scholarly journals Strategies for Reduced-Order Models for Predicting the Statistical Responses and Uncertainty Quantification in Complex Turbulent Dynamical Systems

SIAM Review ◽  
2018 ◽  
Vol 60 (3) ◽  
pp. 491-549 ◽  
Author(s):  
Andrew J. Majda ◽  
Di Qi
Keyword(s):  
Dynamical Systems ◽  
Uncertainty Quantification ◽  
Reduced Order Models ◽  
Reduced Order

Multiscale, Multiphenomena Modeling and Simulation at the Nanoscale: On Constructing Reduced-Order Models for Nonlinear Dynamical Systems With Many Degrees-of-Freedom

2003 ◽  
Vol 70 (3) ◽  
pp. 328-338 ◽  
Author(s):  
E. H. Dowell ◽  
D. Tang
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical Systems ◽  
Total System ◽  
Reduced Order Models ◽  
Efficient Computation ◽  
Linear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Reduced Order ◽  
Value Decomposition

The large number of degrees-of-freedom of finite difference, finite element, or molecular dynamics models for complex systems is often a significant barrier to both efficient computation and increased understanding of the relevant phenomena. Thus there is a benefit to constructing reduced-order models with many fewer degrees-of-freedom that retain the same accuracy as the original model. Constructing reduced-order models for linear dynamical systems relies substantially on the existence of global modes such as eigenmodes where a relatively small number of these modes may be sufficient to describe the response of the total system. For systems with very many degrees-of-freedom that arise from spatial discretization of partial differential equation models, computing the eigenmodes themselves may be the major challenge. In such cases the use of alternative modal models based upon proper orthogonal decomposition or singular value decomposition have proven very useful. In the present paper another facet of reduced-order modeling is examined, i.e., the effects of “local” nonlinearity at the nanoscale. The focus is on nanoscale devices where it will be shown that a combination of global modal and local discrete coordinates may be most effective in constructing reduced-order models from both a conceptual and computational perspective. Such reduced-order models offer the possibility of reducing computational model size and cost by several orders of magnitude.

scholarly journals A Detection Algorithm for Bifurcations in Dynamical Systems using Reduced Order Models

2008 ◽  
Vol 41 (2) ◽  
pp. 10957-10962 ◽  
Author(s):  
Satyajit K. Wattamwar ◽  
Siep Weiland ◽  
Ton Backx
Keyword(s):  
Dynamical Systems ◽  
Detection Algorithm ◽  
Reduced Order Models ◽  
Reduced Order

scholarly journals Reduced Order Models in Analysis of Stochastically Parametered Linear Dynamical Systems

2016 ◽  
Vol 144 ◽  
pp. 1325-1331 ◽  
Author(s):  
Hridya P. Lal ◽  
Siddhesh M. Godbole ◽  
Jainendra K. Dubey ◽  
Sunetra Sarkar ◽  
Sayan Gupta
Keyword(s):  
Dynamical Systems ◽  
Reduced Order Models ◽  
Linear Dynamical Systems ◽  
Reduced Order
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