Enhancing time series forecasting stability with a connected neural dynamical system approach
S. Pourmohammad Azizi, Boumediene Hamzi, Enhancing time series forecasting stability with a connected neural dynamical system approach, Physica D: Nonlinear Phenomena, Volume 483, 2025, 134969, ISSN 0167-2789, https://doi.org/10.1016/j.physd.2025.134969. (https://www.sciencedirect.com/science/article/pii/S0167278925004464) Abstract: Modeling and forecasting complex time-dependent phenomena remain central challenges in the study of 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 yet 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 dynamical 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. Keywords: Nonlinear dynamics; Time series modeling; Neural differential equations; Empirical mode decomposition; Stability analysis; Hybrid dynamical systems; Signal decomposition; Interpretable modeling