Novel approach to time series forecasting based on memristive Hopfield Neural Network with hidden heterogeneous and homogeneous extreme multistability

Deep learning models for time series forecasting frequently suffer from slow convergence and entrapment in local minima due to suboptimal weight initialization. To address these limitations, this paper proposes a novel Dual Memristive Hopfield Neural Network (DMHNN) without equilibrium points. By introducing flux-controlled memristors, the system exhibits complex hidden dynamical behaviors, most notably hidden heterogeneous and homogeneous extreme multistability. Leveraging these high-entropy dynamics, a novel weight initialization framework is developed. A fused architecture is constructed where the five-dimensional physical variables of the chaotic system are mapped one-to-one to the internal gates and recurrent weights of a Long Short-Term Memory network. This physical-logical alignment strategy effectively avoids parameter homogenization inherent in low-dimensional maps. Comprehensive experiments on energy, weather, and financial datasets demonstrate that the proposed method significantly outperforms standard initialization, reducing prediction errors by up to 28.8% on specific datasets. Furthermore, the approach accelerates convergence speed and enhances the capability to escape poor local optima in non-stationary environments.