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Geometric Sampling: An Approach to Uncertainty in High Dimensional Spaces [chapter]

Juan Luis Fernández-Martínez, Michael Tompkins, Tapan Mukerji, David Alumbaugh
2010 Advances in Intelligent and Soft Computing  
Integral to this method is the combination of model reduction techniques, a constrained mapping approach and a sparse sampling scheme.  ...  In the context of nonlinear inversion, the uncertainty problem is that of quantifying the variability in the model space supported by prior information and the observed data.  ...  We acknowledge WesternGeco for allowing us to use and publish the resistivity image data set.  ... 
doi:10.1007/978-3-642-14746-3_31 dblp:conf/smps/MartinezTMA10 fatcat:ajow4xhnwneobjjqsn3yb3voru

A sparse Bayesian framework for conditioning uncertain geologic models to nonlinear flow measurements

Lianlin Li, Behnam Jafarpour
2010 Advances in Water Resources  
We present a Bayesian framework for reconstruction of subsurface hydraulic properties from nonlinear dynamic flow data by imposing sparsity on the distribution of the solution coefficients in a compression  ...  Sparsity of the solution in the DCT (or other appropriate transform) domain can be exploited to formulate deterministic regularization methods to improve the solution of ill-posed nonlinear inverse problems  ...  the application of the sparse Bayesian estimation approach nonlinear dynamic inverse problem where reconstruction of permeability fields from nonlinear dynamic data is considered.  ... 
doi:10.1016/j.advwatres.2010.06.005 fatcat:636hyxdlerhhpgfln2jd74575i

Page 7619 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
problem to determine the minimum energy configuration of a three-dimensional superconductor model.”  ...  The effect of these various graph reduction schemes on the solution of sparse triangular systems is categorized.  ... 

Nonlinear Graph Sparsification for SLAM

Mladen Mazuran, Tipaldi Gian Diego, Spinello Luciano, Wolfram Burgard
2014 Robotics: Science and Systems X  
Experiments performed on several publicly available datasets demonstrate that our method outperforms the state of the art with respect to the Kullback-Leibler divergence and the sparsity of the solution  ...  Our approach is formulated as a convex minimization problem, where we select the set of nonlinear measurements that best approximate the original distribution.  ...  ACKNOWLEDGEMENTS We would like to thank Nicholas Carlevaris-Bianco for providing us with the EECS and Duderstadt datasets and for his invaluable help in the use of GLC.  ... 
doi:10.15607/rss.2014.x.040 dblp:conf/rss/MazuranTSB14 fatcat:7yscihjacbhmvc6kzelybwbowu

Fighting the Curse of Dimensionality: Compressive Sensing in Exploration Seismology

Felix Herrmann, Michael Friedlander, Ozgur Yilmaz
2012 IEEE Signal Processing Magazine  
to effectively fight the curse of dimensionality.  ...  Compressive sensing is a novel nonlinear sampling paradigm, effective for acquiring signals that have a sparse representation in some transform domain.  ...  In order to do the inversion, we must be careful to limit the cost of each matrix-vector multiply, which we accomplish by dimensionality reduction.  ... 
doi:10.1109/msp.2012.2185859 fatcat:txfwrz3hdrfbzjf52ck5dwc2im

Learning high-dimensional nonlinear mapping via compressed sensing

Tomoya Sakai, Daisuke Miyata
2014 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The high-dimensional nonlinear mapping consists of (i) dimensionality reduction by the random projection of the input data, (ii) low-dimensional nonlinear mapping, and (iii) reconstruction of the high-dimensional  ...  output data on the basis of a sparse model.  ...  Further research should include detailed performance evaluation in possible applications such as nonlinear image filtering, tracking, anomaly detection, solving large-scale inverse problem, and so on.  ... 
doi:10.1109/icassp.2014.6854601 dblp:conf/icassp/SakaiM14 fatcat:rmyito6j65de5faiawx36pswem

Page 4156 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
A class of iterative methods for solutions of an arbitrary- dimensional system of nonlinear equations is studied. The iteration converges in finite steps when one solves linear prob- lems.  ...  It is shown that the e versions of both these problems can be reduced to a specific geometric programming problem and a polynomial time algorithm is derived for their solutions having the cost of O((m+  ... 

