Data-driven, variational model reduction of high-dimensional reaction networks

Katsoulakis, Markos A.; Vilanova, Pedro

doi:10.1016/j.jcp.2019.108997

Cited by 14 publications

(11 citation statements)

References 102 publications

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“…x 1 (19). As the architecture complexity of the networks increases from left to right, the models reach lower validation loss (see Table 1) and we get better accuracy of the slow variable (bottom row).…”

Section: Measuring Local Non-orthogonality To the Fast Directionsmentioning

confidence: 86%

“…To this end, we consider a four-dimensional version of system (20) with a one-dimensional slow variable (D s = 1, D f = 3). This setting allows us to visualize, as in the previous section, the accuracy of the encoder by plotting its values on the test dataset against the corresponding values of the slow map (19). We compare the results of such 1, for which we inspect the reconstruction of the slow manifold and compare the values of the slow view to the slow variable (19).…”

Section: Testing the Slow Viewmentioning

confidence: 99%

“…However, the long term evolution of certain aspects of this processes can often be described by much simpler reduced dynamics that captures the essential behavior. Thus, knowing the correct aspects allows to build efficient model reduction techniques that not only decrease the dimension but also accelerate the simulations [8,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Discovery of slow variables in a class of multiscale stochastic systems via neural networks

Zielinski,

Hesthaven

2021

Preprint

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Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential to provide a general framework to automatically discover such representations. In this paper, we consider multiscale stochastic systems with local slow-fast time scale separation and propose a new method to encode in an artificial neural network a map that extracts the slow representation from the system. The architecture of the network consists of an encoder-decoder pair that we train in a supervised manner to learn the appropriate low-dimensional embedding in the bottleneck layer. We test the method on a number of examples that illustrate the ability to discover a correct slow representation. Moreover, we provide an error measure to assess the quality of the embedding and demonstrate that pruning the network can pinpoint an essential coordinates of the system to build the slow representation.

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Section: Measuring Local Non-orthogonality To the Fast Directionsmentioning

confidence: 86%

Section: Testing the Slow Viewmentioning

confidence: 99%

See 1 more Smart Citation

Discovery of slow variables in a class of multiscale stochastic systems via neural networks

Zielinski,

Hesthaven

2021

Preprint

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“…Bayesian methods for chemical reaction kinetics have also been discussed extensively in the literature, especially for model inference and model reduction for large chemical reaction networks [ 5–8 ] or polymer reaction kinetics, [ 9 ] in relation to specific chemical contexts as catalysis, [ 10 ] or combustion, [ 11 ] for large experimental data [ 12 ] or high dimension cases, [ 13 ] as well as for more theoretical aspects like approximation quality and sparsity. [ 14 ] In contrast, applications to polymer chemistry, especially applications to polymer reaction kinetics with a focus on Bayesian PE, were rarely considered: For example, in [15], a Bayesian framework including PE is presented for surfactant‐polymer flooding with no focus on polymer reactions.…”

Section: Introductionmentioning

confidence: 99%

Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples

Wulkow

Telgmann²,

Hungenberg³

et al. 2021

Macro Theory & Simulations

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Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two‐article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.

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“…Bayesian methods for chemical reaction kinetics have also been discussed extensively in the literature, especially for model inference and model reduction for large chemical reaction networks [5][6][7][8] or polymer reaction kinetics, [9] in relation to specific chemical contexts as catalysis, [10] or combustion, [11] for large experimental data [12] or high dimension cases, [13] as well as for more theoretical aspects like approximation quality and sparsity. [14] In contrast, applications to polymer chemistry, especially applications to polymer reaction kinetics with a focus on Bayesian PE, were rarely considered: For example, in [15], a Bayesian framework including PE is presented for surfactantpolymer flooding with no focus on polymer reactions.…”

Section: Introductionmentioning

confidence: 99%

Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples

Wulkow¹,

Telgmann²,

Hungenberg³

et al. 2021

Macro Theory & Simulations

View full text Add to dashboard Cite

Two different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two-article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.

show abstract

Data-driven, variational model reduction of high-dimensional reaction networks

Cited by 14 publications

References 102 publications

Discovery of slow variables in a class of multiscale stochastic systems via neural networks

Discovery of slow variables in a class of multiscale stochastic systems via neural networks

Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples

Deterministic and Stochastic Parameter Estimation for Polymer Reaction Kinetics I: Theory and Simple Examples

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