scholarly journals Non-linear model reduction for uncertainty quantification in large-scale inverse problems

Author(s):  
D. Galbally ◽  
K. Fidkowski ◽  
K. Willcox ◽  
O. Ghattas
2018 ◽  
Vol 49 (6) ◽  
pp. 1788-1803 ◽  
Author(s):  
Mohammad Ebrahim Banihabib ◽  
Arezoo Ahmadian ◽  
Mohammad Valipour

Abstract In this study, to reflect the effect of large-scale climate signals on runoff, these indices are accompanied with rainfall (the most effective local factor in runoff) as the inputs of the hybrid model. Where one-year in advance forecasting of reservoir inflows can provide data to have an optimal reservoir operation, reports show we still need more accurate models which include all effective parameters to have more forecasting accuracy than traditional linear models (ARMA and ARIMA). Thus, hybridization of models was employed for improving the accuracy of flow forecasting. Moreover, various forecasters including large-scale climate signals were tested to promote forecasting. This paper focuses on testing MARMA-NARX hybrid model to enhance the accuracy of monthly inflow forecasts. Since the inflow in different periods of the year has in linear and non-linear trends, the hybrid model is proposed as a means of combining linear model, monthly autoregressive moving average (MARMA), and non-linear model, nonlinear autoregressive model with exogenous (NARX) inputs to upgrade the accuracy of flow forecasting. The results of the study showed enhanced forecasting accuracy through using the hybrid model.


Author(s):  
K Ordaz-Hernandez ◽  
X Fischer ◽  
F Bennis

The current paper presents the study of a neural network-based technique used to create fast, reduced, non-linear behavioural models. The studied approach is the use of artificial neural networks (ANNs) as a model reduction technique to create more efficient models, mostly in terms of computational speed. The test case is the deformation of a cantilever beam under large deflections (geometrical non-linearity). A reduced model is created by means of a multi-layer feed-forward neural network, a type of ANN reported as ‘universal approximator’ in the literature. Then it is compared with two finite-element models: linear (inaccurate for large deflections but fast) and non-linear (accurate but slow). Under large displacements, the reduced model approximates well the non-linear model while having similar speed to the linear model. Unfortunately, the resulting model presents a shortening of its validity domain, as being incapable of approximating the deformed configuration of the cantilever beam under small displacements. In other words, the ANN-based model provides a very good compromise between accuracy and speed within its validity domain, despite the low fidelity presented: accurate for large displacements but inaccurate for small displacements.


2004 ◽  
Vol 37 (13) ◽  
pp. 775-780
Author(s):  
M.-N. Contou-Carrere ◽  
P. Daoutidis

2014 ◽  
Vol 263 ◽  
pp. 1-18 ◽  
Author(s):  
D. Xiao ◽  
F. Fang ◽  
A.G. Buchan ◽  
C.C. Pain ◽  
I.M. Navon ◽  
...  

2020 ◽  
Vol 365 ◽  
pp. 112991 ◽  
Author(s):  
Eric J. Parish ◽  
Christopher R. Wentland ◽  
Karthik Duraisamy

2011 ◽  
Vol 33 (1) ◽  
pp. 407-432 ◽  
Author(s):  
H. P. Flath ◽  
L. C. Wilcox ◽  
V. Akçelik ◽  
J. Hill ◽  
B. van Bloemen Waanders ◽  
...  

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