Temporal Convolution Derived Multi-Layered Reservoir Computing
This work addresses the challenge of predicting chaotic time series with long history dependencies, which is relevant for applications like finance, fluid dynamics, and biology, by offering a more efficient and less random alternative to existing methods.
The paper tackles chaotic time series prediction by proposing a new input mapping method for Reservoir Computing and two novel network architectures that reduce randomness dependence while improving parallelizability and depth. The approach achieves error reductions of up to 85.45% compared to Echo State Networks and 90.72% compared to Gated Recurrent Units on chaotic time series, with up to 99.99% improvement on non-chaotic series.
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. 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 as well as the SantaFe Laser dataset and compare our approaches in regard to their predictive capabilities to Echo State Networks, Autoencoder connected Echo State Networks and Gated Recurrent Units. For the chaotic time series, we observe an error reduction of up to $85.45\%$ compared to Echo State Networks and $90.72\%$ compared to Gated Recurrent Units. Furthermore, we also observe tremendous improvements for non-chaotic time series of up to $99.99\%$ in contrast to the existing approaches.