Abstract A robust, low-order POD-based state estimator, also known as an observer, for the challenging fluid-dynamics test-case of uncertain 2D Boussinesq equations is presented in this paper. The observer design is based on the methodology recently introduced by the authors 1 , which incorporates robustness to bounded model uncertainties, and data-driven auto-tuning of the observer gains. An extensive numerical study on the 2D Boussinesq equations with parametric uncertainties demonstrates the performance of our observer. The reported numerical results show that the proposed observer allows estimation of the complete temperature and velocity fields from a reduced number of measurements. It is also shown that the proposed observer is robust to changes or errors in the value of the Reynolds number. In other words, we show that we can design the observer based on an assumed uncertain value for the Reynolds number, and be able to estimate the temperature and velocity solutions corresponding to actual Reynolds number.

中文翻译：

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具有参数不确定性的二维 Boussinesq 方程降阶模型的数据驱动鲁棒状态估计

摘要 本文提出了一种鲁棒的、基于低阶 POD 的状态估计器，也称为观察器，用于不确定二维 Boussinesq 方程的具有挑战性的流体动力学测试用例。观测器设计基于作者 1 最近引入的方法，该方法结合了对有界模型不确定性的鲁棒性，以及观测器增益的数据驱动自动调整。对具有参数不确定性的 2D Boussinesq 方程的广泛数值研究证明了我们观察者的性能。报告的数值结果表明，所提出的观测器允许通过减少的测量次数来估计完整的温度和速度场。还表明，所提出的观测器对雷诺数值的变化或误差具有鲁棒性。换句话说，