Ohkubo Akane, Inubushi Masanobu
Department of Applied Mathematics, Tokyo University of Science, Shinjuku, Tokyo, 162-8601, Japan.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK.
Sci Rep. 2024 Dec 28;14(1):30918. doi: 10.1038/s41598-024-81880-3.
Reservoir computing is a machine learning framework that exploits nonlinear dynamics, exhibiting significant computational capabilities. One of the defining characteristics of reservoir computing is that only linear output, given by a linear combination of reservoir variables, is trained. Inspired by recent mathematical studies of generalized synchronization, we propose a novel reservoir computing framework with a generalized readout, including a nonlinear combination of reservoir variables. Learning prediction tasks can be formulated as an approximation problem of a target map that provides true prediction values. Analysis of the map suggests an interpretation that the linear readout corresponds to a linearization of the map, and further that the generalized readout corresponds to a higher-order approximation of the map. Numerical study shows that introducing a generalized readout, corresponding to the quadratic and cubic approximation of the map, leads to a significant improvement in accuracy and an unexpected enhancement in robustness in the short- and long-term prediction of Lorenz and Rössler chaos. Towards applications of physical reservoir computing, we particularly focus on how the generalized readout effectively exploits low-dimensional reservoir dynamics.
储层计算是一种利用非线性动力学的机器学习框架，具有显著的计算能力。储层计算的一个决定性特征是，仅对由储层变量的线性组合给出的线性输出进行训练。受最近广义同步数学研究的启发，我们提出了一种具有广义读出的新型储层计算框架，包括储层变量的非线性组合。学习预测任务可以被表述为一个提供真实预测值的目标映射的近似问题。对该映射的分析表明，线性读出对应于映射的线性化，进一步地，广义读出对应于映射的高阶近似。数值研究表明，引入对应于映射二次和三次近似的广义读出，在洛伦兹和罗斯勒混沌的短期和长期预测中，会导致精度的显著提高和鲁棒性的意外增强。对于物理储层计算的应用，我们特别关注广义读出如何有效地利用低维储层动力学。
