标题： 减轻集合数据同化中的方差损失：基于机器学习和无距离的局域化 显示英文标题

标题： Mitigating loss of variance in ensemble data assimilation: machine learning-based and distance-free localization

摘要： 我们提出了两种新的方法，这些方法基于/受机器学习的启发，用于表格数据和无距离定位，以增强集合数据同化的协方差估计。主要目标是通过减轻采样误差导致的方差损失来提高数据同化结果。我们还分析了几种机器学习模型的适用性以及协方差估计的准确性和计算成本之间的平衡。我们引入了两种无距离定位技术，利用专门针对表格数据的机器学习方法。这些方法被集成到集合平滑器多数据同化（ES-MDA）框架中。结果表明，所提出的定位方法提高了协方差的准确性，并增强了数据同化和不确定性量化结果。使用所提出的方法，我们观察到输入变量的方差损失减少。此外，我们比较了多种机器学习模型，评估了它们在计算成本、协方差估计质量和数据匹配方面的适用性。还研究了集合大小的影响，提供了在准确性和计算效率之间取得平衡的见解。我们的研究结果表明，某些机器学习模型更适合这个问题。本研究介绍了两种新方法，这些方法减轻了基于集合的数据同化中的模型参数方差损失，提供了易于实现且不需要任何额外数值模拟或超参数调整的实际解决方案。 显示英文摘要

摘要： We propose two new methods based/inspired by machine learning for tabular data and distance-free localization to enhance the covariance estimations in an ensemble data assimilation. The main goal is to enhance the data assimilation results by mitigating loss of variance due to sampling errors. We also analyze the suitability of several machine learning models and the balance between accuracy and computational cost of the covariance estimations. We introduce two distance-free localization techniques leveraging machine learning methods specifically tailored for tabular data. The methods are integrated into the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) framework. The results show that the proposed localizations improve covariance accuracy and enhance data assimilation and uncertainty quantification results. We observe reduced variance loss for the input variables using the proposed methods. Furthermore, we compare several machine learning models, assessing their suitability for the problem in terms of computational cost, and quality of the covariance estimation and data match. The influence of ensemble size is also investigated, providing insights into balancing accuracy and computational efficiency. Our findings demonstrate that certain machine learning models are more suitable for this problem. This study introduces two novel methods that mitigate variance loss for model parameters in ensemble-based data assimilation, offering practical solutions that are easy to implement and do not require any additional numerical simulation or hyperparameter tuning.