标题： 两相流模型在多孔介质中的集合评分过滤数据同化 显示英文标题

标题： Ensemble Score Filter for Data Assimilation of Two-Phase Flow Models in Porous Media

摘要： 数值建模和模拟多相流在多孔介质中的流动具有挑战性，这是由于关键参数（如渗透率）的不确定性。 为了解决这些挑战，我们提出了一种计算框架，利用新型集合评分滤波器（EnSF）来提高多孔介质中多相流系统的状态估计精度。 两相流模型的正向模拟是通过混合有限元方法实现的，这确保了对压力、速度和饱和度的准确近似。 EnSF利用基于评分的扩散模型来高效地近似过滤分布，避免了基于神经网络方法的计算成本。 通过结合显式评分近似和解析更新机制，EnSF克服了退化问题，并以最小的计算开销处理高维非线性过滤。 数值实验展示了EnSF在渗透率不确定和观测数据不完整的情况下的能力。 显示英文摘要

摘要： Numerical modeling and simulation of two-phase flow in porous media is challenging due to the uncertainties in key parameters, such as permeability. To address these challenges, we propose a computational framework by utilizing the novel Ensemble Score Filter (EnSF) to enhance the accuracy of state estimation for two-phase flow systems in porous media. The forward simulation of the two-phase flow model is implemented using a mixed finite element method, which ensures accurate approximation of the pressure, the velocity, and the saturation. The EnSF leverages score-based diffusion models to approximate filtering distributions efficiently, avoiding the computational expense of neural network-based methods. By incorporating a closed-form score approximation and an analytical update mechanism, the EnSF overcomes degeneracy issues and handles high-dimensional nonlinear filtering with minimal computational overhead. Numerical experiments demonstrate the capabilities of EnSF in scenarios with uncertain permeability and incomplete observational data.