UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908348873441280 |
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| author | Zighed, Ismaël Thome, Nicolas Gallinari, Patrick Sayadi, Taraneh |
| author_facet | Zighed, Ismaël Thome, Nicolas Gallinari, Patrick Sayadi, Taraneh |
| contents | Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise well across different regimes, but also provide a measure of confidence in their predictions. While recent data-driven approaches have begun to address nonlinear reduction techniques to improve predictions in transient environments, challenges remain in terms of robustness and parametrisation. In this work, we present a nonlinear reduction strategy specifically designed for transient flows that incorporates parametrisation and uncertainty quantification. Our reduction strategy features a variational auto-encoder (VAE) that uses variational inference for confidence measurement. We use a latent space transformer that incorporates recent advances in attention mechanisms to predict dynamical systems. Attention's versatility in learning sequences and capturing their dependence on external parameters enhances generalisation across a wide range of dynamics. Prediction, coupled with confidence, enables more informed decision making and addresses the need for more robust models. In addition, this confidence is used to cost-effectively sample the parameter space, improving model performance a priori across the entire parameter space without requiring evaluation data for the entire domain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_23236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows Zighed, Ismaël Thome, Nicolas Gallinari, Patrick Sayadi, Taraneh Machine Learning Fluid Dynamics Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise well across different regimes, but also provide a measure of confidence in their predictions. While recent data-driven approaches have begun to address nonlinear reduction techniques to improve predictions in transient environments, challenges remain in terms of robustness and parametrisation. In this work, we present a nonlinear reduction strategy specifically designed for transient flows that incorporates parametrisation and uncertainty quantification. Our reduction strategy features a variational auto-encoder (VAE) that uses variational inference for confidence measurement. We use a latent space transformer that incorporates recent advances in attention mechanisms to predict dynamical systems. Attention's versatility in learning sequences and capturing their dependence on external parameters enhances generalisation across a wide range of dynamics. Prediction, coupled with confidence, enables more informed decision making and addresses the need for more robust models. In addition, this confidence is used to cost-effectively sample the parameter space, improving model performance a priori across the entire parameter space without requiring evaluation data for the entire domain. |
| title | UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows |
| topic | Machine Learning Fluid Dynamics |
| url | https://arxiv.org/abs/2503.23236 |