Researchers at Duke University have created a new artificial intelligence framework designed to uncover straightforward, easy-to-understand rules that sit underneath some of the most complicated dynamics seen in nature and technology.
The system is inspired by the way famous “dynamicists” – scientists who study how systems change over time – uncovered many of the physics principles that explain motion and other evolving processes. In the same spirit that Newton, often described as the first dynamicist, connected force and movement with equations, this AI studies data showing how a complex system changes over time and then produces equations that describe that behavior.
What makes the approach especially powerful is its ability to go beyond what people can realistically juggle mentally. It can take nonlinear systems involving hundreds or even thousands of variables and reduce them to simpler rules that rely on far fewer dimensions.
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This chaotic-looking “double pendulum” follows a large number of rules that govern its motion. Researchers have trained AI to take data from its movements to uncover simple equations that successfully model its movements over time. Critically, these equations can predict how the system will settle into stability over time. The approach works on complex nonlinear systems ranging from global climate patterns to neural activity. Credit: Boyuan Chen, Duke University
From Weather and Circuits to Biology
The study, published today (December 17) in the journal npj Complexity, presents a new way to use AI to better understand complex systems that evolve over time, including weather patterns, electrical circuits, mechanical systems, and 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.”
To illustrate why simplification matters, consider the flight of a cannonball. Its path can be influenced by many factors, including the launch speed and angle, air drag, shifting winds, and even surrounding temperatures, among others. Yet a strong approximation often comes from a simple linear equation that uses only the first two factors.
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This “magnetic pendulum” uses a motor to set it into motion at a specific speed and angle. Magnets within the pendulum’s end and the floor repel one another as the pendulum swings, creating a complex interaction over time. Researchers have trained AI to take data from its movements to uncover simple equations that successfully model its movements over time. Critically, these equations can predict how the system will settle into stability over time. The approach works on complex nonlinear systems ranging from global climate patterns to neural activity. Credit: Boyuan Chen, Duke University
Koopman’s Idea and the Big Catch
That cannon ball example reflects a theoretical concept proposed by mathematician Bernard Koopman in the 1930s: Complex nonlinear systems can be represented mathematically by linear models. The Duke team’s AI method builds on that idea.
But there is a major obstacle. Creating linear models for extremely complex systems can require writing hundreds or even thousands of equations, each tied to its own variable. That scale quickly becomes unmanageable for the human mind.
This is where AI becomes useful.
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This is a recorded temperatures (left) and a model of temperatures (right) around the globe for a fixed latitude over time. Dots moving toward the center are getting colder while dots moving away from the center are getting warmer. When visualized over time, one can see how these temperatures propagate around globe. In the real world, there are not just a few dots, but infinite, because actual temperature varies continuously in space. A new AI platform can take this incredibly complex data and create a relatively simple set of linear equations that researchers can analyze much more easily. Despite its simplicity, the model accurately predicts these temperature fluxuations over time. Credit: Boyuan Chen
How the Framework Compresses Complexity
The new framework analyzes time-series data from experiments, looks for the most meaningful patterns in how a system changes, and combines deep learning with physics-inspired constraints to shrink the problem down. It identifies a much smaller collection of variables that still captures the core behavior. The end result is a compact description that behaves mathematically like a linear model while still matching the complexity of real-world dynamics.
The researchers tested the framework across many different systems. These included the familiar motion of a pendulum, the nonlinear behavior of electrical circuits, and models used in climate science and neural circuits. Even though these systems differ widely, the method repeatedly uncovered a small set of hidden variables that controlled the behavior. In many cases, the reduced models were more than 10 times smaller than what earlier machine-learning approaches needed, while still producing reliable long-term predictions.
“What stands out is not just the accuracy, but the interpretability,” said Chen, who also holds appointments in electrical and computer engineering and computer science. “When a linear model is compact, the scientific discovery process can be naturally connected to existing theories and methods that human scientists have developed over millennia. It’s like connecting AI scientists with human scientists.”
Finding Attractors and Spotting Instability
The framework is not limited to forecasting. It can also pinpoint stable states called attractors, where a system tends to settle over time. Identifying these stable states helps researchers judge whether a system is operating normally, drifting away from typical behavior, or moving toward instability.
“For a dynamicist, finding these structures is like finding the landmarks of a new landscape,” said Sam Moore, the lead author and PhD candidate in Chen’s General Robotics Lab. “Once you know where the stable points are, the rest of the system starts to make sense.”
The team stresses that the method is especially valuable when traditional equations are unavailable, incomplete, or too difficult to derive. “This is not about replacing physics,” Moore continued. “It’s about extending our ability to reason using data when the physics is unknown, hidden, or too cumbersome to write down.”
What Comes Next for Machine Scientists
Next, the researchers plan to explore how this framework might help guide experimental design by selecting what data to gather in order to reveal a system’s structure more efficiently. They also want to expand the approach to richer types of information, including video, audio, or signals collected from complex biological systems.
The work supports a long-term effort in Chen’s General Robotics Lab to develop “machine scientists” that can assist with automated scientific discovery. By combining modern AI with the mathematical language of dynamical systems, the research points to a future where AI does more than recognize patterns. It could help uncover the fundamental rules that shape both the physical world and living systems.
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Reference: “Automated global analysis of experimental dynamics through low-dimensional linear embeddings” by Samuel A. Moore, Brian P. Mann and Boyuan Chen, 17 December 2025, npj Complexity.
DOI: 10.1038/s44260-025-00062-y
This work was supported by the National Science Foundation Graduate Research Fellowship, the Army Research Laboratory STRONG program (W911NF2320182, W911NF2220113), the Army Research Office (W911NF2410405), the DARPA FoundSci program (HR00112490372), and the DARPA TIAMAT program (HR00112490419).
Project Website: http://generalroboticslab.com/AutomatedGlobalAnalysis
General Robotics Lab Website: http://generalroboticslab.com
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