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

2025-03-29

AI Summary

To address the poor robustness, limited parameter generalization, and lack of predictive confidence in dynamic reduced-order modeling (ROM) of nonstationary flow fields, this paper proposes a novel ROM framework integrating variational autoencoders (VAEs) with attention mechanisms. We introduce a latent-space Transformer into the VAE architecture—first of its kind—to jointly model the dynamics and uncertainty of flow-field latent variables. Furthermore, we devise an uncertainty-aware active sampling strategy to enhance parameter-space exploration efficiency. The method achieves high-fidelity reconstruction of transient flow fields across the full parameter domain under sparse training data, significantly improving cross-regime generalizability. Crucially, the predicted uncertainty is physically interpretable and empirically verifiable, establishing a new paradigm for trustworthy ROMs.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

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• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Develops a dynamic reduced-order model for unsteady flows with uncertainty quantification
• Enhances robustness and generalization in transient flow predictions using VAE
• Uses attention-based latent space transformer to improve parameter space sampling

Innovation

• VAE for uncertainty quantification in ROMs
• Attention-based latent space transformer for dynamics
• Confidence-driven parameter space sampling