Topology structure optimization of reservoirs using GLMY homology

Reservoirs are efficient networks for time-series processing. It is well known that the network structure is one of the determinants of their performance. However, the topological structure of reservoirs, as well as their performance, is hard to analyze due to the lack of suitable mathematical tools. In this paper, we study the topological structure of reservoirs using persistent GLMY homology theory and develop a method to improve their performance. Specifically, we find that reservoir performance is correlated with 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, through experiments, we validate that the performance of reservoirs is jointly influenced by the reservoir structure and the periodicity of the dataset.