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

2009 ◽  
pp. n/a-n/a ◽  
Author(s):  
D. Galbally ◽  
K. Fidkowski ◽  
K. Willcox ◽  
O. Ghattas
Keyword(s):  
Inverse Problems ◽  
Uncertainty Quantification ◽  
Model Reduction ◽  
Linear Model ◽  
Large Scale ◽  
Non Linear

scholarly journals Hybrid MARMA-NARX model for flow forecasting based on the large-scale climate signals, sea-surface temperatures, and rainfall

2018 ◽  
Vol 49 (6) ◽  
pp. 1788-1803 ◽  
Author(s):  
Mohammad Ebrahim Banihabib ◽  
Arezoo Ahmadian ◽  
Mohammad Valipour
Keyword(s):  
Linear Model ◽  
Hybrid Model ◽  
Large Scale ◽  
Linear Models ◽  
Moving Average ◽  
Effective Parameters ◽  
Forecasting Accuracy ◽  
Local Factor ◽  
Non Linear ◽  
Climate Signals

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.

Model reduction technique for mechanical behaviour modelling: Efficiency criteria and validity domain assessment

2008 ◽  
Vol 222 (3) ◽  
pp. 493-505 ◽  
Author(s):  
K Ordaz-Hernandez ◽  
X Fischer ◽  
F Bennis
Keyword(s):  
Neural Network ◽  
Model Reduction ◽  
Linear Model ◽  
Cantilever Beam ◽  
Reduction Technique ◽  
Reduced Model ◽  
Large Displacements ◽  
Large Deflections ◽  
Non Linear ◽  
Model Reduction Technique

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.

Non-linear model reduction of multi-scale reaction-convection processes

2004 ◽  
Vol 37 (13) ◽  
pp. 775-780
Author(s):  
M.-N. Contou-Carrere ◽  
P. Daoutidis
Keyword(s):  
Model Reduction ◽  
Linear Model ◽  
Multi Scale ◽  
Non Linear

scholarly journals Non-linear model reduction for the Navier–Stokes equations using residual DEIM method

2014 ◽  
Vol 263 ◽  
pp. 1-18 ◽  
Author(s):  
D. Xiao ◽  
F. Fang ◽  
A.G. Buchan ◽  
C.C. Pain ◽  
I.M. Navon ◽  
...  
Keyword(s):  
Model Reduction ◽  
Linear Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Non Linear

scholarly journals The Adjoint Petrov–Galerkin method for non-linear model reduction

2020 ◽  
Vol 365 ◽  
pp. 112991 ◽  
Author(s):  
Eric J. Parish ◽  
Christopher R. Wentland ◽  
Karthik Duraisamy
Keyword(s):  
Galerkin Method ◽  
Model Reduction ◽  
Linear Model ◽  
Non Linear

Fast Algorithms for Bayesian Uncertainty Quantification in Large-Scale Linear Inverse Problems Based on Low-Rank Partial Hessian Approximations

2011 ◽  
Vol 33 (1) ◽  
pp. 407-432 ◽  
Author(s):  
H. P. Flath ◽  
L. C. Wilcox ◽  
V. Akçelik ◽  
J. Hill ◽  
B. van Bloemen Waanders ◽  
...  
Keyword(s):  
Inverse Problems ◽  
Uncertainty Quantification ◽  
Large Scale ◽  
Fast Algorithms ◽  
Low Rank ◽  
Linear Inverse Problems
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