Artificial intelligence capable of deriving simple equations from complex systems could mark a significant shift for the digital construction sector. A research team at Duke University has developed a new AI framework that analyses time-series data to uncover understandable mathematical rules governing highly complex, dynamic systems. For industries increasingly driven by data, including digital construction, this approach offers new opportunities to improve modelling, prediction and decision-making across the built environment.
Published on 17 December in npj Complexity, the research addresses a long-standing challenge in science and engineering: how to translate large volumes of data into simplified rules that humans can interpret and use. The AI framework mirrors the work of historical dynamicists, such as Isaac Newton, who derived equations linking force and motion. Instead of manual derivation, the system automatically generates equations that describe how systems evolve over time.
Importantly, the AI does more than replicate human reasoning. It can untangle nonlinear systems with hundreds or thousands of variables and reduce them into compact representations with far fewer dimensions. For digital construction, where infrastructure systems combine structural behaviour, environmental conditions, energy flows and operational data, this ability to simplify complexity is particularly relevant.
“Scientific discovery has always depended on finding simplified representations of complicated processes,” said Boyuan Chen, Director of the General Robotics Lab and Dickinson Family Assistant Professor at Duke University. “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 research builds on a concept first proposed by mathematician Bernard Koopman in the 1930s, which suggested that nonlinear systems could be represented mathematically by linear models. In practical terms, this means complex behaviour can often be approximated by simpler equations without losing essential accuracy. For example, while the path of a projectile depends on many factors, a simple linear equation using velocity and angle can still provide a close approximation.
Historically, applying Koopman theory at scale has been impractical, as it required developing vast numbers of equations that exceed human cognitive limits. The Duke framework addresses this limitation by combining deep learning with physics-inspired constraints. It identifies informative patterns in time-series data and distils them into a small set of hidden variables that capture the system’s essential behaviour.
Real-world complexity
The resulting models behave mathematically like linear systems while still reflecting real-world complexity. When tested across diverse applications—including pendulum motion, electrical circuits, climate models and neural systems—the framework consistently produced reduced models more than ten times smaller than those created using previous machine-learning approaches. Crucially, these models maintained reliable long-term predictive performance.
For the digital construction sector, this has implications for areas such as building performance simulation, digital twins, infrastructure monitoring and smart asset management. Compact, interpretable models could improve confidence in AI-driven predictions, supporting safer design decisions, better operational planning and more efficient lifecycle management.
“What stands out is not just the accuracy, but the interpretability,” Chen explained. “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.”
Beyond prediction, the framework can identify attractors—stable states towards which systems naturally evolve. In construction and infrastructure systems, understanding these states can help engineers identify normal operating conditions, detect drift, and anticipate instability before failures occur.
“For a dynamicist, finding these structures is like finding the landmarks of a new landscape,” said Sam Moore, lead author and PhD candidate in Chen’s lab. “Once you know where the stable points are, the rest of the system starts to make sense.”
The researchers emphasise that the framework is most valuable when traditional equations are incomplete, unknown or impractical to derive. “This is not about replacing physics,” Moore added. “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 plans to explore how the AI could guide experimental design by identifying which data to collect to reveal system structure more efficiently. Future applications may also include richer data types such as video, audio and biological signals—capabilities that align with emerging sensor-driven construction sites and connected infrastructure.
By translating complex data into interpretable equations, this AI framework could strengthen digital construction modelling, enabling clearer insight, improved prediction and more reliable decision-making across the built environment.
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