Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties

2019 ◽  
Vol 349 ◽  
pp. 266-284 ◽  
Author(s):  
Chensen Ding ◽  
Rohit R. Deokar ◽  
Yanjun Ding ◽  
Guangyao Li ◽  
Xiangyang Cui ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Model Order Reduction ◽  
Order Reduction ◽  
High Dimensional ◽  
Model Order ◽  
Material Uncertainties

scholarly journals A Review of Model Order Reduction Methods for Large-Scale Structure Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Kuan Lu ◽  
Kangyu Zhang ◽  
Haopeng Zhang ◽  
Xiaohui Gu ◽  
Yulin Jin ◽  
...  
Keyword(s):  
Complex Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Large Scale Structure ◽  
Scale Structure ◽  
High Dimensional ◽  
Model Order ◽  
Reduction Methods ◽  
Proper Orthogonal

The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

scholarly journals Model order reduction for the simulation of parametric interest rate models in financial risk analysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Andreas Binder ◽  
Onkar Jadhav ◽  
Volker Mehrmann
Keyword(s):  
Model Order Reduction ◽  
Financial Risk ◽  
Large Scale ◽  
Order Reduction ◽  
Parametric Models ◽  
Diffusion Reaction ◽  
High Dimensional ◽  
Reduced Basis ◽  
Model Order ◽  
Reduction Approach

AbstractThis paper presents a model order reduction approach for large scale high dimensional parametric models arising in the analysis of financial risk. To understand the risks associated with a financial product, one has to perform several thousand computationally demanding simulations of the model which require efficient algorithms. We establish a model reduction approach based on a variant of the proper orthogonal decomposition method to generate small model approximations for the high dimensional parametric convection-diffusion-reaction partial differential equations. This approach requires to solve the full model at some selected parameter values to generate a reduced basis. We propose an adaptive greedy sampling technique based on surrogate modeling for the selection of the sample parameter set. The new technique is analyzed, implemented, and tested on industrial data of a floater with cap and floor under the Hull–White model. The results illustrate that the reduced model approach works well for short-rate models.

scholarly journals Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates

2021 ◽  
Author(s):  
Fabio Nobile ◽  
Davide Pradovera
Keyword(s):  
Parameter Space ◽  
Model Order Reduction ◽  
Optimization Problem ◽  
Order Reduction ◽  
Rational Interpolation ◽  
Sparse Grids ◽  
Parametric Model ◽  
High Dimensional ◽  
Model Order ◽  
Interpolation Strategy

We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters.

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