Forecasting Chaotic Multivariate Time Series Based on DB-ICDNet

Abstract

Chaotic time series widely exist in complex scenarios such as nonlinear dynamic systems, financial markets, and meteorological observations. Its strong nonlinearity, sensitivity to initial values, and accumulation of long-term prediction errors make it possible to achieve stable, high-precision multi-step forecasting under limited observation conditions. Prediction is extremely challenging. Traditional linear models are difficult to approach nonlinear dynamics, while conventional deep learning models are prone to phase drift and error amplification during long-step extrapolation. Therefore, this study focuses on the problem of multivariate multi-step forecasting, and proposes a lightweight in-depth forecasting framework DB-ICDNet. In the representation learning stage, the framework extracts long-range dependencies and local perturbations through LSTM and causally inflated TCN, and realizes controlled fusion of information in the near-term window based on the residual gated fusion mechanism. In the prediction stage, it designs a step-size conditional dual-memory cooperative decoder, adaptively retrieves long-term and short-term contexts according to different prediction steps, and gradually generates future trajectories with end observations as anchors through incremental cumulative regression heads, supplemented by consistency constraints to suppress error diffusion. Experiments on Lorenz and Chen theoretical data sets and HS300 real data show that this method has higher accuracy and stability in multi-step prediction, especially in long-step extrapolation, it can effectively maintain the trajectory shape and alleviate error accumulation, which verifies its effectiveness in meeting the challenge of chaotic sequence prediction.