Dynamical Systems

Dynamical systems describe how a system's state changes over time and explain behaviors such as equilibria, oscillations, attractors, bifurcations, and chaos. Researchers analyze these behaviors mathematically and learn models from data using approaches such as Koopman operators, neural ODEs, physics-informed networks, and structure-preserving Hamiltonian models. Applications range from forecasting Lorenz and pendulum dynamics to modeling reaction-diffusion processes, neural activity, and robot motion, often with control and safety guarantees. A central challenge is that accurate short-term predictions do not ensure faithful long-term behavior: learned models can drift, violate physical constraints, or fail to generalize to unseen regimes.