Can a new mathematical framework pinpoint the warning signs before an extreme event? A group of engineers at the Massachusetts Institute of Technology think so.

Researchers at MIT have developed a set of mathematical equations that can be used to identify patterns that precede extreme events, like a rogue wave or instability inside a gas turbine.

"Currently there is no method to explain when these extreme events occur," Themistoklis Sapsis, an associate professor of mechanical and ocean engineering at MIT, said in a news release. "We have applied this framework to turbulent fluid flows, which are the Holy Grail of extreme events. 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 researchers can anticipate the warning signs of extreme events, mitigation efforts could be instigated sooner, potentially preventing loss of life and property.

Typically, scientists look to sophisticated formulas called dynamical equations to predict extreme events. When fed the right combinations of variable values, dynamical equations reveal an extreme event. And when the formulas reveal an extreme event, engineers can be sure the initial conditions -- the variable values that were plugged-in -- are a precursor to disaster.

Ideally, each dynamical equation reflects the specific system's underlying physics. But often, scientists don't entirely understand the complexities of a system's physics. The system models can be faulty and largely theoretical.

What's more, dynamical equations encompass a seemingly infinite number of scenarios -- thousands of variables yielding thousands of results. In fact, many combinations of variable values, describing extremely unlikely scenarios, can yield extreme events.

Researchers at MIT had to find a way to break through this noise.

"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 can also use real world observations to predict extreme events, but because extreme events are so rare, a working formula requires lots and lots of data over long periods of time. Often time, researchers don't have enough usable data to build an accurate set of predictive formulas.

The new framework solves these problems by combining dynamical equations with real world observations.

"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.

The algorithm uses real world data to decide whether or not problematic combinations of conditions are realistic. Sapsis and his research partner, MIT postdoc Mohammad Farazmand, used their new framework to predict instabilities inside a turbulent fluid flow.

The turbulent fluid flow model can describe a variety of real world systems, a perfume of smoke, air movements around a jet engine or airfoil, ocean and atmospheric circulation, or the movement of blood through the heart.

"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.

A follow up simulation proved the problematic scenarios predicted by their framework evolved into extreme events between 75 and 99 percent of the time.

Researchers believe their framework -- detailed this week in the journal Science Advances -- can be used to predict extreme events in a variety of systems.

"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."

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