A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

Kast, Mariella; Guo, Mengwu; Hesthaven, Jan S.

doi:10.1016/j.cma.2020.112947

Cited by 53 publications

(32 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [13,14], latent dynamics and nonlinear mappings are modelled as NODEs and autoencoders, respectively; in [4,[71][72][73], autoencoders are used to learn approximate invariant subspaces of the Koopman operator. Relatedly, there have been studies on learning direct mappings via, for example, a neural network, from parameters (including time parameters) to either latent states or approximate solution states [74][75][76][77][78], where the latent states are computed by using autoencoders or linear POD.…”

Section: Related Work (A) Classical Data-driven Surrogate Modellingmentioning

confidence: 99%

Parameterized neural ordinary differential equations: applications to computational physics problems

Lee

Parish

2021

Proc. R. Soc. A.

View full text Add to dashboard Cite

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter instances. Our extension is inspired by the concept of parameterized ODEs, which are widely investigated in computational science and engineering contexts, where characteristics of the governing equations vary over the input parameters. We apply the proposed parameterized NODEs (PNODEs) for learning latent dynamics of complex dynamical processes that arise in computational physics, which is an essential component for enabling rapid numerical simulations for time-critical physics applications. For this, we propose an encoder–decoder-type framework, which models latent dynamics as PNODEs. We demonstrate the effectiveness of PNODEs on benchmark problems from computational physics.

show abstract

Section: Related Work (A) Classical Data-driven Surrogate Modellingmentioning

confidence: 99%

Parameterized neural ordinary differential equations: applications to computational physics problems

Lee

Parish

2021

Proc. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…Since the low-fidelity evaluations can be computationally cheap, the offline efficiency can be effectively improved by reducing the number of high-fidelity evaluations. Kast et al 66 employ the linear model of coregionalization 67 that expresses the prior of a hierarchy of M solution fidelities as…”

Section: Multifidelity Regressionmentioning

confidence: 99%

“…The high-fidelity RB coefficients are defined by projecting the high-fidelity solution vectors onto the high-fidelity RB. Two alternative ways of evaluating low-fidelity RB coefficients have been given by Kast et al 66 One choice is to project the low-fidelity solution vectors onto a set of POD basis extracted from the low-fidelity snapshots, while the other is to project a reconstructed solution 69 from the bifidelity data set onto the high-fidelity RB. In the latter, the reconstructionq at each parameter location h is defined as a linear combination of the high-fidelity snapshots S H , i.e.…”

Section: Multifidelity Regressionmentioning

confidence: 99%

See 1 more Smart Citation

Non-intrusive reduced-order modeling for fluid problems: A brief review

Yan

Guo

2019

Proceedings of the Institution of Mechanical Engineers, Part G:

Self Cite

View full text Add to dashboard Cite

Despite tremendous progress seen in the computational fluid dynamics community for the past few decades, numerical tools are still too slow for the simulation of practical flow problems, consuming thousands or even millions of computational core-hours. To enable feasible multi-disciplinary analysis and design, the numerical techniques need to be accelerated by orders of magnitude. Reduced-order modeling has been considered one promising approach for such purposes. Recently, non-intrusive reduced-order modeling has drawn great interest in the scientific computing community due to its flexibility and efficiency and undergoes rapid development at present with different approaches emerging from various perspectives. In this paper, a brief review of non-intrusive reduced-order modeling in the context of fluid problems is performed involving three key aspects: i.e. dimension reduction of the solution space, surrogate models, and sampling strategies. Furthermore, non-intrusive reduced-order modelings regarding to some interesting topics such as unsteady flows, shock-dominating flows are also discussed. Finally, discussions on future development of non-intrusive reduced-order modeling for fluid problems are presented.

show abstract

“…However, as mentioned above, POD (and DEIM) needs a number of FOM simulations to construct the ROM. For this reason, [42] implemented a multi-fidelity strategy in which the parametric dependence was reconstructed using a large number of low-fidelity models and a minimal number of high-fidelity evaluations. Other approaches exploit machine learning to construct an input-output relationship, with convolutional neural networks [43] and autoencoders [44], which require the training of a network, again, using preexisting data.…”

Section: Introductionmentioning

confidence: 99%

A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

et al. 2021

View full text Add to dashboard Cite

We present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

show abstract

A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

Cited by 53 publications

References 25 publications

Parameterized neural ordinary differential equations: applications to computational physics problems

Parameterized neural ordinary differential equations: applications to computational physics problems

Non-intrusive reduced-order modeling for fluid problems: A brief review

A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion

Contact Info

Product

Resources

About