Error-feedback three-phase optimization to configurable convolutional echo state network for time series forecasting

Time series forecasting is critical for many real -world applications. Convolutional echo state networks (CESNs) have shown intriguing time series modeling efficacy by combining convolutional neural network (CNN) and echo state network (ESN). However, current CESN models are tailored for the classification tasks and rely on elaborately designed neural architectures. To this end, we propose a novel configurable convolutional echo state network (CCESN) with an innovative error -feedback three-phase optimization (ETO) strategy for time series forecasting. The network is progressively constructed with heterogeneous modular subnetworks, including ESN, CNN, CESN, and reversed CESN modules. This scheme leverages the complementary feature extraction capabilities of convolutional and recurrent neural architectures. To adaptively evolve the CCESN, we propose a novel error -feedback three-phase optimization (ETO) strategy by selecting optimal subnetwork modules while step -wise tuning parameters. Comprehensive experiments are conducted on representative simulated and real -world datasets. The results indicate that ETO-CCESN can adaptively select and evolve heterogeneous subnetworks to acclimatize to varied scenarios, and thus demonstrate significant performance improvements, achieving a 45.69% average enhancement in forecasting accuracy compared to the existing CESN model, and surpassing the best baseline by 8.79% in terms of symmetric mean absolute percentage error across diverse forecasting tasks.