UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows

• URL: http://arxiv.org/abs/2503.23236v2
• Date: Tue, 29 Apr 2025 15:51:44 GMT
• Title: UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows
• Authors: Ismaël Zighed, Nicolas Thome, Patrick Gallinari, Taraneh Sayadi,
• Abstract summary: Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions.<n>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.<n>We present a nonlinear reduction strategy specifically designed for transient flows.
• Score: 27.50487430169627
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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