Using machine learning models to explore the solution space of large nonlinear systems underlying flowsheet simulations with constraints

Ludl, Patrick Otto; Heese, Raoul; Höller, Johannes; Asprion, Norbert; Bortz, Michael

doi:10.1007/s11705-021-2073-7

Cited by 16 publications

(28 citation statements)

References 19 publications

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“…. ; f ðx D Þ 2 Z which are obtained by means of the training data transformation f from the first training step as defined in (14).…”

Section: Training Of a Regression Model Based On The Transformed Datamentioning

confidence: 99%

“…Concerning the training data transformation f underlying our CASIMAC, we use two approaches. In the first approach, we make the same ansatz (14) for the training data transformation f as in all previous examples, that is,…”

Section: Towards Deep Learningmentioning

confidence: 99%

“…namely, we take f to be the average of three training data transformations of the form (14). In short,…”

Section: Plos Onementioning

confidence: 99%

“…In the present paper, by contrast, we propose a simple latent space representation of the original feature space as the core component of a well-calibrated classifier that also works on less complex data sets. In particular, our method has recently been successfully used for an industrial application [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

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Calibrated simplex-mapping classification

Heese

Walczak²,

Bortz³

et al. 2023

PLoS ONE

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We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular (n − 1)-dimensional simplex, n being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains.

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“…. ; f ðx D Þ 2 Z which are obtained by means of the training data transformation f from the first training step as defined in (14).…”

Section: Training Of a Regression Model Based On The Transformed Datamentioning

confidence: 99%

Section: Towards Deep Learningmentioning

confidence: 99%

“…namely, we take f to be the average of three training data transformations of the form (14). In short,…”

Section: Plos Onementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Calibrated simplex-mapping classification

Heese

Walczak²,

Bortz³

et al. 2023

PLoS ONE

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show abstract

“…The novel contribution presented in this work is a significant improvement of utility functions compared to previous work [19], [20]. These utility functions cover different use cases (convergence, feasibility, optimization, cf.…”

Section: Introductionmentioning

confidence: 99%

Adaptively exploring the feature space of flowsheets

Bubel

2023

Preprint

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Simulation and optimization of chemical flowsheets rely on the solution of a large number of non-linear equations. Finding such solutions can be supported by constructing machine-learning based surrogates, relating features and outputs by simple, explicit functions. In order to generate training data for those surrogates computationally efficiently, schemes to adaptively sample the feature space are mandatory. In this article, we present a novel family of utility functions to favor an adaptive, Bayesian exploration of the feature space in order to identify regions that are convergent, fulfill customized inequality constraints and are Pareto-optimal with respect to conflicting objectives. The benefit is illustrated by small toy-examples as well as by industrially relevant chemical flowsheets.

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Adaptively exploring the feature space of flowsheets

Höller,

Bubel,

Heese

et al. 2024

AIChE Journal

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Simulation and optimization of chemical flowsheets rely on the solution of a large number of nonlinear equations. Finding such solutions can be supported by constructing machine learning‐based surrogate models, relating features and outputs by simple, explicit functions. In order to generate training data for those surrogate models computationally efficiently, schemes to adaptively sample the feature space are mandatory. In this article, we present a novel family of utility functions to favor an adaptive, Bayesian exploration of the feature space in order to identify regions that are convergent and fulfill customized inequality constraints. Moreover, points close to the Pareto‐optimal domain with respect to conflicting objectives can be identified, serving as good start values for a multicriteria optimization of the flowsheet. The benefit is illustrated by small toy‐examples as well as by industrially relevant chemical flowsheets.

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Using machine learning models to explore the solution space of large nonlinear systems underlying flowsheet simulations with constraints

Cited by 16 publications

References 19 publications

Calibrated simplex-mapping classification

Calibrated simplex-mapping classification

Adaptively exploring the feature space of flowsheets

Adaptively exploring the feature space of flowsheets

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