SINDy, Sparse Identification of Nonlinear Dynamics, is a different flavor of physics-informed learning: no network, just linear algebra with a sparsity prior. Stack the measured derivatives ẋ into a vector, build a matrix Θ(x) whose columns are candidate functions evaluated at every sample, and solve ẋ = Θ(x)Ξ for the coefficients Ξ. Ordinary least squares gives a dense Ξ, every candidate gets a nonzero coefficient, most of them fitting noise. The insight is that real dynamical laws are sparse: nature writes short equations. So SINDy uses sequentially thresholded least squares (fit, zero every coefficient below λ, refit on the survivors, repeat) which drives Ξ to just the few terms that matter. λ is the knob between an overfit dense model and an oversparse one, and its sweet spot recovers the exact governing equation, coefficients included. Because the result is a formula over named terms, it is interpretable and extrapolates, unlike a black box, you can read what it learned and check it against physics. The catch is the library: SINDy can only discover terms you thought to include, and it needs the derivatives, which are noisy when estimated from data, which is exactly why the threshold matters.