Sparse identification of nonlinear dynamics (SINDy)

SINDy fits an explicit governing equation to data by assuming the dynamics are sparse in a chosen library of candidate functions. One builds a dictionary of terms (polynomials, trigonometric functions, and so on) evaluated along the trajectory, estimates the time derivatives, and solves a sparse regression so that dx/dt equals a short weighted sum of library terms. The output is a compact, human-readable set of differential equations rather than a black-box network — the appeal is interpretability and, when the true dynamics really are sparse in the library, sample efficiency and extrapolation.

Applying SINDy to neural systems is genuinely hard and remains frontier: spikes must first be turned into a smooth low-dimensional state (SINDy is usually run in a latent space from a VAE/autoencoder, as in SINDy-autoencoder pipelines), derivative estimation is noise-sensitive, and the recovered equations depend heavily on the library and the sparsity threshold. It is best viewed as a hypothesis generator for governing equations in a reduced latent space, not a turnkey method for raw high-dimensional recordings.