Parametric reduced order models based on a Riemannian barycentric interpolation

Oulghelou, Mourad; Allery, Cyrille

doi:10.1002/nme.6805

Cited by 8 publications

(4 citation statements)

References 60 publications

(121 reference statements)

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“…If some knowledge exists (reduced basis or data manifold) completing or augmenting data can be performed easily. Interpolating data in complex nonlinear manifolds remains to be quite a technical issue [99]. Data can be augmented by generating extra data by using symmetry considerations or other kind of physics-based knowledge.…”

Section: Data Augmentation and Completionmentioning

confidence: 99%

Empowering engineering with data, machine learning and artificial intelligence: a short introductive review

Chinesta

2022

Adv. Model. and Simul. in Eng. Sci.

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Simulation-based engineering has been a major protagonist of the technology of the last century. However, models based on well established physics fail sometimes to describe the observed reality. They often exhibit noticeable differences between physics-based model predictions and measurements. This difference is due to several reasons: practical (uncertainty and variability of the parameters involved in the models) and epistemic (the models themselves are in many cases a crude approximation of a rich reality). On the other side, approaching the reality from experimental data represents a valuable approach because of its generality. However, this approach embraces many difficulties: model and experimental variability; the need of a large number of measurements to accurately represent rich solutions (extremely nonlinear or fluctuating), the associate cost and technical difficulties to perform them; and finally, the difficulty to explain and certify, both constituting key aspects in most engineering applications. This work overviews some of the most remarkable progress in the field in recent years.

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Section: Data Augmentation and Completionmentioning

confidence: 99%

Empowering engineering with data, machine learning and artificial intelligence: a short introductive review

Chinesta

2022

Adv. Model. and Simul. in Eng. Sci.

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“…More details can be founded in [33]. Note that some alternative approaches exist as presented in [29,30,32].…”

Section: Reduced Basis Interpolationmentioning

confidence: 99%

“…Direct standard approaches such as Lagrange interpolation are often ineffective for basis interpolation. That is why, in the context of reduced-order models in fluid mechanics, a strategy based on interpolation on a tangent space of Grassmann manifold has been recently developed to compute basis functions associated with new parameters [29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Assessing the wall energy efficiency design under climate change using POD reduced order model

Berger,

Allery,

Machard

2022

Preprint

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Within the environmental context, numerical modeling is a promising approach to assess the energy efficiency of building. Resilient buildings need to be designed, capable of adapting to future extreme heat. Simulations are required assuming a one-dimensional heat transfer problem through walls and a simulation horizon of several years (nearly 30). The computational cost associated with such modeling is quite significant and model reduction methods are worth investigating. The objective is to propose a reliable reduced-order model for such long-term simulations. For this, an alternative model reduction approach is investigated, assuming a known Proper Orthogonal Decomposition reduced basis for time, and not for space as usually. The model enables computing parametric solutions using basis interpolation on the tangent space of the Grassmann manifold. Three study cases are considered to verify the efficiency of the reduced-order model. Results highlight that the model has a satisfying accuracy of 10 −3 compared to reference solutions. The last case study focuses on the wall energy efficiency design under climate change according to a four-dimensional parameter space. The latter is composed of the load material emissivity, heat capacity, thermal conductivity and thickness insulation layer. Simulations are carried over 30 years considering climate change. The solution minimizing the wall work rate is determined with a computational ratio of 0.1% compared to standard approaches.

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“…Both explicit and implementation-friendly formulas are available to compute the so-called logarithmic and exponential maps allowing to construct geodesic paths between points of the Grassmann manifold. Several variants of the ITSGM method have been recently proposed [19][20][21] and machine learning algorithms have also been developed to assist nonlinear projection-based reduced order models. 22,23 However, a limitation of the ITSGM method is that it does not exploit the information of the natural ordering of the bases when constructed through POD.…”

Section: Introductionmentioning

confidence: 99%

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

Goutaudier

Nobile

Schiffmann

2023

Numerical Meth Engineering

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SummaryThe proper orthogonal decomposition (POD) is successfully employed in a variety of projection‐based methods for parametric model order reduction (pMOR) of large dynamical systems. It extracts the most energetic modes describing the dynamics of a system from time snapshots of the solution. In practice, these snapshots are computed at user‐defined parameters of the system with a high fidelity model. Then either all the snapshots are concatenated to extract a global POD basis, or a different POD basis is extracted for each parameter value. In the latter case, for unseen target parameters, the POD bases need to be adapted with a dedicated technique. An established method addressing this task is the interpolation on the tangent space to the Grassmann manifold (ITSGM). It interpolates the linear subspaces spanned by the known POD bases, discarding by construction the knowledge on the modes ordering by energy levels. In this paper, we formalize an ordered reduced basis interpolation (ORBI) technique which preserves such ordering. This approach improves the adaptation accuracy of the resulting POD basis as more information is taken into account in the construction of the interpolation operator. Numerical investigations are conducted on the parametric reduced order model of a dynamical system representing a small‐scale gas‐bearings supported rotor. Results show that the proposed method is more accurate than the ITSGM method at a similar computation cost. Trained at only three points of the parameters space, the developed hyper reduced order model (h‐ROM) performs to faster simulations with satisfactory accuracy, even far from the training points.

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Parametric reduced order models based on a Riemannian barycentric interpolation

Cited by 8 publications

References 60 publications

Empowering engineering with data, machine learning and artificial intelligence: a short introductive review

Empowering engineering with data, machine learning and artificial intelligence: a short introductive review

Assessing the wall energy efficiency design under climate change using POD reduced order model

A new method to interpolate POD reduced bases–Application to the parametric model order reduction of a gas bearings supported rotor

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