  Tipping points occur in many real-world systems, at which the system shifts
suddenly from one state to another. The ability to predict the occurrence of
tipping points from time series data remains an outstanding challenge and a
major interest in a broad range of research fields. Particularly, the widely
used methods based on bifurcation theory are neither reliable in prediction
accuracy nor applicable for irregularly-sampled time series which are commonly
observed from real-world systems. Here we address this challenge by developing
a deep learning algorithm for predicting the occurrence of tipping points in
untrained systems, by exploiting information about normal forms. Our algorithm
not only outperforms traditional methods for regularly-sampled model time
series but also achieves accurate predictions for irregularly-sampled model
time series and empirical time series. Our ability to predict tipping points
for complex systems paves the way for mitigation risks, prevention of
catastrophic failures, and restoration of degraded systems, with broad
applications in social science, engineering, and biology.
