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 generalize 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 parametrization. In this work, we present a nonlinear reduction strategy specifically designed for transient flows that incorporates parametrization and uncertainty quantification. Our reduction strategy features a variational autoencoder 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 generalization 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.

Close

PrevNext

View figure in article

• Nonlinear dynamics in fluids
• Dynamical systems
• Machine learning