The writer Malcolm Gladwell popularized the term "tipping points" to refer to the moment when a trend or social behavior crosses a threshold and rapidly spreads everywhere. In physics, tipping points occur when systems—say, Earth's climate—reach an unstable point and topple over into a sea of change that is sometimes irreversible. Examples include global warming or the melting of polar ice caps.
While scientists have previously used AI models to predict smaller changes in weather, such as day-to-day variations, forecasting tipping points comes with more uncertainty and has thus proven more challenging. Now, a new Caltech-led paper demonstrates that an AI program—specifically a type of neural network called a recurrent neural operator (RNO)—can be used to predict when tipping points occur in simple models, including models of a climate-change system and simulations of turbulent airflow over a plane's wing.
The paper was published in the Proceedings of the National Academy of Sciences (PNAS) .
"A tipping point is where you don't have that point of return anymore because it's nonstationary," says Anima Anandkumar , Caltech's Bren Professor of Computing and Mathematical Sciences and the principal author of the study. "Parts of a system are changing in a way so that you cannot bring the system back to its original state. That's why it is seen as something that could be catastrophic."
The new research, cited in a recent report from the United Nations on the importance of tipping points in climate science, was performed by Anandkumar and her colleagues at Caltech, the University of Colorado Boulder (CU Boulder), and the tech company NVIDIA. Because tipping points are so universal, the AI tool has potential applications in the fields of climate science, ecology, epidemiology, aeronautical design, and more.
"This work lays the foundations for characterizing tipping points and predicting when they might occur in the future," Anandkumar says. "We demonstrated it on a simplified climate model and a model of air turbulence over a wing—systems that weren't tractable with earlier methods."
In one part of the study, the researchers looked at a specific climate scenario in which low clouds over the oceans rapidly disappear due to rising carbon dioxide levels—a situation that has been predicted to occur in the future but has not yet been observed. This "point-of-no-return" loss of low cloud cover would further add to global warming. The researchers tested their AI program on simulated data to see if it could forecast when the clouds would disappear. The RNO was able to look more than two years ahead of the expected tipping point in the simulated data and predict its timing with an error of about 11 days.
"In the past, we used AI to learn mostly stationary systems that assume the weather from before will be the same as weather in future," Anandkumar says. "Our group has trained such AI-based weather models successfully in the past and can even predict extreme events like hurricanes with good accuracy. On the other hand, if you want to now model how that climate is changing and account for changes such as the carbon dioxide content, the system is no longer stationary, and you can no longer use standard machine learning principles."
The group's latest AI approach, based on an RNO, differs from other machine learning programs because it incorporates a built-in "memory" that tracks how the physics change over time. The RNO detects when the AI's predictions about the physics of a system no longer make sense, indicating a tipping point is imminent. In other words, when the AI's predictions no longer follow the rules of previously defined physics, a significant shift in the model is about to occur.
"The system is drifting away over time, and the laws from physics are no longer holding at the tipping point," Anandkumar says. "We can use the principles of physics on top of recurrent neural operators to make these predictions of when the tipping point is likely to
The PNAS paper also describes testing the RNO on simulations of airflow over a tilting plane wing to see if it could forecast a tipping point that occurs when the wing's lift drops precipitously. The RNO succeeded in predicting the tipping point, suggesting these kinds of AI programs could potentially help with future aeronautical and aerospace designs.
"In aerodynamics, quantities like the angle of attack can change gradually while the flow itself undergoes a much more abrupt transition, such as the onset of stall or a change in the wake," explains study coauthor Jane Bae (BS '12), assistant professor of aerospace at Caltech and a Susan Wu Scholar. "What is exciting about this work is that the model can recognize when the physics it has learned no longer adequately describes what is happening, providing a warning that the system may be approaching a tipping point. Being able to anticipate these qualitative changes before they occur could ultimately be very useful for aerodynamic prediction and design."
The paper is titled " Tipping Point Forecasting in Non-Stationary Dynamics on Function Spaces ." In addition to Anandkumar, other Caltech authors are alumni Miguel Liu-Schiaffini (BS '25) and Sze Chai Leung (MS '24). Additional authors are Clare E. Singer (PhD '24) of CU Boulder and Nikola Kovachki (BS '16, PhD '22) and Kamyar Azizzadenesheli of NVIDIA. Funding was provided by the Mellon Mays Undergraduate Fellowship; Eric and Wendy Schmidt, through the AI2050 Senior Fellow Schmidt Sciences program; Caltech trustee Charles Trimble (BS '63, MS '64); the Office of Naval Research; the Carver Mead New Adventures Fund; and Caltech's Center for Autonomous Systems and Technologies (CAST). Computational time for the airfoil simulations was provided by the Pittsburgh Supercomputing Center, supported by the National Science Foundation.
Proceedings of the National Academy of Sciences