System Identification

System identification uses observations of a system, often alongside controlled inputs, to infer how it changes over time and how it will respond to new conditions. Approaches range from ARX and state-space or subspace methods to sparse equation discovery with SINDy, Koopman operators, neural ODEs, and physics-structured models such as Hamiltonian networks; Bayesian and active-learning methods help choose experiments and quantify uncertainty. These tools support prediction and control in settings including robotics, industrial processes, physical experiments, and systems observed through video. A central challenge is that accurate prediction on observed data does not guarantee that the underlying laws or parameters are identifiable, especially with sparse, noisy, partial, or weakly excited observations.