Input Mapping for Model Calibration with Application to Wing Aerodynamics

Tao, Siyu; Apley, Daniel W.; Chen, Wei; Garbo, Andrea; Pate, D.; German, Brian

doi:10.2514/1.j057711

Cited by 23 publications

(10 citation statements)

References 45 publications

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“…for modeling these correlated tasks simultaneously and predicting the outputs y * = {y t * } T t=1 at T arbitrary test points x * = {x t * } T t=1 . Besides, we further assume that a prior domain mapping (also known as nominal mapping [37]) g t 0 (.) (1 ≤ t ≤ T ) is available based on practical expert opinion.…”

Section: Heterogeneous Multi-task Gaussian Processmentioning

confidence: 99%

“…Except for the Bayesian calibration proposed in this paper, there are also some other calibrations in literature to tackle multi-task/multi-fidelity modeling in heterogeneous input domains. Inspired by the idea of space mapping in the community of multi-fidelity modeling and optimization [46]- [48], the input mapping calibration (IMC) proposed in [37] attempts to find a better linear mapping than the prior linear domain mapping. Specifically, given a high-fidelity task with N h data D h = {X h , y h } and a related low-fidelity task with N l data D l = {X l , y l }, the IMC approach takes a linear transformation…”

Section: Differences To Other Calibrationsmentioning

confidence: 99%

“…When there exists prior knowledge extracted from expert opinion, for example, the prior domain mappings, we could directly incorporate the inductive bias to achieve input alignment and thereby use the conventional MTGP on the transformed domain, see for example [36]. More flexibly, in order to achieve model calibration, Tao et al [37] proposed to learn a linear embedding to align two tasks with different input domains. Furthermore, given the aligned inputs known at training points, Hebbal et al [38] decided to introduce another GP to model the input transformation.…”

Section: Introductionmentioning

confidence: 99%

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Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains

Liu¹,

Wu²,

Ong³

et al. 2022

Preprint

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Multi-task Gaussian process (MTGP) is a wellknown non-parametric Bayesian model for learning correlated tasks effectively by transferring knowledge across tasks. But current MTGP models are usually limited to the multi-task scenario defined in the same input domain, leaving no space for tackling the practical heterogeneous case, i.e., the features of input domains vary over tasks. To this end, this paper presents a novel heterogeneous stochastic variational linear model of coregionalization (HSVLMC) model for simultaneously learning the tasks with varied input domains. Particularly, we develop the stochastic variational framework with a Bayesian calibration method that (i) takes into account the effect of dimensionality reduction raised by domain mapping in order to achieve effective input alignment; and (ii) employs a residual modeling strategy to leverage the inductive bias brought by prior domain mappings for better model inference. Finally, the superiority of the proposed model against existing LMC models has been extensively verified on diverse heterogeneous multi-task cases.

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Section: Heterogeneous Multi-task Gaussian Processmentioning

confidence: 99%

Section: Differences To Other Calibrationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Learning Multi-Task Gaussian Process Over Heterogeneous Input Domains

Liu¹,

Wu²,

Ong³

et al. 2022

Preprint

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“…These local approaches are suited for the optimization task but may not be adapted for modeling on the entire input space since the mapping is performed around the optimum. A dedicated modeling approach has been developed [26] which consists of an input mapping calibration (IMC) for the entire definition domain of the input space. However, the input mapping calibration is based on the concept that the low-fidelity model has similar trend as the high-fidelity one.…”

Section: X D ]mentioning

confidence: 99%

“…The Input Mapping Calibration (IMC) [26] is an approach that seeks to obtain a potentially better mapping than the nominal mapping. As the space mapping approach, it consists in finding a parametric mapping g β (•).…”

Section: Variable Input Space Parametrizationmentioning

confidence: 99%

Multi-fidelity modeling with different input domain definitions using Deep Gaussian Processes

Hebbal¹,

Brevault²,

Balesdent³

et al. 2020

Preprint

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Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian Processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model increases the expressive power compared to GPs by considering non-linear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low-fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, Deep Gaussian Processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multi-fidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems.

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