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.
To simplify their calculations, the team reduced all such problems to ones taking place within a large network of interacting nodes, the individual elements or entities within a large system. In a financial system, for example, a node might represent a single company, and a node in an ecosystem could stand for a species. The team then designed two artificial neural networks to analyse such systems. The first was optimised to track the connections between different nodes; the other, how individual nodes changed over time.
To train their model, the team needed examples of critical transitions for which lots of data were available. These are hard to find in the real world, because—cue circular logic—they are so hard to predict. Instead, the researchers turned to simplified theoretical systems in which tipping points are known to occur. One was the so-called Kuramoto model of synchronised oscillators, familiar to anyone who has seen footage of out-of-sync pendulums beginning to swing together. Another was a model ecosystem used by scientists to simulate abrupt changes, such as a decline in harvested crops or the presence of pests.
When the researchers were happy that their algorithms could predict critical transitions in these systems, they applied them to the real-world problem of how tropical forests turn to savannah. This has happened many times on Earth, but the details of the transformation remain mysterious. Linked to decreased rainfall, this large-scale natural switch in vegetation type has important implications for any wildlife living in the region, as well as the humans who depend on it.
The researchers got hold of more than 20 years of satellite images of tree coverage and mean annual rainfall data from central Africa and identified the times at which three distinct regions transitioned from tropical forest to savannah. They then wanted to see if training their algorithm on data from two of these regions (with each node standing in for a small area of land) could enable it to correctly predict a transition point in the third. It could.
The team then asked the algorithm to identify the conditions that drove the shift to savannah—or, in other words, to predict an oncoming phase transition. The answer was, as expected, down to annual rainfall. But the AI was able to go further. When annual rainfall dropped from 1,800mm to 1,630mm, the results showed that average tree cover dropped by only about 5%. But if the annual precipitation decreased from 1,630mm to about 1,620mm, the algorithm identified that average tree cover suddenly fell by more than 30% further.
This would be a textbook critical transition. And by predicting it from the raw data, the researchers say they have broken new ground in this field. Previous work, whether with or without the assistance of AI, could not connect the dots so well.
Like with many AI systems, only the algorithm knows what specific features and patterns it identifies to make these predictions. Gang Yan at Tongji University in Shanghai, the paper’s lead author, says his team are now trying to discover exactly what they are. That could help improve the algorithm further, and allow better predictions of everything from infectious outbreaks to the next stockmarket crash. Just how important a moment this is, though, remains difficult to predict.
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