Reduced-order modeling: new approaches for computational physics

Lucia, David J.; Beran, Philip S.; Silva, Walter A.

doi:10.1016/j.paerosci.2003.12.001

Cited by 720 publications

(376 citation statements)

References 112 publications

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“…The application of emulators has emerged in many different fields of science and thus the theoretical background is relatively well developed (e.g. O'Hagan, 2000, 2001;Phillips, 2003;Lucia et al, 2004;van der Merwe et al, 2007;Bliznyuk et al, 2008;Conti et al, 2009;Liu and West, 2009;Castelletti et al, 2012). Two distinct approaches to emulation exist, which we refer to as dynamic emulation and statistical emulation.…”

Section: Emulator Approachesmentioning

confidence: 99%

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

et al. 2017

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Abstract. To describe the underlying processes involved in oceanic plankton dynamics is crucial for the determination of energy and mass flux through an ecosystem and for the estimation of biogeochemical element cycling. Many planktonic ecosystem models were developed to resolve major processes so that flux estimates can be derived from numerical simulations. These results depend on the type and number of parameterizations incorporated as model equations. Furthermore, the values assigned to respective parameters specify a model's solution. Representative model results are those that can explain data; therefore, data assimilation methods are utilized to yield optimal estimates of parameter values while fitting model results to match data. Central difficulties are (1) planktonic ecosystem models are imperfect and (2) data are often too sparse to constrain all model parameters. In this review we explore how problems in parameter identification are approached in marine planktonic ecosystem modelling.We provide background information about model uncertainties and estimation methods, and how these are considered for assessing misfits between observations and model results. We explain differences in evaluating uncertainties in parameter estimation, thereby also discussing issues of parameter identifiability. Aspects of model complexity are addressed and we describe how results from cross-validation studies provide much insight in this respect. Moreover, approaches are discussed that consider time-and spacedependent parameter values. We further discuss the use of dynamical/statistical emulator approaches, and we elucidate issues of parameter identification in global biogeochemical models. Our review discloses many facets of parameter identification, as we found many commonalities between the objectives of different approaches, but scientific insight differed between studies. To learn more from results of planktonic ecosystem models we recommend finding a good balance in the level of sophistication between mechanistic modelling and statistical data assimilation treatment for parameter estimation.

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Section: Emulator Approachesmentioning

confidence: 99%

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

et al. 2017

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“…These are frequent in e.g. aircraft industry [14], where design and certification based on simulations usually involve many parameters and thus require to perform thousands of runs of complete aircraft configurations.…”

Section: Introductionmentioning

confidence: 99%

Reduced order models based on local POD plus Galerkin projection

Rapún

Vega

2010

Journal of Computational Physics

106

101

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A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained vía POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estímate of the error of the Galerkin approximation. Several improvements are introduced that reduce computational complexity and deal with: (a) updating the POD manifold (instead of calculating it) at the end of each Galerkin interval; (b) using only a limited number of mesh points to calcúlate the right hand side of the Galerkin system; and (c) introducing a second error estímate based on a second Galerkin system to account for situations in which qualitative changes in the dynamics occur during the application of the Galerkin system. The resulting method, called local POD plus Galerkin projection method, turns out to be both robust and efficient. For illustration, we consider a time-dependent Fisher-like equation and a complex Ginzburg-Landau equation.

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“…For a comparison between POD and HB we refer to [82]. We remark that the HB method is very efficient in reducing the temporal complexity, as typically only N < 10 terms are needed to accurately represent the solution.…”

Section: πIkmentioning

confidence: 99%

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

Lassila

Manzoni

Quarteroni

et al. 2014

Reduced Order Methods for Modeling and Computational Reduction

164

179

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This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities -which are mainly related either to nonlinear convection terms and/or some geometric variability -that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and -in the unsteady case -long-time stability of the reduced model. Moreover, we provide an extensive list of literature references.

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Reduced-order modeling: new approaches for computational physics

Cited by 720 publications

References 112 publications

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

Reduced order models based on local POD plus Galerkin projection

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

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