Model reduction from partial observations

Herzet, Cédric; Héas, Patrick; Drémeau, Angélique

doi:10.1002/nme.5623

Cited by 3 publications

(10 citation statements)

References 23 publications

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“…These properties are discussed and empirically assessed in the context of our numerical simulations. The present work complements and generalises the works [24,18,10,11,29] in two main respects: it proposes a methodology extending these works to the case of dynamical systems; it provides a Bayesian framework generalising any standard ROM construction to the setup where trajectories to be reduced are not fully known.…”

Section: Introductionmentioning

confidence: 81%

“…F , one may expect the minimisers of (19) to be good approximations of the solutions of (18). Moreover, the numerical optimisation (19) may be far easier than the one of the initial optimisation problem (18). We will provide two instances of such scenarios in Section 4.…”

Section: Practical Identification Of a Minimisermentioning

confidence: 99%

“…In [24], the authors suggest to iteratively enrich the ROM by using point-wise estimates obtained from linear observations and a surrogate model. In [18], the authors propose to refine this approach by including the uncertainty inherent to the point-wise estimates in the reduction process. Stable recovery guarantees are also provided from a worst-case perspective.…”

Section: Introductionmentioning

confidence: 99%

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Reduced Modeling of Unknown Trajectories

Héas

Herzet

2017

Arch Computat Methods Eng

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This paper deals with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system's trajectories is unknown but the following two sources of information are available: \textit{(i)} some "rough" prior knowledge on the system's realisations; \textit{(ii)} a set of "incomplete" observations of the system's trajectories. We propose a Bayesian methodological framework to build reduced-order models (ROMs) by exploiting these two sources of information. We emphasise that complementing the prior knowledge with the collected data provably enhances the knowledge of the distribution of the system's trajectories. We then propose an implementation of the proposed methodology based on Monte-Carlo methods. In this context, we show that standard ROM learning techniques, such e.g. Proper Orthogonal Decomposition or Dynamic Mode Decomposition, can be revisited and recast within the probabilistic framework considered in this paper.~We illustrate the performance of the proposed approach by numerical results obtained for a standard geophysical model

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Section: Introductionmentioning

confidence: 81%

Section: Practical Identification Of a Minimisermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reduced Modeling of Unknown Trajectories

Héas

Herzet

2017

Arch Computat Methods Eng

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“…In recent years, reduced-order modeling techniques have proven to be powerful tools for solving various problems. Important efforts have been dedicated to developing reduced-order models that can provide accurate predictions while dramatically reducing computational time, for a wide range of applications, covering different fields such as fluid mechanics, heat transfer, structural dynamics among others [3,21,26]. Examples with finite-element and finite-volume applications can be found in [49] and [45], respectively.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear diffusive problems in buildings by means of a Spectral reduced-order model

Gasparin

Berger

Dutykh

et al. 2018

Journal of Building Performance Simulation

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This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the solution. The method is compared with both classical Euler implicit and Crank-Nicolson schemes, considered as large original models. Their performance -in terms of accuracy, complexity reduction and CPU time reduction -are discussed for linear and nonlinear cases of moisture diffusive transfer through single and multi-layered one-dimensional domains, considering highly moisture-dependent properties. Results show that the Spectral reducedorder model approach enables to simulate accurately the field of interest. Furthermore, numerical gains become particularly interesting for nonlinear cases since the proposed method can drastically reduce the computer run time, by a factor of 100 , when compared to the traditional Crank-Nicolson scheme for one-dimensional applications.

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“…In recent years, reduced-order modeling techniques have proven to be powerful tools for solving various problems. Important efforts have been dedicated to developing reduced-order models that can provide accurate predictions while dramatically reducing computational time, for a wide range of applications, covering different fields such as fluid mechanics, heat transfer, structural dynamics, among others [2,24,28]. Reduced-order models -such as POD (Proper Orthogonal Decomposition), MBR (Modal Basis Reduction) and PGD (Proper Generalized Decomposition) -have shown a relevant reduction of the computational cost and have been successfully employed by the building physics community [3].…”

Section: Introductionmentioning

confidence: 99%

A spectral method for solving heat and moisture transfer through consolidated porous media

Gasparin

Dutykh

Mendes

2018

Numerical Meth Engineering

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This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem is discretized in time and space domains (method of lines) to obtain a large system of coupled ordinary differential equations (ODEs), which is computationally expensive. To avoid such a cost, this paper proposes a reduced-order method that is faster and accurate, using a much smaller system of ODEs. To demonstrate the benefits of this approach, three case studies are presented.The first one considers nonlinear heat and moisture transfer through one material layer. The second case, ie, highly nonlinear, imposes a high moisture content gradient, simulating a rain-like condition, over a two-layered domain, whereas the last one compares the numerical prediction against experimental data for validation purposes. Results show how the nonlinearities and the interface between materials are easily and naturally treated with the spectral reduced-order method. Concerning the reliability part, predictions show a good agreement with experimental results, which confirm robustness, calculation efficiency, and high accuracy of the proposed approach for predicting the coupled heat and moisture transfer through porous materials. KEYWORDSChebyshev polynomials, heat and moisture transfer, numerical simulation, reduced-order modeling, spectral methods, Tau-Galerkin method Int

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Model reduction from partial observations

Cited by 3 publications

References 23 publications

Reduced Modeling of Unknown Trajectories

Reduced Modeling of Unknown Trajectories

Solving nonlinear diffusive problems in buildings by means of a Spectral reduced-order model

A spectral method for solving heat and moisture transfer through consolidated porous media

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