A sensitivity matrix based methodology for inverse problem formulation

Cintrón-Arias, Ariel; Banks, Harvey Thomas; Capaldi, Alex; Lloyd, Alun L.

doi:10.1515/jiip.2009.034

Cited by 91 publications

(122 citation statements)

References 34 publications

(64 reference statements)

Supporting

Mentioning

114

Contrasting

Order By: Relevance

“…The underlying problem of singularity of the χ T χ matrix is quite common for inverse problems with nonlinear models. A method to handle singularity of the Fisher Information Matrix (χ T χ) as a result of poor parameter identifiability and estimability has recently been introduced in [5]. This algorithm determines which parameter axes lie closest to the ill-conditioned directions of χ T χ and then implements a reduced-order estimation by fixing these associated parameter values at prior estimates.…”

Section: Discussionmentioning

confidence: 99%

Confidence Interval Estimation for an Empirical Model Quantifying the Effect of Soil Moisture and Plant Development on Soybean (Glycine Max (L.) Merr.) Leaf Conductance

Matthews¹,

Smith²,

Fiscus³

2013

Int. J. of Pure and Appl. Math.

View full text Add to dashboard Cite

In this work, we address uncertainty analysis for a model, presented in a separate paper, quantifying the effect of soil moisture and plant age on soybean (Glycine max (L.) Merr.) leaf conductance. To achieve this we present several methods for confidence interval estimation. Estimation of confidence intervals for model parameters and predictions is investigated using asymptotic theory, Monte Carlo methods, and bootstrap methods. predictions under water-stressed environmental conditions when using asymptotic theory and Monte Carlo methods are artificially large due to underlying false assumptions of normality. For this model, where the residuals exhibit heteroscedasticity, the confidence intervals estimated by the wild bootstrap method appear the most realistic of the methods investigated. Of the three methods presented for estimating 95% confidence intervals for model predictions, it is our opinion that the bootstrap method is the most reliable.

show abstract

Section: Discussionmentioning

confidence: 99%

Confidence Interval Estimation for an Empirical Model Quantifying the Effect of Soil Moisture and Plant Development on Soybean (Glycine Max (L.) Merr.) Leaf Conductance

Matthews¹,

Smith²,

Fiscus³

2013

Int. J. of Pure and Appl. Math.

View full text Add to dashboard Cite

show abstract

“…One example of this would be the output sensitivity matrix S(v) = Cx (v), which is used in first order sensitivity analysis [10]. This matrix is also used at each iteration of the optimization method to compute the descent direction when a Gauss-Newton type algorithm is used [8]).…”

Section: Adjoint Approachmentioning

confidence: 99%

“…Once again, the difference between the two approaches lies in the cascades (10) and (12): in the direct approach we have N differential equations with p-column matrices, whereas in the direct approach the left-hand side of (12) contains 1-column vectors. Hence, at the very least, we should expect a gain equivalent to the gain obtained in the stationary case.…”

Section: Computational Comparisonmentioning

confidence: 99%

“…Hence, at the very least, we should expect a gain equivalent to the gain obtained in the stationary case. Another interesting aspect of the adjoint approach appears when the pool sizes are also unknown: in the direct approach equation (10) has to be implicitly derived with respect to m, which leads to a more complex system to express and to solve than (10). In contrast, the structure of the system (12) is independent of the actual unknown parameters in the adjoint approach and only the final step (14) changes.…”

Section: Computational Comparisonmentioning

confidence: 99%

See 1 more Smart Citation

Metabolic Flux Analysis in Isotope Labeling Experiments Using the Adjoint Approach

Mottelet¹,

Gaullier²,

Sadaka³

2017

IEEE/ACM Trans. Comput. Biol. and Bioinf.

View full text Add to dashboard Cite

Abstract-Comprehension of metabolic pathways is considerably enhanced by metabolic flux analysis (MFA-ILE) in isotope labeling experiments. The balance equations are given by hundreds of algebraic (stationary MFA) or ordinary differential equations (nonstationary MFA), and reducing the number of operations is therefore a crucial part of reducing the computation cost. The main bottleneck for deterministic algorithms is the computation of derivatives, particularly for nonstationary MFA. In this article we explain how the overall identification process may be speeded up by using the adjoint approach to compute the gradient of the residual sum of squares. The proposed approach shows significant improvements in terms of complexity and computation time when it is compared with the usual (direct) approach. Numerical results are obtained for the central metabolic pathways of Escherichia coli and are validated against reference software in the stationary case. The methods and algorithms described in this paper are included in the sysmetab software package distributed under an Open Source license at http://forge.scilab.org/index.php/p/sysmetab/.

show abstract

“…called subset selection algorithm (SSA) is proposed that ranks the parameter by two properties, α and κ [9]. The parameter α is correlated to the size of the confidence regions for a parameter set and κ is a measure of how well-conditioned the parameter Jacobean for a parameter set is.…”

Section: Introductionmentioning

confidence: 99%

Parameter Selection in a Combined Cycle Power Plant

Andersson

Åkesson

Link

et al. 2014

Linköping Electronic Conference Proceedings

View full text Add to dashboard Cite

A combined cycle power plant are modeled and considered for calibration. The dynamic model, aimed for start-up optimization, contains 64 candidate parameters for calibration. The number of parameter sets that can be created are huge and an algorithm called subset selection algorithm is used to reduce the number of parameter sets. The algorithm investigates the numerical properties of a calibration from a parameter Jacobean estimated from a simulation of the model with reasonably chosen parameter values. The calibrations were performed with a Levenberg-Marquardt algorithm considering the least squares of eight output signals. The parameter value with the best objective function value resulted in simulations in good compliance to the process dynamics. The subset selection algorithm effectively shows which parameters that are important and which parameters that can be left out.

show abstract

A sensitivity matrix based methodology for inverse problem formulation

Cited by 91 publications

References 34 publications

Confidence Interval Estimation for an Empirical Model Quantifying the Effect of Soil Moisture and Plant Development on Soybean (Glycine Max (L.) Merr.) Leaf Conductance

Confidence Interval Estimation for an Empirical Model Quantifying the Effect of Soil Moisture and Plant Development on Soybean (Glycine Max (L.) Merr.) Leaf Conductance

Metabolic Flux Analysis in Isotope Labeling Experiments Using the Adjoint Approach

Parameter Selection in a Combined Cycle Power Plant

Contact Info

Product

Resources

About