Automated reverse engineering of nonlinear dynamical systems

TLDR

Complex nonlinear dynamics arise in many scientific and engineering fields, yet extracting the underlying differential equations directly from observations remains a challenging problem. The study introduces a method that automatically generates symbolic equations for nonlinear coupled dynamical systems directly from time‑series data. The method models each variable separately, perturbs and destabilizes the system to reveal hidden dynamics, and automatically simplifies the resulting ordinary differential equations, and is applicable to any system described by ODEs with observable variables, as demonstrated on four simulated and two real systems. The resulting symbolic models provide explanatory insight, indicating that automated reverse‑engineering of nonlinear systems may increasingly aid understanding of complex systems.

Abstract

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated "reverse engineering" approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future.