Efficient forecasting of chaotic systems with block-diagonal and binary reservoir computing

Abstract

The prediction of complex nonlinear dynamical systems with the help of machine learning has become increasingly popular in different areas of science. In particular, reservoir computers, also known as echo-state networks, turned out to be a very powerful approach, especially for the reproduction of nonlinear systems. The reservoir, the key component of this method, is usually constructed as a sparse, random network that serves as a memory for the system. In this work, we introduce block-diagonal reservoirs, which implies that a reservoir can be composed of multiple smaller reservoirs, each with its own dynamics. Furthermore, we take out the randomness of the reservoir by using matrices of ones for the individual blocks. This breaks with the widespread interpretation of the reservoir as a single network. In the example of the Lorenz and Halvorsen systems, we analyze the performance of block-diagonal reservoirs and their sensitivity to hyperparameters. We find that the performance is comparable to sparse random networks and discuss the implications with regard to scalability, explainability, and hardware realizations of reservoir computers.

Complex quantum networks: a topical review

“…Less computational efficient but very much used due to its transparent interpretation, is the community detection algorithm that finds the hierarchical clustering of the network by iteratively removing links with high betweenness centrality, a network science measure that is higher on links that bridge across different communities. Strong modularity has been found to play a role in for example reservoir computing [67][68][69], a form of machine learning where a classical or a quantum system plays the role of a recurrent neural network.…”

The connectivity degree controls the difficulty in reservoir design of random boolean networks

“…This approach may illuminate the unique characteristics of attractors that contribute to performance. With a more nuanced comprehension of the relationship between attractor dynamics and performance, future research could leverage multiple attractor categories within a pool of multiple reservoirs, as demonstrated in Ma et al ( 2023 ), using a block-diagonal weight matrix. This strategy could potentially enhance the computational capabilities while reducing the computational costs of RBN reservoirs.…”