Review of multi-fidelity models

Fernández-Godino, M. Giselle

doi:10.48550/arxiv.1609.07196

Cited by 47 publications

(73 citation statements)

References 84 publications

(113 reference statements)

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“…During the past decades, many multi-fidelity models have been proposed to fulfill this goal. We refer to (Fernández-Godino et al, 2016) and (Peherstorfer et al, 2018) for detailed literature reviews. Among all of the methods, GP based approaches have caught most attention in this area due to their ability to incorporate prior beliefs, interpolate complex functional patterns and quantify uncertainties (Fernández-Godino et al, 2016).…”

Section: Application I: Multi-fidelity Modelingmentioning

confidence: 99%

“…We refer to (Fernández-Godino et al, 2016) and (Peherstorfer et al, 2018) for detailed literature reviews. Among all of the methods, GP based approaches have caught most attention in this area due to their ability to incorporate prior beliefs, interpolate complex functional patterns and quantify uncertainties (Fernández-Godino et al, 2016). The last ability is critical to fuse observations across different fidelities effectively.…”

Section: Application I: Multi-fidelity Modelingmentioning

confidence: 99%

“…(2) the AR method (Kennedy and O'Hagan, 2000). AR is the most classical and widely-used multi-fidelity modeling approach (Laurenceau and Sagaut, 2008;Fernández-Godino et al, 2016;Bailly and Bailly, 2019);…”

Section: Application I: Multi-fidelity Modelingmentioning

confidence: 99%

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Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling

Yue¹,

Kontar²

2021

Preprint

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In this paper, we propose FGPR: a Federated Gaussian process (GP) regression framework that uses an averaging strategy for model aggregation and stochastic gradient descent for local client computations.Notably, the resulting global model excels in personalization as FGPR jointly learns a global GP prior across all clients. The predictive posterior then is obtained by exploiting this prior and conditioning on local data which encodes personalized features from a specific client. Theoretically, we show that FGPR converges to a critical point of the full log-likelihood function, subject to statistical error. Through extensive case studies we show that FGPR excels in a wide range of applications and is a promising approach for privacy-preserving multi-fidelity data modeling.

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Section: Application I: Multi-fidelity Modelingmentioning

confidence: 99%

Section: Application I: Multi-fidelity Modelingmentioning

confidence: 99%

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Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling

Yue¹,

Kontar²

2021

Preprint

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“…In comparison to the conventional single-task learning, multi-task learning (MTL) [1] provides a new learning paradigm to leverage knowledge across re-lated tasks for improving the generalization performance of tasks. The community of multi-task learning has overlaps with other domains like transfer learning [2], multi-view learning [3] and multi-fidelity modeling [4]. Among current MTL paradigms, multi-task Gaussian process (MTGP), the topic of this paper, inherits the non-parametric, Bayesian property of Gaussian process (GP) [5] to have not only the prediction mean but also the associated prediction variance, thus showcasing widespread applications, e.g., multi-task regression and classification, multi-variate time series analysis [6], multi-task Bayesian optimization [7,8], and multi-view learning [9].…”

Section: Introductionmentioning

confidence: 99%

Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization

Liu¹,

Ding²,

Xie³

et al. 2021

Preprint

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Multi-task regression attempts to exploit the task similarity in order to achieve knowledge transfer across related tasks for performance improvement. The application of Gaussian process (GP) in this scenario yields the non-parametric yet informative Bayesian multi-task regression paradigm. Multi-task GP (MTGP) provides not only the prediction mean but also the associated prediction variance to quantify uncertainty, thus gaining popularity in various scenarios. The linear model of coregionalization (LMC) is a well-known MTGP paradigm which exploits the dependency of tasks through linear combination of several independent and diverse GPs. The LMC however suffers from high model complexity and limited model capability when handling complicated multi-task cases. To this end, we develop the neural embedding of coregionalization that transforms the latent GPs into a high-dimensional latent space to induce rich yet diverse behaviors. Furthermore, we use advanced variational inference as well as sparse approximation to devise a tight and compact evidence lower bound (ELBO) for higher quality of scalable model inference. Extensive numerical experiments have been conducted to verify the higher prediction quality and better generalization of our model, named NSVLMC, on various real-world multi-task datasets and the cross-fluid modeling of unsteady fluidized bed.

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“…Recently, there has been a surging interest in developing efficient uncertainty quantification algorithms by leveraging the strengths of multiple models where costs and fidelity, to be intended as the capacity of correctly describing the problem under consideration, vary. This approach is known in the literature as the multi-fidelity method [27,79,80].…”

Section: Introductionmentioning

confidence: 99%

Multi-fidelity methods for uncertainty propagation in kinetic equations

Dimarco¹,

Liu²,

Pareschi³

et al. 2021

Preprint

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The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand, precisely because of the curse of dimensionality, the construction of simplified models capable of providing approximate solutions at a computationally reduced cost has always represented one of the main research strands in the field of kinetic equations. Approximations based on suitable closures of the moment equations or on simplified collisional models have been studied by many authors. In the context of uncertainty quantification, it is therefore natural to take advantage of such models in a multi-fidelity setting where the original kinetic equation represents the high-fidelity model, and the simplified models define the low-fidelity surrogate models. The scope of this article is to survey some recent results about multi-fidelity methods for kinetic equations that are able to accelerate the solution of the uncertainty quantification process by combining high-fidelity and low-fidelity model evaluations with particular attention to the case of compressible and incompressible hydrodynamic limits. We will focus essentially on two classes of strategies: multifidelity control variates methods and bi-fidelity stochastic collocation methods. The various approaches considered are analyzed in light of the different surrogate models used and the different numerical techniques adopted. Given the relevance of the specific choice of the surrogate model, an application-oriented approach has been chosen in the presentation.

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Review of multi-fidelity models

Cited by 47 publications

References 84 publications

Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling

Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modeling

Scalable Multi-Task Gaussian Processes with Neural Embedding of Coregionalization

Multi-fidelity methods for uncertainty propagation in kinetic equations

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