A research team at Duke University has developed a new AI framework that can uncover simple, understandable rules that govern some of the most complex dynamics found in nature and technology.

The AI system works much like how history's great "dynamicists"—those who study systems that change over time—discovered many laws of physics that govern such systems' behaviors. Similar to how Newton, the first dynamicist, derived the equations that connect force and movement, the AI takes data about how complex systems evolve over time and generates equations that accurately describe them.

The AI, however, can go even further than human minds, untangling complicated nonlinear systems with hundreds, if not thousands, of variables into simpler rules with fewer dimensions.

The work, published in the journal npj Complexity, offers scientists a new way to leverage AI to help understand complex systems that change over time—such as the weather, electrical circuits, mechanical systems and even biological signals.

"Scientific discovery has always depended on finding simplified representations of complicated processes," said Boyuan Chen, director of the General Robotics Lab and the Dickinson Family Assistant Professor of Mechanical Engineering and Materials Science at Duke.

"We increasingly have the raw data needed to understand complex systems, but not the tools to turn that information into the kinds of simplified rules scientists rely on. Bridging that gap is essential."

The trajectory of a cannon ball depends on many variables such as exit velocity and angle, air drag, varying wind speeds, and even ambient temperatures, among many others. However, a very close approximation can be found by a simple linear equation that only uses the first two.

This is an example of a theoretical idea originally proposed by mathematician Bernard Koopman in the 1930s: Complex nonlinear systems can be represented mathematically by linear models. The new AI approach builds on this concept.

There is, however, a catch. To find linear models of extremely complex systems, one needs to develop hundreds, if not thousands, of equations involving just as many variables. And human minds do not handle such large numbers very well.