融合深度神经网络与地理加权的时空非平稳关系建模方法

There are several disadvantages of existing geographically weighted regression and its extended methods, such as inadequate description and expression for space-time proximity, difficulties in the complicated construction of weighting kernels and the accurate estimation of spatio-temporal non-stationarity. To resolve the mentioned problems and improve the ability of non-stationary relationship modelling, the theories and methods of artificial intelligence are introduced to fully utilize its superior computing and fitting abilities. Based on the space and time distance metrics, a multi-level space-time deep neural network is designed to realize the unified representation and parametric description of spatio-temporal proximity. Aiming at the accurate construction of weighting kernel function, a geo-weighted neural network is established by incorporating multiple linear regression and neural network model. Considering the spatio-temporal weighting features, an adaptive learning rate training algorithm is proposed. Then, using the neural network system's dynamic learning and iterative optimization capability, efficient estimation of the spatio-temporal non-stationarity are implemented. Our research is expected to make theoretical innovations and methods breakthroughs in the modelling of non-stationary relationships by fully utilizing the superior computing and fitting abilities of modern deep learning methods. With the goal of unified expression of spatio-temporal proximity and accurate estimation of spatio-temporal non-stationarity, new theory and method of space-time neural network weighted regression are established to comprehensively improve the ability of the non-stationary relationship modelling.

针对现有时空非平稳关系建模方法存在时空邻近关系表达不充分、核函数解算不精准等问题，以人工智能方法为驱动，充分利用深度神经网络的超强非线性拟合与计算能力，解决“时空邻近关系如何统一表达”和“时空非平稳性如何精准解算”两个基础问题。从时空邻近性构造切入，研究时空邻近关系的多层次深度神经网络表达方法，实现复杂时空邻近关系的统一集成与参数化解析；围绕权重核函数的复杂精准解构，建立融合回归分析的地理时空加权神经网络，设计面向时空加权特征的自适应优化训练算法，利用神经网络系统的动态学习与迭代优化能力，实现时空非平稳性的精确解构与高效计算。项目研究有望综合利用现代深度学习方法对于复杂地理系统的拟合与计算优势，实现时空非平稳关系建模的理论创新与模型突破，建立较为完备的地理时空神经网络加权回归新方法体系，全面提升地理时空非平稳关系的建模能力与应用水平。

时空非平稳性解算是分析地理过程内在机理与作用机制的重要方法，是GIS时空统计与推理的基础难题。地理大数据时代，由于数据获取的时空粒度与精度都大幅提升，时空非平稳关系的空间特征更加复杂化、时空维度趋向一体化，使得所需表达的时空邻近关系和时空权重函数的复杂度均显著提高，使得现有的时空非平稳关系建模方法面临“时空邻近关系表达不充分”和“核函数时空非平稳性解算不精准”的问题。.本项目充分融合时空加权思想和深度神经网络模型，提出了基于深度神经网络的时空邻近关系统一表达理论和基于地理时空加权神经网络的非平稳性精准解算模型，并构建了其诊断分析方法，形成了地理时空神经网络加权回归理论与方法体系，实现了时空邻近关系的充分表达和时空非平稳性的精确计算。项目通过模拟数据集和现实应用案例对模型方法进行了充分论证，相较于经典时空回归模型，地理时空神经网络加权回归模型具有更高的拟合精度和更优的预测性能，在时空非平稳性解算方面具有显著的优越性，并在海洋、大气和社会经济等领域开展了应用，实现了近岸海域水质与富营养化状况变化评价、全国大气污染物大面空间精准估计以及城市房价空间格局分析与影响因素探究。.项目建立了一套较为完备的地理时空神经网络加权回归新方法，得到了国内外同行的积极引用和使用，提升了地理时空非平稳关系的精度与应用水平，具备积极的学术影响力。相关成果发表论文17篇，其中SCI/SSCI论文14篇，标志性论文在IJGIS等期刊上发表。