提出可量化不确定性的动态降维模型,提升非定常流模拟的精度与可信度。
UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flows
- 用变分自编码器+注意力机制实现参数化动态降维
- 预测同时输出置信度,支持跨参数空间高效采样
- 适合需高可靠性模拟的工程流体场景
降阶模型(ROM)在流体力学中通过低成本预测发挥关键作用,但要广泛适用,必须兼具跨工况泛化能力与预测置信度。现有数据驱动方法虽改善了瞬态环境下的非线性降维,但在鲁棒性与参数化方面仍存挑战。本文提出一种专为非定常流设计的非线性降维策略,集成参数化与不确定性量化。采用变分自编码器(VAE)结合变分推断实现置信度估计,利用注意力机制增强的潜在空间变压器预测动力系统演化。注意力机制对序列建模与外部参数依赖性的捕捉提升了跨多种动力学行为的泛化能力。预测结果附带置信度,支持更明智的决策,并可用于低成本采样参数空间,无需全域评估数据即可预先提升模型性能。
原文摘要 · Abstract (English)
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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