Design optimization using hyper-reduced-order models

Amsallem, David; Zahr, Matthew J.; Choi, Youngsoo; Farhat, Charbel

doi:10.1007/s00158-014-1183-y

Cited by 132 publications

(65 citation statements)

References 40 publications

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“…Whilst the model typically has a horizontal resolution of 2.8 • × 2.8 • , with 60 vertical levels up to 0.1 hPa, the high computational burden of the variational framework requires that a coarser resolution of 5.6 • × 5.6 • , with 31 vertical levels up to 10 hPa is used whilst testing the inverse model. Previous studies have attempted to alleviate the computational burden of the data assimilation or inversion process using reduced versions of non-linear models (Amsallem et al, 2013;Stefanescu et al, 2014), or with incremental optimisation using low-resolution linearised models (Courtier et al, 1994). Further study is necessary to explore the potential for these methods with the TOMCAT model.…”

Section: The Tomcat Ctmmentioning

confidence: 99%

Development of a variational flux inversion system (INVICAT v1.0) using the TOMCAT chemical transport model

et al. 2014

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Abstract. We present a new variational inverse transport model, named INVICAT (v1.0), which is based on the global chemical transport model TOMCAT, and a new corresponding adjoint transport model, ATOMCAT. The adjoint model is constructed through manually derived discrete adjoint algorithms, and includes subroutines governing advection, convection and boundary layer mixing, all of which are linear in the TOMCAT model. We present extensive testing of the adjoint and inverse models, and also thoroughly assess the accuracy of the TOMCAT forward model's representation of atmospheric transport through comparison with observations of the atmospheric trace gas SF 6 . The forward model is shown to perform well in comparison with these observations, capturing the latitudinal gradient and seasonal cycle of SF 6 to within acceptable tolerances. The adjoint model is shown, through numerical identity tests and novel transport reciprocity tests, to be extremely accurate in comparison with the forward model, with no error shown at the level of accuracy possible with our machines. The potential for the variational system as a tool for inverse modelling is investigated through an idealised test using simulated observations, and the system demonstrates an ability to retrieve known fluxes from a perturbed state accurately. Using basic off-line chemistry schemes, the inverse model is ready and available to perform inversions of trace gases with relatively simple chemical interactions, including CH 4 , CO 2 and CO.

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Section: The Tomcat Ctmmentioning

confidence: 99%

Development of a variational flux inversion system (INVICAT v1.0) using the TOMCAT chemical transport model

et al. 2014

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“…Nevertheless, for optimization with largescale nonlinear computational models, the introduction of parametric reduced-order models are often necessary (see for instance [3,24]). Concerning the algorithms for solving optimization problems under uncertainties, many methods have been proposed in the literature such as the gradientbased learning that is adapted to convex problems [48,89], the global search algorithms such as the stochastic algorithms, the genetic algorithm, and the evolutionary algorithms [14,46].…”

Section: Algorithms For Solving Optimization Problems Under Uncertainmentioning

confidence: 99%

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

Soize

2017

Comput Mech

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This paper deals with the optimal design of a titanium mesoscale implant in a cortical bone for which the apparent elasticity tensor is modeled by a non-Gaussian random field at mesoscale, which has been experimentally identified. The external applied forces are also random. The design parameters are geometrical dimensions related to the geometry of the implant. The stochastic elastostatic boundary value problem is discretized by the finite element method. The objective function and the constraints are related to normal, shear, and von Mises stresses inside the cortical bone. The constrained nonconvex optimization problem in presence of uncertainties is solved by using a probabilistic learning algorithm that allows for considerably reducing the numerical cost with respect to the classical approaches.

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“…To achieve this, we will consider hyper-reduction [2,6]. The hyper-reduction approaches we consider rely on the same paradigm of expansion through a basis as we use for the solution state itself.…”

Section: Hyper-reduction For Galerkin Projectionmentioning

confidence: 99%

“…Due to the non-polynomial nonlinearities that arise in standard roughness parameterizations and stabilized FEM approximations, further reduction of the nonlinearities in the SWE are required to break dependence on the fine-scale dimension [2]. We evaluate two types of socalled hyper-reduction for our reduced models: Discrete Empirical Interpolation (DEIM) [5,13] and gappy POD [14,23].…”

Section: Introductionmentioning

confidence: 99%

Projection-Based Model Reduction for Finite Element Approximation of Shallow Water Flows

Farthing¹,

Lozovskiy²,

Kees³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The shallow water equations (SWE) are used to model a wide range of environmental flows from dam breaks and riverine hydrodynamics to hurricane storm surge and atmospheric processes. Despite significant gains in numerical model efficiency stemming from algorithmic and hardware improvements, accurate shallow water modeling can still be very computationally intensive. The resulting computational expense remains as a barrier to the inclusion of fully resolved two-dimensional shallow water models in many applications, particularly when the analysis involves optimal design, parameter inversion, risk assessment, and/or uncertainty quantification.Here, we consider projection-based model reduction as a way to alleviate the computational burden associated with high-fidelity shallow-water approximations in ensemble forecast and sampling methodologies. In order to develop a robust approach that can resolve advectiondominated problems with shocks as well as more smoothly varying riverine and estuarine flows, we consider techniques using both Galerkin and Petrov-Galerkin projection on global bases provided by Proper Orthogonal Decomposition (POD). To achieve realistic speedup, we consider alternative methods for the reduction of the non-polynomial nonlinearities that arise in typical finite element formulations. We evaluate the schemes' performance by considering their accuracy and robustness for test problems in one and two space dimensions.

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Design optimization using hyper-reduced-order models

Cited by 132 publications

References 40 publications

Development of a variational flux inversion system (INVICAT v1.0) using the TOMCAT chemical transport model

Development of a variational flux inversion system (INVICAT v1.0) using the TOMCAT chemical transport model

Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm

Projection-Based Model Reduction for Finite Element Approximation of Shallow Water Flows

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