A Modified Levenberg-Marquardt Algorithm for Large-Scale Inverse Problems

1993 ◽  
pp. 367-378 ◽  
Author(s):  
C. R. Vogel ◽  
J. G. Wade
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt

Modified Levenberg Marquardt Algorithm for Inverse Problems

2010 ◽  
pp. 623-632 ◽  
Author(s):  
Muthu Naveen ◽  
Shankar Jayaraman ◽  
Vinay Ramanath ◽  
Shamik Chaudhuri
Keyword(s):  
Inverse Problems ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt

Comparison of an Artificial Neural Network and a Multiple Linear Regression in Predicting the Heat of Combustion of Diesel Fuel Based on Hydrocarbon Groups

2020 ◽  
Vol 71 (6) ◽  
pp. 66-74
Author(s):  
Younis M. Younis ◽  
Salman H. Abbas ◽  
Farqad T. Najim ◽  
Firas Hashim Kamar ◽  
Gheorghe Nechifor
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Diesel Fuel ◽  
Back Propagation ◽  
Second Step ◽  
Heating Value ◽  
Network Training ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Propagation Network

A comparison between artificial neural network (ANN) and multiple linear regression (MLR) models was employed to predict the heat of combustion, and the gross and net heat values, of a diesel fuel engine, based on the chemical composition of the diesel fuel. One hundred and fifty samples of Iraqi diesel provided data from chromatographic analysis. Eight parameters were applied as inputs in order to predict the gross and net heat combustion of the diesel fuel. A trial-and-error method was used to determine the shape of the individual ANN. The results showed that the prediction accuracy of the ANN model was greater than that of the MLR model in predicting the gross heat value. The best neural network for predicting the gross heating value was a back-propagation network (8-8-1), using the Levenberg�Marquardt algorithm for the second step of network training. R = 0.98502 for the test data. In the same way, the best neural network for predicting the net heating value was a back-propagation network (8-5-1), using the Levenberg�Marquardt algorithm for the second step of network training. R = 0.95112 for the test data.

An object-oriented optimization framework for large-scale inverse problems

2021 ◽  
pp. 104790
Author(s):  
Ettore Biondi ◽  
Guillaume Barnier ◽  
Robert G. Clapp ◽  
Francesco Picetti ◽  
Stuart Farris
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Object Oriented ◽  
Optimization Framework

hIPPYlib

2021 ◽  
Vol 47 (2) ◽  
pp. 1-34
Author(s):  
Umberto Villa ◽  
Noemi Petra ◽  
Omar Ghattas
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Low Rank ◽  
Scalable Algorithms ◽  
Low Rank Approximation ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Bayesian Inverse Problems ◽  
Rank Approximation ◽  
Extensible Software

We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with (possibly) infinite-dimensional parameter fields (which are high-dimensional after discretization). hIPPYlib overcomes the prohibitively expensive nature of Bayesian inversion for this class of problems by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. The key property of the algorithms implemented in hIPPYlib is that the solution of the inverse problem is computed at a cost, measured in linearized forward PDE solves, that is independent of the parameter dimension. The mean of the posterior is approximated by the MAP point, which is found by minimizing the negative log-posterior with an inexact matrix-free Newton-CG method. The posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. The construction of the posterior covariance is made tractable by invoking a low-rank approximation of the Hessian of the log-likelihood. Scalable tools for sample generation are also discussed. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists and provides an environment that expedites the development of new algorithms.

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