用同调理论优化储层网络结构，提升时序数据处理性能。
Topology Structure Optimization of Reservoirs Using GLMY Homology
- 基于持久性GLMY同调理论分析储层拓扑结构
- 通过调整一维同调环优化结构，显著提升性能
- 适合研究神经网络拓扑与动态系统建模的学者
储层网络是高效的时间序列处理模型，其性能高度依赖于网络结构。然而，由于缺乏合适的数学工具，储层的拓扑结构及其性能难以分析。本文利用持久性GLMY同调理论研究储层拓扑结构，提出一种性能优化方法。研究表明，储层性能与一维GLMY同调群密切相关。据此，我们通过修改一维同调群的最小代表圈来优化储层结构。实验验证表明，储层性能同时受结构设计和数据集周期性的影响。
原文摘要 · Abstract (English)
Reservoir is an efficient network for time series processing. It is well known that network structure is one of the determinants of its performance. However, the topology structure of reservoirs, as well as their performance, is hard to analyzed, due to the lack of suitable mathematical tools. In this paper, we study the topology structure of reservoirs using persistent GLMY homology theory, and develop a method to improve its performance. Specifically, it is found that the reservoir performance is closely related to the one-dimensional GLMY homology groups. Then, we develop a reservoir structure optimization method by modifying the minimal representative cycles of one-dimensional GLMY homology groups. Finally, by experiments, it is validated that the performance of reservoirs is jointly influenced by the reservoir structure and the periodicity of the dataset.
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