ANYONE CAN spot a tipping point after it’s been crossed. Also known as critical transitions, such mathematical cliff-edges influence everything from the behaviour of financial markets and the spread of disease to the extinction of species. The financial crisis of 2007-09 is often described as one. So is the moment that covid-19 went global. The real trick, therefore, is to spot them before they happen. But that is fiendishly difficult.

Computer scientists in China now show that artificial intelligence (AI) can help. In a study published in the journal Physical Review X, the researchers accurately predicted the onset of tipping points in complicated systems with the help of machine-learning algorithms. The same technique could help solve real-world problems, they say, such as predicting floods and power outages, buying valuable time.