Uncertainty assessment for inverse problems in high dimensional spaces using particle swarm optimization and model reduction techniques

Global optimization methods including particle swarm optimization are usually used to solve optimization problems when the number of parameters is low (hundreds). Also, to be able to find a good solution typically involves multiple evaluations of the objective (or cost) function. Thus, both a large...

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Bibliographic Details
Published in:Mathematical and computer modelling Vol. 54; no. 11; pp. 2889 - 2899
Main Authors: Fernández-Martínez, J.L., Mukerji, T., García-Gonzalo, E., Fernández-Muñiz, Z.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.12.2011
Elsevier
Subjects:
algorithms
Calculus of variations and optimal control
Exact sciences and technology
Inverse problems
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Model reduction techniques
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
oil fields
principal component analysis
PSO
Sciences and techniques of general use
system optimization
Uncertainty
uncertainty analysis
Uncertainty
Inverse problems
Model reduction techniques
PSO
Transcendental equation
Optimization method
Stochastic method
Algorithm
Global solution
Inverse problem
Non linear equation
Particle method
Numerical analysis
Applied mathematics
Algebraic equation
Variational calculus
Cost function
Simulation model
Sampling
Mathematical model
Computer aided analysis
Mathematical programming
ISSN:0895-7177, 1872-9479
Online Access:Get full text
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Summary:Global optimization methods including particle swarm optimization are usually used to solve optimization problems when the number of parameters is low (hundreds). Also, to be able to find a good solution typically involves multiple evaluations of the objective (or cost) function. Thus, both a large number of parameters and very costly forward evaluations hamper the use of global algorithms in inverse problems. In this paper, we address the first problem showing that the sampling can be performed in a reduced model space. The reduction of the dimension is accomplished in this case by the principal component analysis computed on a set of scenarios that are built based on prior information using stochastic simulation techniques. The use of a reduced base helps to regularize the inverse problem and to find a set of equivalent models that fit the data within a prescribed tolerance, allowing uncertainty analysis around the minimum misfit solution. We show the application of this idea to a history matching problem of a synthetic oil reservoir, using different members of the PSO family to perform sampling on the reduced model space.
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ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.07.009