Data-driven discovery and control of multistable nonlinear systems and hysteresis via structured Neural ODEs

Researchers Ike Griss Salas and Ethan King have introduced a novel, structured Neural Ordinary Differential Equation (NODE) architecture designed to tackle a core challenge in systems engineering: identifying and controlling complex, multistable physical systems from limited data. Many engineered processes, from robotic actuators to chemical reactors, exhibit nonlinear dynamics that settle into one of several stable states (equilibria) based on control inputs. Traditional data-driven discovery struggles because stable dynamics provide little excitation, and models are often non-unique. The proposed architecture imposes a specific mathematical structure—F(x,u) = f(x)(x - g(x,u))—where f(x) < 0 ensures the system is contractive (stable) and g(x,u) learns the map to multiple attractor states. This structure acts as a strong inductive bias, guiding the AI to learn physically plausible and stable dynamics even from short, potentially underexciting data sequences.

This approach has proven effective across several nonlinear benchmark systems. The key innovation is that by learning the implicit equilibrium map `g`, the model not only accurately captures multiple basins of attraction and hysteresis effects but also enables efficient, gradient-based design of feedback controllers. Instead of treating the AI model as a black-box simulator, engineers can now directly leverage the learned structure to compute control actions that steer the system to a desired stable state. This bridges a significant gap between pure system identification and practical control synthesis, moving AI from a passive modeling tool to an active component in control system design. The work, detailed in the arXiv preprint 2603.27024, represents a meaningful step toward more reliable and interpretable AI for physical system automation.