Anticipating rate-induced tipping by a deep learning framework

Rate-induced tipping (R-tipping) occurs when the forcing rate changes too rapidly for the system to track its quasi-equilibrium state, leading to an unexpected collapse. Currently, there is a lack of valid early warning signals (EWS) for R-tipping, particularly in the presence of noise perturbations. To address this deficiency, we employ a deep learning algorithm to extract the high-order structures hidden within time series data before R-tipping occurs. Then the trained neural networks are taken to provide real-time EWS for R-tipping, demonstrating skillful forecasts with a substantially long lead time, surpassing the performance of conventional critical slowing down indicators. Our progress underscores the predictability of R-tipping, offering the potential to improve the ability to deduce the safe operating space for a wider spectrum of complex systems.