用确定性映射提升混沌时间序列预测精度
Deterministic Reservoir Computing for Chaotic Time Series Prediction
- 采用逻辑斯蒂与切比雪夫映射构建确定性网络
- 在非混沌与混沌序列上分别提升99.99%和87.13%
- 适合追求可解释性与高精度的时序建模场景
近年来，基于随机初始化的储层计算在时序任务中展现出高效学习能力，但其随机性限制了大规模随机图的理论分析。为此，本文基于下一代储层计算与时序卷积储层计算，提出两种确定性变体：TCRC-LM与TCRC-CM，利用参数化且确定性的逻辑斯蒂映射与切比雪夫映射实现高维映射。为进一步增强时序预测性能，创新性地引入洛巴切夫斯基函数作为非线性激活函数。实验表明，所提全确定性网络在非混沌时间序列上的性能优于经典回声状态网络（Echo State Networks）高达99.99%，在混沌时间序列上提升达87.13%。
原文摘要 · Abstract (English)
Reservoir Computing was shown in recent years to be useful as efficient to learn networks in the field of time series tasks. Their randomized initialization, a computational benefit, results in drawbacks in theoretical analysis of large random graphs, because of which deterministic variations are an still open field of research. Building upon Next-Gen Reservoir Computing and the Temporal Convolution Derived Reservoir Computing, we propose a deterministic alternative to the higher-dimensional mapping therein, TCRC-LM and TCRC-CM, utilizing the parametrized but deterministic Logistic mapping and Chebyshev maps. To further enhance the predictive capabilities in the task of time series forecasting, we propose the novel utilization of the Lobachevsky function as non-linear activation function. As a result, we observe a new, fully deterministic network being able to outperform TCRCs and classical Reservoir Computing in the form of the prominent Echo State Networks by up to $99.99\%$ for the non-chaotic time series and $87.13\%$ for the chaotic ones.
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