Sparse Identification of Nonlinear Dynamics

Sparse identification of nonlinear dynamics seeks simple, interpretable equations that explain how a system changes over time, often for ordinary or partial differential equations. A common approach, SINDy, fits a sparse set of terms from a candidate library; weak and integral formulations, active sampling, and neural or symbolic methods aim to handle noisy data, limited observations, and complex features. These methods are used across physical and engineering systems, from fluid and climate dynamics to oscillators and control. A central challenge is that noisy or uninformative trajectories and ill-conditioned or incomplete libraries can make distinct equations hard to distinguish, so reliable recovery depends on both the method and the data.