Delay-coupled multi-branch reservoir computing with cross-pooled interactions for long-horizon chaotic dynamics forecasting

Long-horizon forecasting of chaotic dynamics remains highly challenging because of the extreme sensitivity to initial conditions and the rapid accumulation of prediction errors during temporal evolution. To address this issue, this paper proposes DCP-MBRC, a delay-coupled multi-branch reservoir computing framework with cross-pooled interactions, for high-performance long-horizon chaotic forecasting. The proposed framework employs multiple reservoir branches operating with different capacities, where delayed coupling and nonlinear delayed interaction terms are embedded within each branch to enhance modeling of history-dependent dynamics and nonlinear temporal evolution. Cross-pooled interaction mechanisms are further constructed across branches to explicitly capture inter-branch state correlations and improve multi-branch information fusion, simultaneously boosting the model's memory capacity and nonlinear representation ability for chaotic evolution. Experiments on four typical chaotic systems, namely the Rössler system, the coupled Lorenz system, the Mackey–Glass delay system, and a 4D hyperchaotic system, demonstrate that DCP-MBRC consistently outperforms the baselines in terms of long-horizon forecasting accuracy and valid prediction length. Furthermore, attractor reconstruction, power spectral density analysis, and reconstructed bifurcation diagrams show that the proposed method preserves the intrinsic dynamical structures of the target systems more faithfully. Ablation and parameter studies further quantify the effects of key components, i.e., delayed coupling, cross-pooled interactions, and design parameters, on the predictability of chaotic systems. These results indicate that DCP-MBRC provides an effective and robust data-driven approach for long-horizon chaotic dynamics forecasting, with clear advantages in both predictive performance and dynamical fidelity.