MSK-TCN: multi-scale stacked kernel temporal convolutional network for multivariate chaotic time series prediction

Abstract While multivariate chaotic systems inherently exhibit cross-variable dynamical coupling, existing modeling approaches often neglect the distinct chaotic properties embedded within individual variables. To address this critical limitation, we propose a M ulti-scale S tacked K ernel T emporal C onvolutional N etwork (MSK-TCN) that systematically decouples variable-specific chaotic dynamics from multivariate interactions. The framework introduces three core innovations: (1) To solve the modeling difficulties caused by the different embedding dimensions of the multivariate phase space reconstruction, Channel-independent Embedding is designed to unify the embedding dimensions of the different variables and to expand the receptive fields of the model; (2) To be able to more fully and accurately inscribe the chaotic attractor of each variable in the phase space, Stacked Kernel (SK) is constructed and Multi-scale SK (MSK) is used to inscribe the chaotic attractor locally and globally and capture the chaotic properties of each variable; (3) An Independent Mixer is proposed to further extract the chaotic properties of each variable at multiple scales through variable independence and to capture the correlation between variables at multiple scales through feature independence. The single-step and multi-step prediction experiments conducted on the Lorenz, Rossler, and Power datasets show that the MSK-TCN model exhibits lower RMSE and MAE, as well as a higher R2. These indicators fully demonstrate that the proposed model has a significant advantage in prediction accuracy and is significantly superior to eight mainstream comparison models such as ModernTCN and DLinear through the generalized likelihood ratio test. This work provides a new paradigm for variable independent and multi-scale stacked convolutional networks to predict multivariate chaotic time series.