A Survey on the Low-Dimensional-Model-based Electromagnetic Imaging

Lianlin Li, Martin Hurtado, Feng Xu, Bing Chen Zhang, Tian Jin, Tie Jun Cui, Marija Nikolic Stevanovic, Arye Nehorai
2018 Foundations and Trends® in Signal Processing  
As argued above, the nonlinear inverse scattering, i.e. A θ being nonlinear, is limited to the small-scale problem due to its very expensive computational cost.  ...  In practice, one resorts to the linearized approximate solution to the rigorous inverse scattering problem, for example, Born-approximation [127, 23] .  ... 
doi:10.1561/2000000103 fatcat:xbxreie4dvbsdldobt5kp5gou4

Online interpolation point refinement for reduced order models using a genetic algorithm [article]

Syuzanna Sargsyan, Steven L. Brunton, J. Nathan Kutz
2016 arXiv   pre-print
of the nonlinear terms.  ...  The method achieves nearly optimal interpolation points with only a few generations of the search, making it potentially useful for online refinement of the sparse sampling used to construct a projection  ...  The DEIM algorithm has been particularly successful for nonlinear model reduction of time-dependent problems.  ... 
arXiv:1607.07702v1 fatcat:x5yoz2aujzcedop6mlduqvvukq

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

D. Galbally, K. Fidkowski, K. Willcox, O. Ghattas
2009 International Journal for Numerical Methods in Engineering  
We present a model reduction approach to the solution of large-scale statistical inverse problems in a Bayesian inference setting.  ...  model, making tractable the solution of the statistical inverse problem that would otherwise require many years of CPU time.  ...  Conclusions This paper presents an application of nonlinear model reduction to an inverse problem solution in a Bayesian inference setting.  ... 
doi:10.1002/nme.2746 fatcat:vt3lvuhldzdc5pp4m6yozdrw3a

Hessian-based adaptive sparse quadrature for infinite-dimensional Bayesian inverse problems

Peng Chen, Umberto Villa, Omar Ghattas
2017 Computer Methods in Applied Mechanics and Engineering  
In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems  ...  Dimension-independent and faster convergence than O(N^-1/2) is demonstrated for a linear as well as a nonlinear inverse problem whose posterior distribution can be effectively approximated by a Gaussian  ...  of the sparse quadrature in both a linear and a nonlinear inverse problem.  ... 
doi:10.1016/j.cma.2017.08.016 fatcat:pztn7fbfyvbtxcdou5bnc7lkai

Page 687 of Mathematical Reviews Vol. , Issue 81B [page]

1981 Mathematical Reviews  
for a linear pencil; (2) reduction of the solution of a spectral problem for a regular linear pencil of degenerate matrices to solution of the same problem for a constant matrix of smaller dimensions;  ...  Author’s introduction: “We propose several conceptually related algorithms that allow (1) reduction of the solution of a spectral problem for a polynomial matrix pencil of any degree to the same problem  ... 

Stable Recovery Of Sparse Vectors From Random Sinusoidal Feature Maps [article]

Mohammadreza Soltani, Chinmay Hegde
2017 arXiv   pre-print
Our algorithm can be extended to other types of structured inverse problems, such as demixing a pair of sparse (but incoherent) vectors.  ...  Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a random Gaussian matrix, and then computing an element-wise sinusoid.  ...  of MF-Sparse for more generic structured inverse problems.  ... 
arXiv:1701.06607v2 fatcat:nkwieo74irertkrluqmu7zm7ca

Some applications of compressed sensing in computational mechanics: model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction

R. Ibañez, E. Abisset-Chavanne, E. Cueto, A. Ammar, J. -L. Duval, F. Chinesta
2019 Computational Mechanics  
We consider a wide variety of applications, such as model order reduction, manifold learning, data-driven applications and nonlinear dimensionality reduction.  ...  In other words, it is able to reconstruct a signal at less than 2Q samplings per second, where Q stands for the highest frequency content of the signal.  ...  Acknowledgements This work has been supported by the Spanish Ministry of Economy and Competitiveness through Grants Numbers DPI2017-85139-C2-1-R and DPI2015-72365-EXP and by the Regional Government of  ... 
doi:10.1007/s00466-019-01703-5 fatcat:5d7vvksvojh3te2vxlyghei2ye

Dimensionality reduction for efficient Bayesian estimation of groundwater flow in strongly heterogeneous aquifers

Thierry A. Mara, Noura Fajraoui, Alberto Guadagnini, Anis Younes
2016 Stochastic environmental research and risk assessment (Print)  
Bayesian inversion of the optimal sparse KLE is then inferred using Markov Chain Monte Carlo (MCMC) samplers.  ...  The distinctive aim of this work is to present an efficient approach for the stochastic inverse modeling of fully saturated groundwater flow in these types of strongly heterogeneous domains.  ...  Acknowledgements The authors are grateful to the French National Research Agency who funded this work through the program AAP Blanc -SIMI 6 project RESAIN (n • ANR-12-BS06-0010-02).  ... 
doi:10.1007/s00477-016-1344-1 fatcat:kgsrgegci5a4pcjcvimplidpcy
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