TITLE: AI Uncovers Simple Rules in Complex Systems

AI Framework Simplifies Complex Dynamics

A new artificial intelligence tool developed by researchers can extract simple mathematical rules from highly complex systems that evolve over time, offering scientists a clearer path to understanding phenomena in physics, engineering, climate science and biology.

The framework, detailed in a study published online December 17 in the journal npj Complexity, analyzes time-series data to identify underlying patterns. It transforms intricate nonlinear interactions involving hundreds or thousands of variables into compact linear models that retain essential behaviors while being far easier to interpret.

This approach addresses a longstanding challenge in scientific discovery: bridging vast datasets with the simplified representations that drive theoretical advances. As systems like weather patterns or biological networks grow more intricate, traditional methods often fall short, leaving researchers without workable equations.

The AI draws inspiration from historical figures in dynamics, such as Isaac Newton, who linked forces to motion through elegant equations. Modern extensions build on 1930s mathematician Bernard Koopman's theory, which posits that nonlinear systems can be linearly represented -- though typically requiring an unwieldy number of equations.

How the AI Processes Data

At its core, the system uses deep learning combined with physics-inspired constraints to sift through experimental data. It focuses on how systems change over time, pinpointing a minimal set of variables that govern evolution.

For instance, consider a cannonball's trajectory, influenced by speed, angle, air resistance, wind and temperature. While reality is chaotic, a basic linear equation using just initial conditions approximates the path effectively. The AI automates this simplification for far more demanding scenarios.

In testing, the framework was applied to diverse examples: the oscillatory swing of a pendulum, nonlinear responses in electrical circuits, simulations in climate modeling and activity in neural circuits. Across these, it consistently derived models with fewer dimensions -- often more than 10 times smaller than those from conventional machine learning techniques -- while maintaining reliable long-term forecasts.

The resulting equations behave linearly, allowing integration with established scientific tools developed over centuries. This interpretability is key, as it enables researchers to connect AI outputs to human-derived theories, fostering collaborative discovery.

Identifying Stability and Risks

Beyond forecasting, the tool reveals structural features like attractors -- stable states toward which systems converge. These 'landmarks' help assess normal operation, gradual shifts or impending breakdowns.

In practical terms, this could flag anomalies in mechanical devices, predict climate tipping points or monitor biological signals for disease indicators. For dynamicists, mapping these elements demystifies otherwise opaque landscapes.

The method shines where physics-based equations are absent, incomplete or overly burdensome. It extends data-driven reasoning without supplanting fundamental principles, filling gaps in knowledge for emerging technologies and natural processes.

Broader Implications for Science

Looking forward, the researchers aim to enhance the framework for guiding experiments, prioritizing data collection to uncover structures efficiently. Plans include adapting it for multimedia inputs like video and audio, particularly in biology.

This work aligns with efforts to create 'machine scientists' that automate hypothesis generation and rule extraction. By merging AI with dynamical systems mathematics, it promises to illuminate rules shaping physical and living worlds.

The development was supported by grants from the National Science Foundation, Army Research Laboratory, Army Research Office and DARPA programs. Additional resources are available at the project's website and a related video demonstration.

The framework's versatility underscores AI's potential to accelerate discovery in an era of data abundance, where complexity once hindered progress. As applications expand, it could redefine how scientists tackle the universe's most elusive puzzles.