This AI finds simple rules where humans see only chaos
Date: December 22, 2025
Source: Duke University
A team at Duke University has built an AI framework that distills highly complex, nonlinear systems into compact, readable equations. It works across physics, engineering, climate models, and biology-especially where traditional equations are missing or too unwieldy to write down.
Why this matters for scientists
Progress in science depends on simple models that capture essential behavior without drowning in variables. We've got more data than ever, but turning it into usable rules is the bottleneck. This method closes that gap: from raw time-series to equations researchers can inspect, test, and build on.
Rooted in a classic idea
The approach builds on the Koopman perspective from the 1930s: represent nonlinear dynamics with linear operators in a higher-dimensional space. In practice, that's been tough at scale. The Duke system uses AI to make it tractable-learning the right variables so a linear model is both compact and faithful to reality. For background, see the Koopman operator.
What makes it different
- Reduces systems with hundreds or thousands of variables to a small set of latent coordinates.
- Produces interpretable, linear dynamics that connect cleanly to existing theory and methods.
- Consistently yields models more than 10× smaller than many prior ML approaches while keeping long-horizon accuracy.
- Finds structure (e.g., attractors) in addition to making forecasts.
How it works (high level)
The framework ingests time-series data and searches for the most informative patterns in how the system evolves. It combines deep learning with physics-inspired constraints to discover a minimal set of hidden variables. In that space, the dynamics are linear-simple enough to analyze-yet still match the measured behavior.
Evidence across domains
The team validated the method on systems ranging from a pendulum to nonlinear electronic circuits, climate models, and neural circuits. Despite their differences, the AI identified a small number of governing variables and produced compact models that held up for long-term predictions.
Beyond prediction: stability and warning signs
The framework can reveal attractors-stable states where a system naturally settles. That helps researchers tell whether a system is steady, drifting, or edging toward instability. As one team member put it, once you find the landmarks, the rest of the map comes into focus.
Where this is useful
- When first-principles equations are unknown, incomplete, or too complex.
- Model reduction for faster simulation, control, or design optimization.
- System identification and fault detection from operational data.
- Early-warning indicators for regime shifts in climate, biology, or engineered systems.
- Active experimental design: prioritize measurements that expose the system's true structure.
Resources
- Project site: Automated Global Analysis
- Video explainer: Watch on YouTube
- Lab: General Robotics Lab (Duke)
Publication and support
The research appears online (December 17) in npj Complexity. Support came from 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).
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