A variety of dynamic factors lead to these bursts of instability, and scientists often employ advanced mathematical formulas to determine whether current or future conditions are likely to result in an extreme event. However, this approach can lead to inaccurate projections that are based on incomplete or misleading details.
To address these limitations, a team of engineers has developed a framework for identifying key patterns that can be used to forecast an extreme event, which they detail in a study published Friday in the journal Science Advances.
“We have applied this framework to turbulent fluid flows, which are the Holy Grail of extreme events,” said co-author Themistoklis Sapsis, an associate professor of mechanical and ocean engineering at the Massachusetts Institute of Technology. “They’re encountered in climate dynamics in the form of extreme rainfall, in engineering fluid flows such as stresses around an airfoil, and acoustic instabilities inside gas turbines.
“If we can predict the occurrence of these extreme events, hopefully we can apply some control strategies to avoid them.”
Existing formulas for predicting extreme events rely on a series of initial conditions, or values for specific variables, which researchers use to solve equations under those circumstances. If the results indicate an extreme event, scientists can conclude that some of the conditions or variables could serve as warning signs.
The factors used in these dynamical equations are based on a system’s underlying physics. However, the physics that influence complex systems are often unclear or not fully known, and contain key modeling errors, according to Sapsis.
Equations for systems in which the physics are largely known can produce a significant number of possible outcomes and supposed precursors for extreme events, reflecting the volume of initial conditions used to evaluate these formulas. Some of these precursors, or initial states, might not be applicable to real-world scenarios, leading researchers to focus on factors that never actually materialize.
“If we just blindly take the equations and start looking for initial states that evolve to extreme events, there is a high probability we will end up with initial states that are very exotic, meaning they will never ever occur for any practical situation,” Sapsis said. “So equations contain more information than we really need.”
Scientists have also used available system data to identify key warning signs. As extreme events occur rarely, approaches based solely on existing data would require a massive amount of information over an extended period of time to be able to definitively identify such predictive factors.
The new framework, on the other hand, employs computer algorithms that combine both equations and available data to identify the extreme event precursors that are most likely to occur.
“We are looking at the equations for possible states that have very high growth rates and become extreme events, but they are also consistent with data, telling us whether this state has any likelihood of occurring, or if it’s something so exotic that, yes, it will lead to an extreme event, but the probability of it occurring is basically zero,” Sapsis said.
As such, the framework serves as a filter that removes misleading or theoretically impossible conditions.
The team tested their method on a model of turbulent fluid flow – a prototype system that describes a chaotic fluid, such as the airflow around a jet engine or ocean and atmospheric circulation.
“We used the equations describing the system, as well as some basic properties of the system, expressed through data obtained from a small number of numerical simulations, and we came up with precursors which are characteristic signals, telling us before the extreme event starts to develop, that there is something coming up,” Sapsis said.
To test the accuracy of their approach, the researchers then simulated turbulent fluid flow, looking for precursors that their algorithm predicted. The team found that the precursors led to extreme events between 75 and 99 percent of the time, varying based on the complexity of the fluid flow simulated.
The framework is also general enough to be used on a variety of systems, according to Sapsis.
“This happens in random places around the world, and the question is being able to predict where these vortices or hotspots of extreme events will occur,” Sapsis said. “If you can predict where these things occur, maybe you can develop some control techniques to suppress them.”
Sapsis plans to test the team’s method on scenarios in which fluid flows against a boundary or wall, such as ocean currents against oil risers or air flows around jet planes.