Chaotic time series prediction based on dynamic adaptive reconstruction transformer

Time-series data contain essential information reflecting dynamic processes in natural phenomena and human activities. In chaotic systems, the inherent nonlinear dynamics and high sensitivity to initial conditions present considerable challenges for traditional prediction techniques. Conventional chaotic time-series prediction typically employs Phase Space Reconstruction (PSR), yet the selection of delay time and embedding dimension relies on prior statistical criteria, which are often misaligned with prediction objectives and lead to suboptimal PSR performance [1]. Although deep learning approaches have improved nonlinear modeling capabilities in recent years, they generally fail to explicitly leverage the geometric characteristics of PSR. This study proposes a Dynamically Adaptive Reconstruction Transformer (DARTS) that reformulates the PSR objective from “statistical criteria optimization” to “prediction loss minimization,” enabling end-to-end optimization of delay vectors and embedding dimensions. Through the incorporation of multi-head attention mechanisms, DARTS integrates the geometric features of PSR with the sequential properties of time-series data and improves long-range dependency modeling through position encoding and value encoding. Using differentiable interpolation, DARTS transforms discrete time series into continuous signals, facilitating gradient-based updates of delay parameters, while employing Transformer self-attention to capture cross-time-scale complex dependencies. Experimental evaluations on the Lorenz system and NASA lithium battery datasets demonstrate that DARTS substantially reduces long-term prediction errors compared with conventional methods, effectively mitigates interference from redundant features, and offers an accurate and interpretable solution for high-dimensional non-stationary chaotic time-series predicting.