The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long history pose an exceptionally difficult problem. While machine learning has shown to be a promising approach for predicting such time series, it either demands long training time and much training data when using deep recurrent neural networks. Alternative, when using a reservoir computing approach it comes with high uncertainty and typically a high number of random initializations and extensive hyper-parameter tuning when using a reservoir computing approach. In this paper, we focus on the reservoir computing approach and propose a new mapping of input data into the reservoir's state space. Furthermore, we incorporate this method in two novel network architectures increasing parallelizability, depth and predictive capabilities of the neural network while reducing the dependence on randomness. For the evaluation, we approximate a set of time series from the Mackey-Glass equation, inhabiting non-chaotic as well as chaotic behavior and compare our approaches in regard to their predictive capabilities to echo state networks and gated recurrent units. For the chaotic time series, we observe an error reduction of up to $85.45\%$ and up to $87.90\%$ in contrast to echo state networks and gated recurrent units respectively. Furthermore, we also observe tremendous improvements for non-chaotic time series of up to $99.99\%$ in contrast to existing approaches.

该研究聚焦于采用储层计算方法，提出了一种新的输入数据映射方案，并将其应用于两种创新的网络结构，提高了神经网络的并行性、深度和预测能力，同时减少了对随机性的依赖。在对来自 Mackey-Glass 方程的一组时间序列进行评估时，与回声状态网络和门控循环单元相比，对于混沌时间序列，误差减少了高达 85.45%，对于非混沌时间序列，改进达到了高达 99.99%。

基于时间卷积的多层储备计算