Interval reservoir computing: theory and case studies

The time series data in many applications, for example, wind power and vehicle trajectory, show 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 the novel interval reservoir computing method. The proposed interval reservoir computing can capture the underlying evolution of the stochastic dynamical system for time series data using the recurrent neural network (RNN). On the other hand, by formulating a chance-constrained optimization problem, interval reservoir computing outputs a set of parameters in the RNN, which maps to an interval of prediction values. The capacity of the interval is the smallest one satisfying the condition 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 an 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. In addition, the confidence probability over the feasibility goes to 1 very quickly as the sample number increases.