Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238, USA.
Chaos. 2022 Jul;32(7):073116. doi: 10.1063/5.0071926.
Echo state networks are a fast training variant of recurrent neural networks excelling at approximating nonlinear dynamical systems and time series prediction. These machine learning models act as nonlinear fading memory filters. While these models benefit from quick training and low complexity, computation demands from a large reservoir matrix are a bottleneck. Using control theory, a reduced size replacement reservoir matrix is found. Starting from a large, task-effective reservoir matrix, we form a controllability matrix whose rank indicates the active sub-manifold and candidate replacement reservoir size. Resulting time speed-ups and reduced memory usage come with minimal error increase to chaotic climate reconstruction or short term prediction. Experiments are performed on simple time series signals and the Lorenz-1963 and Mackey-Glass complex chaotic signals. Observing low error models shows variation of active rank and memory along a sequence of predictions.
回声状态网络是一种快速训练的递归神经网络变体，擅长于逼近非线性动力系统和时间序列预测。这些机器学习模型充当非线性的渐消记忆滤波器。虽然这些模型受益于快速训练和低复杂度，但来自大型储层矩阵的计算需求是一个瓶颈。我们使用控制理论找到了一个更小的替换储层矩阵。从一个大的、有效的储层矩阵开始，我们形成一个可控性矩阵，其秩表示活动子流形和候选替换储层大小。在混沌气候重建或短期预测方面，所得的时间加速和减少的内存使用是以最小的误差增加为代价的。实验在简单的时间序列信号和 Lorenz-1963 和 Mackey-Glass 复杂混沌信号上进行。观察低误差模型表明，随着预测序列的进行，活跃秩和记忆会发生变化。
