Identification of Parameters in Distributed Parameter Systems by Regularization

Kravaris, Costas; Seinfeld, John H.

doi:10.1137/0323017

Cited by 239 publications

(102 citation statements)

References 17 publications

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“…Thus minimizing sequences for J0 are bounded in QR and hence compact in Q; this is, in some sense, roughly equivalent to minimizing J over a restriction of Q which is compact even though the minimization of J, only produces (hopefully) an approximation to the minimizer for the original 131 criterion J. In the cases considered below, we use QR = H while Q= C (which corresponds to A=C and R =H 2 in the notation of [5]). …”

mentioning

confidence: 99%

“…An alternative but essentially theoretically equivalent approach involves the use of Tikhonov regularization as formulated by Kravaris and Seinfeld in [5]. One restricts the parameter set to QR a Q with QR compactly imbedded in Q and then modifies the original least squares criterion J 2 to minimize J =J + 3 q R where R is the norm in QR and 0 is a regularization parameter.…”

mentioning

confidence: 99%

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A Comparison of Stability and Convergence Properties of Techniques for Inverse Problems,

Banks¹,

Iles²

1986

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mentioning

confidence: 99%

mentioning

confidence: 99%

A Comparison of Stability and Convergence Properties of Techniques for Inverse Problems,

Banks¹,

Iles²

1986

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“…Therefore, we conclude that the gradient can be obtained as (16). Recall the estimates (4) and (15) of the primal and the adjoint states, respectively.…”

Section: Proof We Introduce the Notationmentioning

confidence: 63%

“…The adjoint-based method for PDE-constrained optimization problems requires more careful analysis than ODE-constrained optimization problems because the solution of the PDEs does not always have enough differentiability and regularity to guarantee the existence of a well-defined gradient. Furthermore, the differentiability and regularity of the solution highly depend on the type of the PDE: therefore, the method has been customized to several types of PDEs and used in relevant applications [1,16,14,3,13,30].…”

Section: Introductionmentioning

confidence: 99%

Regularization-based identification for level set equations

Yang

Tomlin

2013

52nd IEEE Conference on Decision and Control

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An optimization-based method for identifying the speed profile of a moving surface from image data is studied. If the dynamic surface motion is modeled by a level set equation, the identification problem can be formulated as an optimization problem constrained with the level set equation whose (viscosity) solution, in general, has kinks. The non-differentiable solution prevents us from having a bounded gradient of the cost function of the optimization problem. To overcome this difficulty, we develop a novel identification approach using a regularized level set equation. The regularization guarantees the differentiability of the cost function and the boundedness of the gradient. Using numerical optimization techniques with the adjoint-based gradient, we solve the identification problem. We perform a numerical test to validate that the solution of an optimization problem with a regularized level set equation converges to the solution of the same optimization problem with an unregularized level set equation as the regularization factor tends to zero. The performance and usefulness of the method are demonstrated by a biological example in which we estimate the forces (per density) of actin and myosin in cell polarization.

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“…The stability and convergence results obtained here are based on [7], [14], [25] and [9]. We choose D(G …”

Section: Resultsmentioning

confidence: 99%

The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media

et al. 2007

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Abstract. Deep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid invasion of reservoir production zones, fines migration in oil fields, industrial filtering, bacteria, viruses or contaminants transport in groundwater, etc. The basic features of the process are particle capture by the porous medium and consequent permeability reduction.Models for deep bed filtration contain two quantities that represent rock and fluid properties: the filtration function, which is the fraction of particles captured per unit particle path length, and formation damage function, which is the ratio between reduced and initial permeabilities. These quantities cannot be measured directly in the laboratory or in the field; therefore, they must be calculated indirectly by solving inverse problems. The practical petroleum and environmental engineering purpose is to predict injectivity loss and particle penetration depth around wells. Reliable prediction requires precise knowledge of these two coefficients.In this work we determine these quantities from pressure drop and effluent concentration histories measured in one-dimensional laboratory experiments. The recovery method consists of optimizing deviation functionals in appropriate subdomains; if necessary, a Tikhonov regularization term is added to the functional. The filtration function is recovered by optimizing a non-linear functional with box constraints; this functional involves the effluent concentration history. The permeability reduction is recovered likewise, taking into account the filtration function already found, and the functional involves the pressure drop history. In both cases, the functionals are derived from least square formulations of the deviation between experimental data and quantities predicted by the model.

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Identification of Parameters in Distributed Parameter Systems by Regularization

Cited by 239 publications

References 17 publications

A Comparison of Stability and Convergence Properties of Techniques for Inverse Problems,

A Comparison of Stability and Convergence Properties of Techniques for Inverse Problems,

Regularization-based identification for level set equations

The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media

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