Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning
In this study, the numerical solutions to the Elder problem are analyzed using Big Data technologies and data-driven approaches. The steady-state solutions to the Elder problem are investigated with regard to Rayleigh numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/Ma...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Big Data and Cognitive Computing |
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| Online Access: | https://www.mdpi.com/2504-2289/7/1/52 |
| _version_ | 1797613464345116672 |
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| author | Roman Khotyachuk Klaus Johannsen |
| author_facet | Roman Khotyachuk Klaus Johannsen |
| author_sort | Roman Khotyachuk |
| collection | DOAJ |
| description | In this study, the numerical solutions to the Elder problem are analyzed using Big Data technologies and data-driven approaches. The steady-state solutions to the Elder problem are investigated with regard to Rayleigh numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>a</mi></mrow></semantics></math></inline-formula>), grid sizes, perturbations, and other parameters of the system studied. The complexity analysis is carried out for the datasets containing different solutions to the Elder problem, and the time of the highest complexity of numerical solutions is estimated. An approach to the identification of transient fingers and the visualization of large ensembles of solutions is proposed. Predictive models are developed to forecast steady states based on early-time observations. These models are classified into three possible types depending on the features (predictors) used in a model. The numerical results of the prediction accuracy are given, including the estimated confidence intervals for the accuracy, and the estimated time of 95% predictability. Different solutions, their averages, principal components, and other parameters are visualized. |
| first_indexed | 2024-03-11T06:55:10Z |
| format | Article |
| id | doaj.art-17970d71962c4d72bc39f8f78e67c35b |
| institution | Directory Open Access Journal |
| issn | 2504-2289 |
| language | English |
| last_indexed | 2024-03-11T06:55:10Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Big Data and Cognitive Computing |
| spelling | doaj.art-17970d71962c4d72bc39f8f78e67c35b2023-11-17T09:37:17ZengMDPI AGBig Data and Cognitive Computing2504-22892023-03-01715210.3390/bdcc7010052Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine LearningRoman Khotyachuk0Klaus Johannsen1Faculty of Mathematics and Natural Sciences, University of Bergen, 5020 Bergen, NorwayNORCE Norwegian Research Center AS, 5008 Bergen, NorwayIn this study, the numerical solutions to the Elder problem are analyzed using Big Data technologies and data-driven approaches. The steady-state solutions to the Elder problem are investigated with regard to Rayleigh numbers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>a</mi></mrow></semantics></math></inline-formula>), grid sizes, perturbations, and other parameters of the system studied. The complexity analysis is carried out for the datasets containing different solutions to the Elder problem, and the time of the highest complexity of numerical solutions is estimated. An approach to the identification of transient fingers and the visualization of large ensembles of solutions is proposed. Predictive models are developed to forecast steady states based on early-time observations. These models are classified into three possible types depending on the features (predictors) used in a model. The numerical results of the prediction accuracy are given, including the estimated confidence intervals for the accuracy, and the estimated time of 95% predictability. Different solutions, their averages, principal components, and other parameters are visualized.https://www.mdpi.com/2504-2289/7/1/52scientific Big DataElder problemnumerical PDEcomplexity analysismachine learning |
| spellingShingle | Roman Khotyachuk Klaus Johannsen Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning Big Data and Cognitive Computing scientific Big Data Elder problem numerical PDE complexity analysis machine learning |
| title | Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning |
| title_full | Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning |
| title_fullStr | Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning |
| title_full_unstemmed | Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning |
| title_short | Analysis of the Numerical Solutions of the Elder Problem Using Big Data and Machine Learning |
| title_sort | analysis of the numerical solutions of the elder problem using big data and machine learning |
| topic | scientific Big Data Elder problem numerical PDE complexity analysis machine learning |
| url | https://www.mdpi.com/2504-2289/7/1/52 |
| work_keys_str_mv | AT romankhotyachuk analysisofthenumericalsolutionsoftheelderproblemusingbigdataandmachinelearning AT klausjohannsen analysisofthenumericalsolutionsoftheelderproblemusingbigdataandmachinelearning |