Equations of mind: Data science for inferring nonlinear dynamics of socio-cognitive systems - ScienceDirect
Fig. 1. A representation of the first step of the SINDy algorithm. The researcher collects samples of data in matrix 𝑋 . These might be several variables ( 𝑥 , 𝑦 , etc.) collected at a given sample rate. The researcher then obtains a representation of the first-order derivative of the data (bottom left), and then uses a feature function f to generate a set of derived variables of interest (bottom right). The function f in many cases may simply multiply these original variables (generating polynomial terms). Note: Cell shading is meant to connote variation in any such data matrices. Fig. 2. In the second step for SINDy, an iterative thresholding approach is taken to fit a matrix of coefficients, 𝐵 . 𝐵 is a sparse matrix, where all coefficients remaining are above some threshold, ∊ . Once this matrix 𝐵 is established, we can fully state the estimated dynamic system. Fig. 3. Top: We illustrate iterating the logistic map under two values of the control parameter a. When 𝑎 =