Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation
When training a parametric surrogate to represent a real-world complex system in real time, there is a common assumption that the values of the parameters defining the system are known with absolute confidence. Consequently, during the training process, our focus is directed exclusively towards opti...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Technologies |
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| Online Access: | https://www.mdpi.com/2227-7080/12/2/20 |
| _version_ | 1797296962081390592 |
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| author | Sergio Torregrosa David Muñoz Vincent Herbert Francisco Chinesta |
| author_facet | Sergio Torregrosa David Muñoz Vincent Herbert Francisco Chinesta |
| author_sort | Sergio Torregrosa |
| collection | DOAJ |
| description | When training a parametric surrogate to represent a real-world complex system in real time, there is a common assumption that the values of the parameters defining the system are known with absolute confidence. Consequently, during the training process, our focus is directed exclusively towards optimizing the accuracy of the surrogate’s output. However, real physics is characterized by increased complexity and unpredictability. Notably, a certain degree of uncertainty may exist in determining the system’s parameters. Therefore, in this paper, we account for the propagation of these uncertainties through the surrogate using a standard Monte Carlo methodology. Subsequently, we propose a novel regression technique based on optimal transport to infer the impact of the uncertainty of the surrogate’s input on its output precision in real time. The OT-based regression allows for the inference of fields emulating physical reality more accurately than classical regression techniques, including advanced ones. |
| first_indexed | 2024-03-07T22:12:24Z |
| format | Article |
| id | doaj.art-c4374751888f42bab494037b2b1e86b4 |
| institution | Directory Open Access Journal |
| issn | 2227-7080 |
| language | English |
| last_indexed | 2024-03-07T22:12:24Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Technologies |
| spelling | doaj.art-c4374751888f42bab494037b2b1e86b42024-02-23T15:36:15ZengMDPI AGTechnologies2227-70802024-02-011222010.3390/technologies12020020Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty EvaluationSergio Torregrosa0David Muñoz1Vincent Herbert2Francisco Chinesta3PIMM Laboratory, Arts et Métiers Institute of Technology, 151 Boulevard de l’Hopital, 75013 Paris, FrancePIMM Laboratory, Arts et Métiers Institute of Technology, 151 Boulevard de l’Hopital, 75013 Paris, FranceSTELLANTIS, 10 Boulevard de l’Europe, 78300 Poissy, FrancePIMM Laboratory, Arts et Métiers Institute of Technology, 151 Boulevard de l’Hopital, 75013 Paris, FranceWhen training a parametric surrogate to represent a real-world complex system in real time, there is a common assumption that the values of the parameters defining the system are known with absolute confidence. Consequently, during the training process, our focus is directed exclusively towards optimizing the accuracy of the surrogate’s output. However, real physics is characterized by increased complexity and unpredictability. Notably, a certain degree of uncertainty may exist in determining the system’s parameters. Therefore, in this paper, we account for the propagation of these uncertainties through the surrogate using a standard Monte Carlo methodology. Subsequently, we propose a novel regression technique based on optimal transport to infer the impact of the uncertainty of the surrogate’s input on its output precision in real time. The OT-based regression allows for the inference of fields emulating physical reality more accurately than classical regression techniques, including advanced ones.https://www.mdpi.com/2227-7080/12/2/20uncertainty quantificationMonte Carloartificial intelligenceparametric metamodeling |
| spellingShingle | Sergio Torregrosa David Muñoz Vincent Herbert Francisco Chinesta Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation Technologies uncertainty quantification Monte Carlo artificial intelligence parametric metamodeling |
| title | Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation |
| title_full | Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation |
| title_fullStr | Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation |
| title_full_unstemmed | Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation |
| title_short | Parametric Metamodeling Based on Optimal Transport Applied to Uncertainty Evaluation |
| title_sort | parametric metamodeling based on optimal transport applied to uncertainty evaluation |
| topic | uncertainty quantification Monte Carlo artificial intelligence parametric metamodeling |
| url | https://www.mdpi.com/2227-7080/12/2/20 |
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