Researchers at Duke University have created a new artificial intelligence framework designed to uncover clear, easy-to-understand rules behind some of the most complicated dynamics seen in nature and modern technology.
The system is inspired by the work of history's great "dynamicists" -- scientists who study systems that change over time. Just as Isaac Newton, often considered the first dynamicist, developed equations linking force and motion, this AI analyzes data that shows how complex systems evolve and then produces equations that accurately describe that behavior.
What sets this approach apart is its ability to handle complexity far beyond human capacity. The AI can take nonlinear systems involving hundreds or even thousands of interacting variables and reduce them to simpler rules with far fewer dimensions.
The research, published December 17 online in the journal npj Complexity, introduces a powerful new way for scientists to use AI to study systems that evolve over time -- including weather patterns, electrical circuits, mechanical devices, 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."
A classic example of simplification comes from physics. The path of a cannon ball depends on many factors, including launch speed and angle, air resistance, changing wind conditions, and even ambient temperature. Despite this complexity, a close approximation of its motion can be captured with a simple linear equation that uses only the launch speed and angle.
This kind of simplification reflects a theoretical concept introduced by mathematician Bernard Koopman in the 1930s. Koopman showed that complex nonlinear systems can be represented mathematically using linear models. The new AI framework builds directly on this idea.
There is an important challenge, however. Representing highly complex systems with linear models often requires constructing hundreds or even thousands of equations, each tied to a different variable. Handling that level of complexity is difficult for human researchers.
That is where artificial intelligence becomes especially valuable.
The framework studies time-series data from experiments and identifies the most meaningful patterns in how a system changes. It combines deep learning with constraints inspired by physics to narrow down the system to a much smaller set of variables that still capture its essential behavior. The outcome is a compact model that behaves mathematically like a linear system while remaining faithful to real-world complexity.
To test the approach, the researchers applied it to a wide variety of systems. These ranged from the familiar swinging motion of a pendulum to the nonlinear behavior of electrical circuits, as well as models used in climate science and neural circuits. Although these systems differ greatly, the AI consistently uncovered a small number of hidden variables that governed their behavior. In many cases, the resulting models were more than 10 times smaller than those produced by earlier machine-learning methods, while still delivering 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."
The framework does more than make predictions. It can also identify stable states, known as attractors, where a system naturally settles over time. Recognizing these states is critical for determining whether a system is operating normally, slowly drifting, or approaching 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 researchers note that this method is especially useful when traditional equations are unavailable, incomplete, or too complex 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."
Looking ahead, the team is exploring how the framework could help guide experimental design by actively selecting which data to collect in order to reveal a system's structure more efficiently. They also plan to apply the method to richer forms of data, including video, audio, and signals from complex biological systems.
This research supports a long-term goal in Chen's General Robotics Lab to develop "machine scientists" that assist with automated scientific discovery. By linking modern AI with the mathematical language of dynamical systems, the work points toward a future in which AI does more than recognize patterns. It may help uncover the fundamental rules that shape both the physical world and living systems.
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).
General Robotics Lab Website: http://generalroboticslab.com