Parallel BiLSTM–transformer networks for forecasting chaotic dynamics

Chaotic time series exhibit intrinsic multi-scale correlations that make long-term forecasting extremely challenging. In this paper, we develop a hybrid parallel architecture that integrates transformer and bidirectional long short-term memory (BiLSTM) networks, designed to capture complementary aspects of chaotic dynamics. The transformer branch extracts global dependencies arising from long-range temporal correlations, while the BiLSTM branch resolves short-scale structures linked to local stretching and folding mechanisms. Their jointly learned representations are fused through a feature-integration module, yielding a unified description that enhances predictive accuracy and robustness. We evaluate the framework on the Lorenz system across two representative tasks: (i) autonomous evolution prediction using time-delay embeddings and (ii) inference of unmeasured variables, a fundamental problem in nonlinear observability. The hybrid model consistently outperforms single-branch architectures in both tasks. These results highlight the utility of combining global attention mechanisms with local recurrent dynamics for modeling complex systems. Remarkably, in the inference task, it achieves stable reconstruction over arbitrarily long time horizons, which provides a practical tool for monitoring variables that are difficult or hazardous to measure, with implications for engineering diagnostics, environmental and physiological monitoring, and the analysis and control of high-dimensional nonlinear dynamics.