The Empirical Cross Gramian for Parametrized Nonlinear Systems

Himpe, Christian; Ohlberger, Mario

doi:10.1016/j.ifacol.2015.05.163

Cited by 7 publications

(5 citation statements)

References 7 publications

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“…Generally, each of the structure-preserving model order reduction methods in Sect. 4 can be used with either, we opted to use the averaging ansatz for all of the following methods since their computation is without exception based on parametric empirical Gramians [71].…”

Section: Parametric Model Reductionmentioning

confidence: 99%

Model order reduction for gas and energy networks

2021

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To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query gas network simulation task can be accelerated by model reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling natural gas transport, are a challenging application for model order reduction algorithms.For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and parametric model reduction for nonlinear systems. This research resulted in the (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of and associated numerical experiments testing model reduction adapted to gas network models.

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Section: Parametric Model Reductionmentioning

confidence: 99%

Model order reduction for gas and energy networks

2021

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“…Empirical Gramians may also be applied to parametric systems. Here, the approach from [28] is utilized, which follows the general principle behind empirical Gramians: averaging over an operating region. Hence, given a pre-selected sampling from parameter-space Θ h , an average (controllability, observability, cross, or non-symmetric cross) Gramian is computable [6]:…”

Section: Parametric Empirical Gramiansmentioning

confidence: 99%

Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms

Himpe¹

2020

Preprint

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“…For the selected data-driven methods, averaging means that for a set of parameter samples the associated trajectories or derived quantities (such as the utilized system Gramians) are averaged, while accumulating refers to the concatenation of trajectories or derived quantities (such as the projectors). Generally, each of the methods in Section 4 can be used with either averaging or accumulating, we opted to use the averaging ansatz for all of the following methods since their computation is without exception based on parametric empirical Gramians [62]…”

Section: Parametric Model Reductionmentioning

confidence: 99%

Model Order Reduction for Gas and Energy Networks

Himpe,

Grundel,

Benner

2020

Preprint

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To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these new circumstances, a vast number of possible scenarios, incorporating uncertain supply and demand, has to be simulated ahead of time. This many-query task can be accelerated by model order reduction, yet, large-scale, nonlinear, parametric, hyperbolic partial differential(-algebraic) equation systems, modeling gas transport, are a challenging application for model reduction algorithms. For this industrial application, we bring together the scientific computing topics of: mathematical modeling of gas transport networks, numerical simulation of hyperbolic partial differential equation, and model order reduction for nonlinear parametric systems. This research resulted in the morgen (Model Order Reduction for Gas and Energy Networks) software platform, which enables modular testing of various combinations of models, solvers, and model reduction methods. In this work we present the theoretical background on systemic modeling and structured, data-driven, system-theoretic model reduction for gas networks, as well as the implementation of morgen and associated numerical experiments testing model reduction adapted to gas network models.

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The Empirical Cross Gramian for Parametrized Nonlinear Systems

Cited by 7 publications

References 7 publications

Model order reduction for gas and energy networks

Model order reduction for gas and energy networks

Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms

Model Order Reduction for Gas and Energy Networks

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