Numerical methods for experimental design of large-scale linear ill-posed inverse problems

2008 ◽  
Vol 24 (5) ◽  
pp. 055012 ◽  
Author(s):  
E Haber ◽  
L Horesh ◽  
L Tenorio
2012 ◽  
Vol 58 (210) ◽  
pp. 795-808 ◽  
Author(s):  
Marijke Habermann ◽  
David Maxwell ◽  
Martin Truffer

AbstractInverse problems are used to estimate model parameters from observations. Many inverse problems are ill-posed because they lack stability, meaning it is not possible to find solutions that are stable with respect to small changes in input data. Regularization techniques are necessary to stabilize the problem. For nonlinear inverse problems, iterative inverse methods can be used as a regularization method. These methods start with an initial estimate of the model parameters, update the parameters to match observation in an iterative process that adjusts large-scale spatial features first, and use a stopping criterion to prevent the overfitting of data. This criterion determines the smoothness of the solution and thus the degree of regularization. Here, iterative inverse methods are implemented for the specific problem of reconstructing basal stickiness of an ice sheet by using the shallow-shelf approximation as a forward model and synthetically derived surface velocities as input data. The incomplete Gauss-Newton (IGN) method is introduced and compared to the commonly used steepest descent and nonlinear conjugate gradient methods. Two different stopping criteria, the discrepancy principle and a recent- improvement threshold, are compared. The IGN method is favored because it is rapidly converging, and it incorporates the discrepancy principle, which leads to optimally resolved solutions.


2011 ◽  
Vol 52 (1) ◽  
pp. 293-314 ◽  
Author(s):  
Eldad Haber ◽  
Zhuojun Magnant ◽  
Christian Lucero ◽  
Luis Tenorio

1983 ◽  
Vol 45 (5) ◽  
pp. 1237-1245 ◽  
Author(s):  
O. M. Alifanov
Keyword(s):  

Geosciences ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 41
Author(s):  
Tim Jurisch ◽  
Stefan Cantré ◽  
Fokke Saathoff

A variety of studies recently proved the applicability of different dried, fine-grained dredged materials as replacement material for erosion-resistant sea dike covers. In Rostock, Germany, a large-scale field experiment was conducted, in which different dredged materials were tested with regard to installation technology, stability, turf development, infiltration, and erosion resistance. The infiltration experiments to study the development of a seepage line in the dike body showed unexpected measurement results. Due to the high complexity of the problem, standard geo-hydraulic models proved to be unable to analyze these results. Therefore, different methods of inverse infiltration modeling were applied, such as the parameter estimation tool (PEST) and the AMALGAM algorithm. In the paper, the two approaches are compared and discussed. A sensitivity analysis proved the presumption of a non-linear model behavior for the infiltration problem and the Eigenvalue ratio indicates that the dike infiltration is an ill-posed problem. Although this complicates the inverse modeling (e.g., termination in local minima), parameter sets close to an optimum were found with both the PEST and the AMALGAM algorithms. Together with the field measurement data, this information supports the rating of the effective material properties of the applied dredged materials used as dike cover material.


2021 ◽  
pp. 104790
Author(s):  
Ettore Biondi ◽  
Guillaume Barnier ◽  
Robert G. Clapp ◽  
Francesco Picetti ◽  
Stuart Farris

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