Critical prediction of first-order phase transitions based on next-generation reservoir computing

In complex systems, accurately predicting the critical points of first-order phase transitions, such as explosive death, is crucial for early warning and risk management. This study constructs a parameter-aware next-generation reservoir computing (PNGRC) framework to achieve accurate prediction of critical transition. The framework embeds control parameters into the nonlinear vector autoregressive model to generate high-order nonlinear feature vectors that jointly encode system states and parameter information. The forward and backward trajectories under parameter variations are captured in the training stage, and the bidirectional parameter-aware model is constructed to effectively identify the bistable structure and transition paths within hysteresis regions. We evaluate the PNGRC framework on three representative coupled oscillator systems, highlighting its capability to identify first-order critical points across complex dynamical regimes. The results show that the PNGRC framework not only accurately reconstructs system trajectories under training parameters, but also generalizes well to unseen conditions, effectively capturing the period-doubling bifurcation structure and hysteresis phenomena. Compared to traditional parameter-aware reservoir computing, the PNGRC framework substantially reduces data requirements and training time. This work provides an efficient data-driven paradigm for predicting first-order phase transitions.