An inverse problem in reaction kinetics

Santosa, Fadil; Weitz, Benjamin

doi:10.1007/s10910-011-9835-2

Cited by 9 publications

(7 citation statements)

References 8 publications

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“…We further analyze how the following modifications-the absolute Newton step and the Armijo second-order line search-influence frequency of convergence. To estimate the influence, provided by the absolute Newton step, we calculate a quantity of absolute = [total percent of points converged to global solution given the absolute Newton step modification (options 5-8, 10) is used] -[total percent of points converged to global solution given the modification is not used (options [1][2][3][4]9)]. For example, the influence provided by the absolute Newton step for the A → B → C reaction is A→B→C = [50 + 50 + 63 + 63 + 38]% -[38 + 38 + 50 + 50 + 25]% = 264% -201% = 63%.…”

Section: Resultsmentioning

confidence: 99%

“…Second, multiple solutions may exist due to nonuniqueness of the kinetic model itself: Different chemical networks can account for the same experimental data, a well‐known external factor . Santosa and Weitz state the problem: “The mathematical model of the kinetic system leads to a system of ordinary differential equations…It is possible for a system involving multiple species with different reaction rates to lead to exactly the same set of differential equations.” Balogh et al have conducted a detailed study on this topic and state that kinetic schemes involving consecutive (first‐order) reactions can be easily confused with those involving reversible second‐order or pseudo–first‐order reactions. They note that if there exist several kinetic schemes describing experimental data equally well, then it is not possible to choose the right model without additional chemical information, for example, knowledge of the stoichiometry, the number of absorbing species, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Second, multiple solutions may exist due to nonuniqueness of the kinetic model itself: Different chemical networks can account for the same experimental data, a well-known external factor. Santosa and Weitz [2] state the problem: "The mathematical model of the kinetic system leads to a system of ordinary differential equations . .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Петров

Dergachev

2017

Int. J. Chem. Kinet.

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The same experimental data can often be equally well described by multiple mathematically equivalent kinetic schemes. In the present work, we investigate several model‐fitting algorithms and their ability to distinguish between mechanisms and derive the correct kinetic parameters for several different reaction classes involving consecutive reactions. We have conducted numerical experiments using synthetic experimental data for six classes of consecutive reactions involving different combinations of first‐ and second‐order processes. The synthetic data mimic time‐dependent absorption data as would be obtained from spectroscopic investigations of chemical kinetic processes. The connections between mathematically equivalent solutions are investigated, and analytical expressions describing these connections are derived. Ten optimization algorithms based on nonlinear least squares methods are compared in terms of their computational cost and frequency of convergence to global solutions. Performance is discussed, and a preferred method is recommended. A response surface visualization technique of projecting five‐dimensional data onto the three‐dimensional search space of the minimal function values is developed.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Equivalency of Kinetic Schemes: Causes and an Analysis of Some Model Fitting Algorithms

Петров

Dergachev

2017

Int. J. Chem. Kinet.

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“…Kerner Polynomialization and Ψ Kow ) are proven to fully preserve deterministic dynamics, thus there is no point in using approximate expansions (which provide approximate dynamics and does not even aim for full preservation of information) for chemical inversion if even precise methods available do not succeed in preserving deterministic expectations in the chemical simulation. However, deterministic dynamics are known to manifest differently in stochastic settings 3 , and it may very well turn out that series expansions are more optimal for chemical inversion.…”

Section: Closing Remarksmentioning

confidence: 99%

“…This induces the second category of inverse problems, where a set of desirable properties are provided (such as time series realizations), and compatible reaction networks are constructed. It has been shown that unique inversion is impossible in deterministic settings, due to differing reaction networks translating into identical ODE systems describing their dynamics [3]. However, a general inversion framework for designing any reaction network compatible with any desired property of interest has yet to be presented.…”

Section: Introductionmentioning

confidence: 99%

Chemical Integration of ODEs using Idealized Abstract Solutions

Lee¹

2023

Preprint

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In this work, we propose a general inversion framework to non-uniquely invert a very large class of ordinary differential equations (ODEs) into chemical reaction networks. A thorough treatment of the relevant chemical reaction network theory from the literature is given. Various simulation results are provided to augment the selection procedure for the inverse framework, where a previously known kineticization strategy is shown to be deterministically excellent but undesirable in chemical simulations. The utility of the framework is verified by simulating reaction network forms of meaningful ODE systems, and their time series are analyzed. In particular, we provide simulations of deterministic chaotic attractors whose newly discovered reaction networks are non-equivalent with any existing chemical interpretations within the literature, as well as presenting exemplary figures which may form a roadmap to the successful biochemical implementation of the integration of ODE systems.

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