Hybrid kernel approach to improving the numerical stability of machine learning for parametric equations with Gaussian processes in the noisy and noise-free data assumptions

Esmaeilbeigi, Mohsen; Cheraghi, M.

doi:10.1007/s00366-023-01818-7

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2024

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Cited by 3 publications

References 21 publications

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Novel approaches for hyper-parameter tuning of physics-informed Gaussian processes: application to parametric PDEs

Ezati,

Esmaeilbeigi,

Kamandi

2024

Engineering with Computers

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Novel approaches for hyper-parameter tuning of physics-informed Gaussian processes: application to parametric PDEs

Ezati,

Esmaeilbeigi,

Kamandi

2024

Engineering with Computers

View full text Add to dashboard Cite

Analyzing the effects of various isotropic and anisotropic kernels on critical heat flux prediction using Gaussian process regression

Soleimani,

Esmaeilbeigi,

Cavoretto

et al. 2024

Engineering Applications of Artificial Intelligence

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An active-subspace-enhanced support vector regression model for high-dimensional uncertainty quantification

Zhou,

Gong,

Zhang

2024

Preprint

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The computational costs of surrogate model-assisted uncertainty quantification methods become intractable for high dimensional problems. However, many high-dimensional problems are intrinsically low dimensional, if the output response exhibits some special structure that can be exploited within a low-dimensional subspace, known as the active subspace in the literature. Active subspace extracts linear combinations of all the original inputs, which may obscure the fact that only several inputs are active in the low-dimensional space. Motivated by this fact, this paper proposes a new surrogate modeling method which imposes sparsity in the active subspace to achieve a better performance for dimension reduction. Information given by sparse active subspace is integrated in the kernel structure of the support vector regression model to ensure superior performance for high dimensional problems. We demonstrate the proposed method on several benchmark applications, comprising an analytical function and two engineering applications of increasing dimensionality and complexity.

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Hybrid kernel approach to improving the numerical stability of machine learning for parametric equations with Gaussian processes in the noisy and noise-free data assumptions

Cited by 3 publications

References 21 publications

Novel approaches for hyper-parameter tuning of physics-informed Gaussian processes: application to parametric PDEs

Novel approaches for hyper-parameter tuning of physics-informed Gaussian processes: application to parametric PDEs

Analyzing the effects of various isotropic and anisotropic kernels on critical heat flux prediction using Gaussian process regression

An active-subspace-enhanced support vector regression model for high-dimensional uncertainty quantification

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