Adaptive approach for nonlinear sensitivity analysis of reaction kinetics

Horenko, Illia; Lorenz, Sönke; Schütte, Christof; Huisinga, Wilhelm

doi:10.1002/jcc.20234

Cited by 14 publications

(9 citation statements)

References 11 publications

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“…By merely looking at the classical residuum F R , no model can be favored. However, according to the overlap information F L , the Contois kinetic of (28) ought to be rejected. For the remaining two candidates, the squared distance between the mean values of the data distribution and the average of (5), abbreviated Table 5 by avg.traj., favors the Monod kinetics (27).…”

Section: Numerical Experimentsmentioning

confidence: 97%

Discrimination of dynamical system models for biological and chemical processes

et al. 2007

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In technical chemistry, systems biology and biotechnology, the construction of predictive models has become an essential step in process design and product optimization. Accurate modelling of the reactions requires detailed knowledge about the processes involved. However, when concerned with the development of new products and production techniques for example, this knowledge often is not available due to the lack of experimental data. Thus, when one has to work with a selection of proposed models, the main tasks of early development is to discriminate these models. In this article, a new statistical approach to model discrimination is described that ranks models wrt. the probability with which they reproduce the given data. The article introduces the new approach, discusses its statistical background, presents numerical techniques for its implementation and illustrates the application to examples from biokinetics.

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Section: Numerical Experimentsmentioning

confidence: 97%

Discrimination of dynamical system models for biological and chemical processes

et al. 2007

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“…As shown in [13] this formulation also covers an ODE with stochastic parameters, which are treated as independent and constant additional states.…”

Section: Error Controlled Uncertainty Analysismentioning

confidence: 99%

Adaptive Gaussian particle method for the solution of the Fokker‐Planck equation

Scharpenberg¹,

Lukáčová-Medviová²

2012

Z Angew Math Mech

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The Fokker-Planck equation describes the evolution of the probability density for a stochastic ordinary differential equation (SODE) or a deterministic ordinary differential equation (ODE) with stochastic initial values. A solution strategy for this partial differential equation (PDE) up to a relatively large number of dimensions is based on particle methods using Gaussians as basis functions. An initial probability density is decomposed into a sum of multivariate normal distributions and these are propagated according to the ODE. The decomposition as well as the propagation is subject to possibly large numerical errors due to the difficulty to control the spatial residual over the whole domain.In this paper a new particle method is derived, which allows a deterministic error control for the resulting probability density. It is based on global optimization and allows an adaption of an efficient surrogate model for the residual estimation. Error controlled uncertainty analysisFor any numerical application knowledge about the accuracy of the applied method is essential. If we simulate a physical system, further knowledge about the effect of uncertainties in the input parameters is vital for the assessment and validation of the results. In [7] it is noted that uncertain input data does not only lead to an uncertain solution but to an uncertain solution error as well.In the following both aspects will be covered for stochastic uncertainties within a system of ordinary differential equa-The ODE itself is considered deterministic, but the initial data is assumed to be uncertain. As shown in [13] this formulation also covers an ODE with stochastic parameters, which are treated as independent and constant additional states.

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“…, N t denote the corresponding means, inverses of the covariance matrices and normalization constants 3 , respectively. For details, see [6,5]. The initial approximation also defines the Galerkin basis {B j (·; t 0 ) : j = 1, .…”

Section: Adaptive Density Propagationmentioning

confidence: 99%

“…The problem is reformulated in terms of the well-established Frobenius-Perron theory, involving the semigroup of FrobeniusPerron operators. In order to approximate the semi-group numerically, we adopt and substantially extend the adaptive Gaussian-based particle method TRAIL [6] that has originally been developed in the context of molecular dynamics [6] and recently be transferred to reaction systems [5]. The approach is based on two ingredients, (i) a time-dependent Galerkin ansatz space of Gaussian basis functions , and (ii) a propagation of the density w.r.t.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Approach for Modelling Variability in Pharmacokinetics

Weiße

Horenko

Huisinga

2006

Computational Life Sciences II

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Abstract. We present an improved adaptive approach for studying systems of ODEs affected by parameter variability and state space uncertainty. Our approach is based on a reformulation of the ODE problem as a transport problem of a probability density describing the evolution of the ensemble of systems in time. The resulting multidimensional problem is solved by representing the probability density w.r.t. an adaptively chosen Galerkin ansatz space of Gaussian distributions. Due to our improvements in adaptivity control, we substantially improved the overall performance of the original algorithm and moreover inherited the theoretical property that the number of Gaussian distribution stays constant for linear ODEs to the numerical scheme. We illustrate the approach in application to dynamical systems describing the pharmacokinetics of drugs and xenobiotics, where variability in physiological parameters is important to be considered.

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Adaptive approach for nonlinear sensitivity analysis of reaction kinetics

Cited by 14 publications

References 11 publications

Discrimination of dynamical system models for biological and chemical processes

Discrimination of dynamical system models for biological and chemical processes

Adaptive Gaussian particle method for the solution of the Fokker‐Planck equation

Adaptive Approach for Modelling Variability in Pharmacokinetics

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