Enhancing time series forecasting stability with a connected neural dynamical system approach

Abstract

Modeling and forecasting complex time-dependent phenomena remain central challenges in the study nonlinear dynamical systems. Traditional machine learning models, while effective in capturing statistical dependencies, often fail to represent the underlying physical dynamics or maintain stability in long-term evolution. Conversely, classical dynamical systems frameworks offer interpretability and theoretical grounding but face limitations when applied to high-dimensional, noisy, and discretely sampled data. To bridge these paradigms, we propose the Connected Dynamical System Decomposition of Signal Learning (C2DS-L) framework - a hybrid approach that integrates empirical mode decomposition with neural differential modeling under a stability-constrained learning process. The method decomposes signals into intrinsic oscillatory components, reconstructs their latent governing equations using neural differential operators, and enforces dynamical consistency across interconnected subsystems. This yields a data-driven dynamically coherent representation of temporal evolution. Numerical experiments on synthetic and real-world datasets demonstrate that C2DS-L achieves improved predictive accuracy and dynamical stability compared with existing neural and traditional models. Moreover, its decomposition-based formulation provides insight into the structure and interactions of underlying namical modes. The results highlight C2DS-L as a viable pathway toward unifying data-driven learning with dynamical systems theory for interpretable and stable time series modeling.