Interval Reservoir Computing: Theory and Case Studies

Lan-Da Gao¹ Zhen-Hua Li¹ Meng-Yi Wu^1* Qing-Lan Fan¹ Ling Xu¹ Zhuo-Min Zhang¹ Yi-Peng Zhang¹ Yanyue Liu¹

• ¹Research Institute of Highway, Ministry of Transport, China

The time series data in many applications, for example, wind power and vehicle trajectory, shows significant uncertainty. Using a single prediction value of wind power as feedback information for wind turbine control or unit commitment is not enough since the uncertainty of the prediction is not described. This paper addresses the uncertainty issue in time series data forecasting by proposing a novel interval reservoir computing. The proposed interval reservoir computing can capture the underlying evolution of the stochastic dynamical system for time series data using Recurrent Neural Network (RNN). On the other hand, by formulating a chance-constrained optimization problem, interval reservoir computing outputs a set of parameters in RNN, which maps to an interval of prediction values. The capacity of the interval is the smallest one satisfying that the probability of having a prediction inside the interval is lower than the required level. The scenario approach solves the formulated chance-constrained optimization problem. We implemented experimental data-based validation to evaluate the proposed method. The validation results show that the proposed interval reservoir computing can give a tight interval of time series data forecasting values for wind power and traffic trajectory. Besides, the confidence probability over the feasibility goes to $1$ very quickly as the sample number increases.