Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

Deng, Yixiang

doi:10.4208/cicp.oa-2020-0151

Cited by 9 publications

(2 citation statements)

References 33 publications

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“…Since we use univariate observable in the theoretical framework, we illustrate the same scenario here for consistency and conciseness. Formulations for the multivariate cases can be deduced based on our results and the gradient-enhanced Kriging/Cokriging methods (see, e.g., [29,15,8]).…”

Section: Sketch Of Proofmentioning

confidence: 99%

Augmented Gaussian random field: Theory and computation

Zhang¹,

Yang²,

Tindel³

et al. 2022

DCDS-S

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<p style='text-indent:20px;'>We propose the novel augmented Gaussian random field (AGRF), which is a universal framework incorporating the data of observable and derivatives of any order. Rigorous theory is established. We prove that under certain conditions, the observable and its derivatives of any order are governed by a single Gaussian random field, which is the aforementioned AGRF. As a corollary, the statement "the derivative of a Gaussian process remains a Gaussian process" is validated, since the derivative is represented by a part of the AGRF. Moreover, a computational method corresponding to the universal AGRF framework is constructed. Both noiseless and noisy scenarios are considered. Formulas of the posterior distributions are deduced in a nice closed form. A significant advantage of our computational method is that the universal AGRF framework provides a natural way to incorporate arbitrary order derivatives and deal with missing data. We use four numerical examples to demonstrate the effectiveness of the computational method. The numerical examples are composite function, damped harmonic oscillator, Korteweg-De Vries equation, and Burgers' equation.</p>

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Section: Sketch Of Proofmentioning

confidence: 99%

Augmented Gaussian random field: Theory and computation

Zhang¹,

Yang²,

Tindel³

et al. 2022

DCDS-S

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“…The key benefit is the use of low-fidelity data, along with a limited number of high-fidelity data, reducing the overall cost in acquiring the data to construct the surrogate model. Cokriging [21], the multifidelity version of Kriging, and its variants [22,23], while becoming popular in design and analysis tasks, still suffers from the issues associated with Kriging [18].…”

Section: Introductionmentioning

confidence: 99%

Gradient-enhanced multifidelity neural networks for high-dimensional function approximation

Nagawkar¹,

Leifsson²

2021

Preprint

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In this work, a novel multifidelity machine learning (ML) model, the gradient-enhanced multifidelity neural networks (GEMFNNs), is proposed. This model is a multifidelity version of gradient-enhanced neural networks (GENNs) as it uses both function and gradient information available at multiple levels of fidelity to make function approximations. Its construction is similar to multifidelity neural networks (MFNNs). This model is tested on three analytical function, a one, two, and a 20 variable function. It is also compared to neural networks (NNs), GENNs, and MFNNs, and the number of samples required to reach a global accuracy of 0.99 coefficient of determination (R 2 ) is measured. GEMFNNs required 18, 120, and 600 high-fidelity samples for the one, two, and 20 dimensional cases, respectively, to meet the target accuracy. NNs performed best on the one variable case, requiring only ten samples, while GENNs worked best on the two variable case, requiring 120 samples. GEMFNNs worked best for the 20 variable case, while requiring nearly eight times fewer samples than its nearest competitor, GENNs. For this case, NNs and MFNNs did not reach the target global accuracy even after using 10,000 high-fidelity samples. This work demonstrates the benefits of using gradient as well as multifidelity information in NNs for high-dimensional problems.

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Gradient-Based Physics-Informed Neural Network

Beniwal,

Kumar

2023

Lecture Notes in Networks and Systems

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Multifidelity Data Fusion via Gradient-Enhanced Gaussian Process Regression

Cited by 9 publications

References 33 publications

Augmented Gaussian random field: Theory and computation

Augmented Gaussian random field: Theory and computation

Gradient-enhanced multifidelity neural networks for high-dimensional function approximation

Gradient-Based Physics-Informed Neural Network

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