Estimates coefficients for set of ordinary differential equations governing system variables.
Returns a matrix B of coefficients specifying the relationship between dx and Theta
Matrix of raw data
Matrix of main system variable dervatives; if NULL, it estimates with finite differences from xs
Sample interval, if data continuously sampled; default = 1
Matrix of features; if not supplied, assumes polynomial features of order 3
Threshold to use for iterated least squares sparsification (Brunton et al.)
The function will compute a goodness of fit if supplied with an expected coefficient matrix B; default = NULL
Verbose mode outputs Theta and dx values in their entirety; default = FALSE
Number of iterations to conduct the least-square threshold sparsification; default = 10
When set to TRUE, prints an igraph plot of variables as a graph structure; default = FALSE
Rick Dale and Harish S. Bhat
Uses the "left-division" approach of Brunton et al. (2016), and implements least-squares sparsification, and outputs coefficients after iterations stabilize.
Dale, R. and Bhat, H. S. (in press). Equations of mind: data science for inferring nonlinear dynamics of socio-cognitive systems. Cognitive Systems Research.
Brunton, S. L., Proctor, J. L., and Kutz, J. N. (2016). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932-3937.