A team at Stanford has shown that using fewer, higher-quality data points can speed up complex simulations. The method could impact fields from aircraft certification to climate modeling.
Anyone who has seen a fluid mechanics simulation in action, relied on a weather model to anticipate an oncoming hurricane, or seen a flight simulator put a virtual, billion-dollar jet design through its paces, knows that the mathematics of simulation are almost impossibly complex. Even on the fastest supercomputers, these calculations can sometimes take days to complete.
Now, researchers at Stanford University have discovered a way to not only expedite modeling calculations but actually produce better results by gathering fewer but higher-quality data and removing redundancies that bog down traditional approaches. They achieved this by using a new approach that simplifies the data inputs to speed calculations.
“The key takeaway from this work is that, by being smart about what data we collect, we can significantly reduce the amount of data required to construct accurate models of complex systems,” said Joshua Ott, a doctoral student in aeronautics and astronautics and first author of a new paper presented at the Learning for Dynamics & Control Conference (L4DC 2025). “If you can simplify the data inputs, you make the math easier.”
Simplify to expedite
The vision, explains co-author Mykel Kochenderfer, professor of aeronautics and astronautics, is to reduce the scale of the calculations to only the most important, enabling elimination of redundant data and acceleration of calculation times.
“Our work involves new methods for efficiently learning the behavior of complex systems—like aircraft, weather, or financial markets—by collecting smart, targeted data,” Kochenderfer said. “Understanding these systems accurately is important in science and engineering, but gathering the necessary data can be time-consuming and expensive.”
In lay terms, the team’s approach to the problem was to force it through a series of smaller, easier-to-solve approximations, allowing them to solve the problems extremely quickly.
“Technically, that type of modeling is not as accurate as if you did the full optimization, but we solve it many more times, and over time we narrow in on better answers, faster,” Ott explained.
Valid proof
The team experimentally validated its method in three unrelated simulation environments using two conventional techniques. “Just to give you an idea of the scale of these problems: An aircraft simulation typically has perhaps 20 dimensions to calculate, but a fluid flow simulation may have 50,000 or more.”
In one experiment, they did calculations of fluids flowing past a rotating cylinder—the sort of problem that has 50,000-plus inputs. In another, they simulated the flight of an F-16 fighter jet, reducing the inputs to just four controls—throttle percentage, elevator, aileron, and rudder deflections.
“It’s quite a difference in scale, but the method still works at both scales,” Ott said. “That’s pretty cool.”
Last, to demonstrate the usefulness of their method in real-world situations, the team integrated its method into X-Plane, a highly realistic flight simulator for pilot training and research purposes. X-Plane required real-time updates and adjustments to control inputs based on the current state of the aircraft. They then used a simulated Cessna 172 in X-Plane to demonstrate the real-time use-case of their method.
“This last example, in particular, showcases the practical applicability of our method in scenarios that require adaptive and responsive control strategies and the speed of our method to update estimates and replan onboard a running aircraft,” said Stephen Boyd, professor of electrical engineering, an expert in control systems and senior author of the paper.
In the real world
The researchers note that this approach might significantly lessen time to certify new aircraft designs to ensure that aircraft are safe and meet performance standards, potentially lowering costs for both airlines and passengers. It might also be applied to climate systems to improve climate projections and identifying areas where current models tend to be most uncertain to refine our understanding of climate patterns, improve predictions, and better inform policy decisions.
In that regard, next up for the team, Ott said, is a research collaboration with the Air Force Test Pilot School looking at applying it to their T-38 jets.
“The T-38 is quite a bit faster than a Cessna 172. Demonstrating our method onboard the T-38 in real time could open doors for future avenues to accelerate the flight test and certification process across the board,” Ott said. “We’re trying to work in a way that we can get the best of both worlds—the accuracy of the traditional methods and the speed of our pared-down approach. It should be a fun challenge.”
