Collaborative Research: Data Assimilation for Turbulent Flows: Dynamic Model Learning and Solution Capturing

协作研究：湍流数据同化：动态模型学习和解决方案捕获

• 批准号: 2206762
• 负责人: Jared Whitehead
• 金额: $ 17.47万
• 依托单位: Brigham Young University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2206762&HistoricalAwards=false
• 关键词: Collaborative; Research; Data; Assimilation; Turbulent

The world is full of complex, multi-scale phenomena that can be challenging to predict due to their underlying chaotic nature. For example, fast and accurate predictions of weather phenomena (both terrestrial and solar), ocean dynamics, and groundwater flow are vital to economic growth and stability. These predictions typically incorporate computer simulations of mathematical models; however, to make accurate predictions, these models need to be properly "initialized"; that is, they need to know the current state of the system very precisely and the models need to be adjusted based on actual observations of the system in question. For example, in order to accurately predict the weather, models often require the current state of the weather to be known on the scale of a few inches, but weather observation stations are often spaced several miles apart. Since weather is a highly chaotic phenomenon, small errors in the observations and/or sparsity in the actual observations can lead to significant errors in the predictions. To address this issue in the past several decades a collection of techniques known as "data assimilation" have been developed. Data assimilation incorporates observational data into the mathematical model of the system of interest in order to drive the prediction to the correct state. However, the standard data assimilation techniques, known as the Kalman filter and four-dimensional variational (4D-VAR) approaches, are very computationally costly, and major challenges still exist when adapting them to complex systems. Recently, a new algorithm for data assimilation, known as the Azouani-Olson-Titi (AOT) algorithm has emerged as a fast, robust, highly accurate technique which is easy to adapt to a wide variety of models, and which is computationally inexpensive to add to an already existing computational model. This project will not only extend and improve the AOT algorithm, but it will also use new ideas and technologies invented by the PIs and coauthors to adapt the AOT framework to learn more about the underlying mathematical model itself, further improving predictive capabilities. This project fosters mentoring undergraduate and graduate students, interdisciplinary research, and interaction with national labs. The impacts of this project will be far-reaching and will pave the way for new techniques which will greatly speed up data assimilation in simulations of highly complicated fluid flows, introduce novel techniques for parameter learning and model reconstruction, and provide a computational approach to investigating fundamental mathematical problems. The computational technologies and mathematical tools developed will be useful to scientists and engineers in other fields as well.This project builds on previous work of the PIs on the AOT algorithm, which showed that this algorithm can be adapted to learn the (unknown) parameters of the system, and even the form of the model itself, while simultaneously recovering the "true" state of the system. Extensions of the preliminary work will be carried out, and rigorous justification for convergence of the algorithm will be completed for physically interesting systems, including noisy data and sparse-in-time observations. In addition, several extensions of AOT itself will be numerically tested and rigorously investigated: nudging for intermittent observations, as well as nudging based on moving observers. AOT will also be implemented and tested for a multi-physics large-scale model of the Earth's oceans, for the Richards equation for soil moisture, and for a simplified fluids experiment using real-time collected data. This project will optimize observer requirements for better accuracy, significantly lowering costs. The methods described here have the potential to reduce production and computational cost for experiments, making them more useful to researchers working on real world problems. Moreover, novel proof methods will be developed to prove convergence in the cases of nonlinear AOT algorithms, AOT-based on moving observers, AOT-based model recovery, temperature-based AOT, and extensions of AOT to geophysical settings.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

世界充满了复杂的、多尺度的现象，由于其潜在的混沌性质，预测起来具有挑战性。 例如，快速准确地预测天气现象（陆地和太阳）、海洋动力学和地下水流对于经济增长和稳定至关重要。 这些预测通常结合了数学模型的计算机模拟；然而，为了做出准确的预测，这些模型需要进行适当的“初始化”；也就是说，他们需要非常精确地了解系统的当前状态，并且需要根据对相关系统的实际观察来调整模型。 例如，为了准确预测天气，模型通常需要在几英寸的范围内了解当前的天气状态，但气象观测站往往相距数英里。 由于天气是一种高度混乱的现象，观测中的小错误和/或实际观测中的稀疏性可能会导致预测中的重大错误。 为了解决这个问题，在过去的几十年里，一系列被称为“数据同化”的技术被开发出来。 数据同化将观测数据纳入感兴趣系统的数学模型中，以将预测推向正确的状态。 然而，标准数据同化技术，即卡尔曼滤波器和四维变分（4D-VAR）方法，计算成本非常高，并且在将其适应复杂系统时仍然存在重大挑战。 最近，出现了一种新的数据同化算法，称为 Azouani-Olson-Titi (AOT) 算法，它是一种快速、稳健、高精度的技术，易于适应各种模型，并且计算成本低廉添加到已有的计算模型。 该项目不仅将扩展和改进AOT算法，还将利用PI和合著者发明的新思想和技术来调整AOT框架，以更多地了解底层数学模型本身，进一步提高预测能力。 该项目促进本科生和研究生的指导、跨学科研究以及与国家实验室的互动。 该项目的影响将是深远的，将为新技术铺平道路，从而大大加快高度复杂流体流动模拟中的数据同化速度，引入参数学习和模型重建的新技术，并提供一种计算方法来研究基本数学问题。开发的计算技术和数学工具也将对其他领域的科学家和工程师有用。该项目建立在 PI 之前关于 AOT 算法的工作的基础上，该工作表明该算法可以适用于学习（未知）参数系统，甚至模型本身的形式，同时恢复系统的“真实”状态。将进行初步工作的扩展，并将针对物理上有趣的系统（包括噪声数据和稀疏时间观测）完成算法收敛的严格论证。此外，AOT 本身的几个扩展将进行数值测试和严格研究：间歇性观察的推动，以及基于移动观察者的推动。 AOT 还将针对地球海洋的多物理场大型模型、土壤湿度的理查兹方程以及使用实时收集的数据进行简化的流体实验进行实施和测试。该项目将优化观察员的要求，以提高准确性，从而显着降低成本。这里描述的方法有可能降低实验的生产和计算成本，使它们对研究现实世界问题的研究人员更有用。此外，还将开发新颖的证明方法来证明非线性 AOT 算法、基于移动观察者的 AOT、基于 AOT 的模型恢复、基于温度的 AOT 以及 AOT 到地球物理设置的扩展情况下的收敛性。该奖项反映了 NSF 的法定要求使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Concurrent MultiParameter Learning Demonstrated on the Kuramoto--Sivashinsky Equation

Kuramoto-Sivashinsky 方程演示的并发多参数学习

• DOI: 10.1137/21m1426109
• 发表时间: 2022-10
• 期刊: SIAM Journal on Scientific Computing
• 影响因子: 3.1
• 作者: Pachev, Benjamin;Whitehead, Jared P.;McQuarrie, Shane A.
• 通讯作者: McQuarrie, Shane A.

Dynamically learning the parameters of a chaotic system using partial observations

使用部分观测动态学习混沌系统的参数

• DOI: 10.3934/dcds.2022033
• 发表时间: 2022-01
• 期刊: Discrete and Continuous Dynamical Systems
• 影响因子: 1.1
• 作者: Carlson, Elizabeth;Hudson, Joshua;Larios, Adam;Martinez, Vincent R.;Ng, Eunice;Whitehead, Jared P.
• 通讯作者: Whitehead, Jared P.