标题： 一种混合的空间插值框架：融合数据驱动与领域知识 显示英文标题

标题： A Hybrid Framework for Spatial Interpolation: Merging Data-driven with Domain Knowledge

摘要： 通过散乱观测数据集的插值来估计空间分布信息，通常会忽略领域知识在理解空间依赖性方面的重要作用。此外，这些数据集的特征通常仅限于散乱观测点的空间坐标。本文提出了一种混合框架，该框架结合了数据驱动的空间依赖性特征提取与基于规则的空间依赖性函数映射，以增强领域知识。我们在两个对比的应用场景中展示了我们框架的优越性能，突出了其在重建分布场时捕获更局部化空间特征的能力。此外，我们强调了通过应用变换模糊规则增强非线性估计能力的潜力，并量化了与观测数据集相关的固有不确定性。我们的框架通过协同结合观测数据与基于规则的领域知识，引入了一种创新的空间信息估计方法。 显示英文摘要

摘要： Estimating spatially distributed information through the interpolation of scattered observation datasets often overlooks the critical role of domain knowledge in understanding spatial dependencies. Additionally, the features of these data sets are typically limited to the spatial coordinates of the scattered observation locations. In this paper, we propose a hybrid framework that integrates data-driven spatial dependency feature extraction with rule-assisted spatial dependency function mapping to augment domain knowledge. We demonstrate the superior performance of our framework in two comparative application scenarios, highlighting its ability to capture more localized spatial features in the reconstructed distribution fields. Furthermore, we underscore its potential to enhance nonlinear estimation capabilities through the application of transformed fuzzy rules and to quantify the inherent uncertainties associated with the observation data sets. Our framework introduces an innovative approach to spatial information estimation by synergistically combining observational data with rule-assisted domain knowledge.