AI Tool Uncovers Governing Equations for Complex Systems
Researchers at Clarkson University have introduced KANDy, an artificial intelligence framework capable of extracting the underlying mathematical equations that govern complex and chaotic dynamical systems directly from observational data. The tool addresses a persistent limitation in contemporary machine learning, where predictive models often function as uninterpretable black boxes. By prioritizing discoverability alongside accuracy, KANDy delivers models that are both highly predictive and scientifically transparent. Built upon Kolmogorov-Arnold Networks, KANDy was specifically engineered to handle the nonlinear, noisy, and unpredictable characteristics typical of physical systems. Developed by Research Associate Kevin Slote and Research Assistant Professor Jeremie Fish under the supervision of Erik Bollt, the architecture successfully identifies governing equations in scenarios where conventional equation-discovery methods typically fail. The research team validated the system across a range of rigorous benchmarks, including discrete and continuous dynamical systems, chaotic partial differential equations, and the complex topological structure of the Hopf fibration. The successful recovery of these mathematical relationships demonstrates KANDy’s capacity to capture deeper structural properties of nonlinear phenomena. This advancement provides engineers and scientists with a reliable, data-driven methodology for modeling physical systems without requiring prior theoretical assumptions. The framework’s ability to balance interpretability with predictive performance positions it as a significant step toward transparent, physics-informed artificial intelligence. The study detailing the development and validation of KANDy has been published as a preprint on arXiv. The software is available for public testing and implementation, with installation guidelines and source code hosted on GitHub.
