahid; Kirby, Robert; Narayan, Akil

doi:10.48550/arxiv.2103.15342

Cited by 2 publications

(7 citation statements)

References 44 publications

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“…• Simulating ε S is difficult without making further assumptions. We resolve the first two problems by taking a similar bandit-learning approach as in [33], with the loss function articulated in Section 4.2 and 4.3. For the third issue, we will assume that ε S is Gaussian to make the estimation procedure more convenient and efficient.…”

Section: Empirical Cdf Estimator Under Linear Regressionmentioning

confidence: 99%

“…In this section, we introduce an exploration-exploitation strategy following the ideas in [33]. Since neither the best parametric model nor the corresponding coefficients are known, it is necessary to expend some effort (budget) to decide on S before committing to (4.1).…”

Section: Exploration and Exploitationmentioning

confidence: 99%

“…Multilevel estimators are considered universal in the sense that they rely only on correlation, which is used as an input for the estimator construction. A similar approach has recently been developed in [33] which assumes a linear model assumption but does not require a priori knowledge of correlation statistics.…”

mentioning

confidence: 99%

“…Many recent advances on the multifidelity methods centered around the efficient estimation of the expectation of scalar-valued QoIs associated with the high-fidelity model [7,21,10,28,27,33]. Under appropriate correlation/cost conditions and for a fixed budget, the estimators from these methods are significantly more accurate than the classical MC estimator using i.i.d.…”

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confidence: 99%

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Budget-limited distribution learning in multifidelity problems

Narayan

2021

Preprint

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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.

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Section: Empirical Cdf Estimator Under Linear Regressionmentioning

confidence: 99%

Section: Exploration and Exploitationmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Budget-limited distribution learning in multifidelity problems

Narayan

2021

Preprint

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“…variate method. If the latter benefit did not exist, one would require the usage of either an approximate control variate approach [34,68] or other approaches [76,94].…”

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confidence: 99%

Control Variate Polynomial Chaos: Optimal Fusion of Sampling and Surrogates for Multifidelity Uncertainty Quantification

Fujii¹,

Wang²,

Gorodetsky³

2022

Preprint

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We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems such as automotive propulsion systems. Our approach is to build upon ideas from multifidelity uncertainty quantification to leverage the benefits of both sampling and surrogate modeling, while mitigating their downsides. In particular, the surrogate model is selected to exploit problem structure, such as smoothness, and offers a highly correlated information source to the original nonlinear dynamical system. We utilize an intrusive generalized Polynomial Chaos surrogate because it avoids any statistical errors in its construction and provides analytic estimates of output statistics. We then leverage a Monte Carlo-based Control Variate technique to correct the bias caused by the surrogate approximation error. The primary theoretical contribution of this work is the analysis and solution of an estimator design strategy that optimally balances the computational effort needed to adapt a surrogate compared with sampling the original expensive nonlinear system. While previous works have similarly combined surrogates and sampling, to our best knowledge this work is the first to provide rigorous analysis of estimator design. We deploy our approach on multiple examples stemming from the simulation of mechanical automotive propulsion system models. We show that the estimator is able to achieve orders of magnitude reduction in mean squared error of statistics estimation in some cases under comparable costs of purely sampling or purely surrogate approaches.

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A bandit-learning approach to multifidelity approximation

Cited by 2 publications

References 44 publications

Budget-limited distribution learning in multifidelity problems

Budget-limited distribution learning in multifidelity problems

Control Variate Polynomial Chaos: Optimal Fusion of Sampling and Surrogates for Multifidelity Uncertainty Quantification

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