Function-on-Function Kriging, With Applications to Three-Dimensional Printing of Aortic Tissues

Chen, Jialei; Mak, Simon; Joseph, V. Roshan; Zhang, Chuck

doi:10.1080/00401706.2020.1801255

Cited by 26 publications

(11 citation statements)

References 36 publications

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“…Gaussian processes (GPs) [42] are a popular choice for emulation of computer simulations [43] and have been exploited in diverse applications from rocket design [44] to 3D printing [45]. GPs are an essential tool for Bayesian parameter estimation of complex simulation models, where they are used to efficiently interpolate between full model runs taken on a sparse set of design points in a high-dimensional parameter space, largely due to their ability to efficiently provide a probabilistic quantification of the incurred interpolation uncertainty.…”

Section: B Gaussian Process Emulationmentioning

confidence: 99%

Efficient emulation of relativistic heavy ion collisions with transfer learning

Liyanage,

Ji,

Everett

et al. 2022

Preprint

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Measurements from the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) can be used to study the properties of quark-gluon plasma. Systematic constraints on these properties must combine measurements from different collision systems and methodically account for experimental and theoretical uncertainties. Such studies require a vast number of costly numerical simulations. While computationally inexpensive surrogate models ("emulators") can be used to efficiently approximate the predictions of heavy ion simulations across a broad range of model parameters, training a reliable emulator remains a computationally expensive task. We use transfer learning to map the parameter dependencies of one model emulator onto another, leveraging similarities between different simulations of heavy ion collisions. By limiting the need for large numbers of simulations to only one of the emulators, this technique reduces the numerical cost of comprehensive uncertainty quantification when studying multiple collision systems and exploring different models.

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Section: B Gaussian Process Emulationmentioning

confidence: 99%

Efficient emulation of relativistic heavy ion collisions with transfer learning

Liyanage,

Ji,

Everett

et al. 2022

Preprint

Self Cite

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“…Tan (2019) introduces a functional-input GP model for finite element models. Chen et al (2021) propose a spectral-distance correlation function and apply it to 3D printing. To the best of our knowledge, most of the existing methods are restrictive to specific applications, while a systematical study is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Functional-Input Gaussian Processes with Applications to Inverse Scattering Problems

Sung¹,

Wang²,

Cakoni³

et al. 2022

Preprint

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Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are scarce.Motivated by an inverse scattering problem in which functional inputs representing the support and material properties of the scatterer are involved in the partial differential equations, a new class of kernel functions for functional inputs is introduced for GPs.Based on the proposed GP models, the asymptotic convergence properties of the resulting mean squared prediction errors are derived and the finite sample performance is demonstrated by numerical examples. In the application to inverse scattering, a surrogate model is constructed with functional inputs, which is crucial to recover the reflective index of an inhomogeneous isotropic scattering region of interest for a given far-field pattern.

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“…Therefore, stochastic computer simulations can be viewed as those having distribution inputs. There are a few papers on the design and modeling issues of computer experiments with function inputs (Muehlenstaedt, Fruth, and Roustant 2017;Tan 2019;Betancourt, Bachoc, Kleina et al 2020;Chen, Mak, Joseph et al 2021), but very limited on distribution inputs. Bachoc, Gamboa, Loubes et al (2018) constructed the Wasserstein distance-based Gaussian process model with a onedimensional distribution input.…”

Section: Introductionmentioning

confidence: 99%

Design and analysis of computer experiments with both numeral and distribution inputs

Li¹,

Chen²,

Xiong³

2022

Preprint

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Nowadays stochastic computer simulations with both numeral and distribution inputs are widely used to mimic complex systems which contain a great deal of uncertainty.This paper studies the design and analysis issues of such computer experiments. First, we provide preliminary results concerning the Wasserstein distance in probability measure spaces. To handle the product space of the Euclidean space and the probability measure space, we prove that, through the mapping from a point in the Euclidean space to the mass probability measure at this point, the Euclidean space can be isomorphic to the subset of the probability measure space, which consists of all the mass measures, with respect to the Wasserstein distance. Therefore, the product space can be viewed as a product probability measure space. We derive formulas of the Wasserstein distance between two components of this product probability measure space. Second, we use the above results to construct Wasserstein distance-based space-filling criteria in the product space of the Euclidean space and the probability measure space. A class of optimal Latin hypercube-type designs in this product space are proposed. Third, we present a Wasserstein distance-based Gaussian process model to analyze data from computer experiments with both numeral and distribution inputs. Numerical examples and real applications to a metro simulation are presented to show the effectiveness of our methods.

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Function-on-Function Kriging, With Applications to Three-Dimensional Printing of Aortic Tissues

Cited by 26 publications

References 36 publications

Efficient emulation of relativistic heavy ion collisions with transfer learning

Efficient emulation of relativistic heavy ion collisions with transfer learning

Functional-Input Gaussian Processes with Applications to Inverse Scattering Problems

Design and analysis of computer experiments with both numeral and distribution inputs

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