A local approach to parameter space reduction for regression and classification tasks

Romor, Francesco; Tezzele, Marco; Rozza, Gianluigi

doi:10.48550/arxiv.2107.10867

Cited by 4 publications

(6 citation statements)

References 29 publications

(50 reference statements)

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“…Future works will focus on improving the accuracy of constraints evaluations, for example with a multi-fidelity approximation of the scalar output and not only for the reconstruction of the entire field. 23 Another possibility is the exploitation of local information with local active subspaces 64 or nonlinear techniques, based on kernels 65 or level-sets, 66,67 to further improve the regression performance of the low-fidelity model. Other physical constraints can also be considered such as the position of the center of mass.…”

Section: Discussionmentioning

confidence: 99%

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls

Tezzele

Fabris

Sidari

et al. 2022

Numerical Meth Engineering

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Nowadays, the shipbuilding industry is facing a radical change toward solutions with a smaller environmental impact. This can be achieved with low emissions engines, optimized shape designs with lower wave resistance and noise generation, and by reducing the metal raw materials used during the manufacturing. This work focuses on the last aspect by presenting a complete structural optimization pipeline for modern passenger ship hulls which exploits advanced model order reduction techniques to reduce the dimensionality of both input parameters and outputs of interest. We introduce a novel approach which incorporates parameter space reduction through active subspaces into the proper orthogonal decomposition with interpolation method. This is done in a multi‐fidelity setting. We test the whole framework on a simplified model of a midship section and on the full model of a passenger ship, controlled by 20 and 16 parameters, respectively. We present a comprehensive error analysis and show the capabilities and usefulness of the methods especially during the preliminary design phase, finding new unconsidered designs while handling high dimensional parameterizations.

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Section: Discussionmentioning

confidence: 99%

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls

Tezzele

Fabris

Sidari

et al. 2022

Numerical Meth Engineering

Self Cite

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“…Further investigations could involve the use of different fidelities based on extensions of AS, such as kernel active subspaces [40], or local active subspaces [41]. This could also greatly improve datadriven non-intrusive reduced order methods [44,45,46] through modal coefficients reconstruction and prediction for parametric problems [52].…”

Section: Conclusion and Future Perspectivesmentioning

confidence: 99%

“…Reduction in parameter space through AS has been proven successful in a diverse range of applications such as: shape optimization [29,15,12,10], car aerodynamics studies [33], hydrologic models [19], naval and nautical engineering [51,31], coupled with intrusive reduced order methods in cardiovascular studies [48], in CFD problems in a data-driven setting [11,50]. A kernel-based extension of AS for both scalar and vectorial functions can be found in [40], while for a new local approach to parameter space reduction see [41].…”

Section: Introductionmentioning

confidence: 99%

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

Romor¹,

Tezzele²,

Mrosek³

et al. 2021

Preprint

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Multi-fidelity models are of great importance due to their capability of fusing information coming from different simulations and sensors. Gaussian processes are employed for nonparametric regression in a Bayesian setting. They generalize linear regression embedding the inputs in a latent manifold inside an infinite-dimensional reproducing kernel Hilbert space. We can augment the inputs with the observations of low-fidelity models in order to learn a more expressive latent manifold and thus increment the model's accuracy. This can be realized recursively with a chain of Gaussian processes with incrementally higher fidelity. We would like to extend these multi-fidelity model realizations to case studies affected by a high-dimensional input space but with low intrinsic dimensionality. In these cases physical supported or purely numerical low-order models are still affected by the curse of dimensionality when queried for responses. When the model's gradient information is provided, the existence of an active subspace, or a nonlinear transformation of the input parameter space, can be exploited to design low-fidelity response surfaces and thus enable Gaussian process multi-fidelity regression, without the need to perform new simulations. This is particularly useful in the case of data scarcity. In this work we present a new multi-fidelity approach involving active subspaces and nonlinear level-set learning method. We test the proposed numerical method on two different high-dimensional benchmarks, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of GP response surfaces.

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“…Successful applications of parameter space reduction with active subspaces can be found in many engineering fields: naval and nautical problems, 18 shape optimization, [19][20][21][22] car aerodynamics studies, 23 inverse problems, 24,25 cardiovascular studies coupled with intrusive model order reduction, 26 for the study of high-dimensional parametric PDEs, 27 and in CFD problems in a data-driven setting, 28,29 among others. New extensions of AS have also been developed in the recent years such as AS for multivariate vector-valued functions, 30 a kernel approach for AS for scalar and vectorial functions, 31 a localization extension for both regression and classification tasks, 32 and sequential learning of active subspaces. 33 The multi-fidelity setting has been used to find an active subspace given different fidelity models.…”

Section: Introductionmentioning

confidence: 99%

Multi‐fidelity data fusion through parameter space reduction with applications to automotive engineering

Romor,

Tezzele,

Mrosek

et al. 2023

Numerical Meth Engineering

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Multi‐fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high‐dimensional scalar functions with low intrinsic dimensionality. By introducing a low dimensional bias we can fight the curse of dimensionality affecting these quantities of interest, especially for many‐query applications. We seek a gradient‐based reduction of the parameter space through linear active subspaces or a nonlinear transformation of the input space. Then we build a low‐fidelity response surface based on such reduction, thus enabling nonlinear autoregressive multi‐fidelity Gaussian process regression without the need of running new simulations with simplified physical models. This has a great potential in the data scarcity regime affecting many engineering applications. In this work we present a new multi‐fidelity approach that involves active subspaces and the nonlinear level‐set learning method, starting from the preliminary analysis previously conducted (Romor F, Tezzele M, Rozza G. Proceedings in Applied Mathematics & Mechanics. Wiley Online Library; 2021). The proposed framework is tested on two high‐dimensional benchmark functions, and on a more complex car aerodynamics problem. We show how a low intrinsic dimensionality bias can increase the accuracy of Gaussian process response surfaces.

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A local approach to parameter space reduction for regression and classification tasks

Cited by 4 publications

References 29 publications

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls

Multi-fidelity data fusion through parameter space reduction with applications to automotive engineering

Multi‐fidelity data fusion through parameter space reduction with applications to automotive engineering

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