sindy {sindyr}

Run main SINDy function

Description

Estimates coefficients for set of ordinary differential equations governing system variables.

Arguments

xs

Matrix of raw data

dx

Matrix of main system variable dervatives; if NULL, it estimates with finite differences from xs

dt

Sample interval, if data continuously sampled; default = 1

Theta

Matrix of features; if not supplied, assumes polynomial features of order 3

lambda

Threshold to use for iterated least squares sparsification (Brunton et al.)

B.expected

The function will compute a goodness of fit if supplied with an expected coefficient matrix B; default = NULL

verbose

Verbose mode outputs Theta and dx values in their entirety; default = FALSE

fit.its

Number of iterations to conduct the least-square threshold sparsification; default = 10

plot.eq.graph

When set to TRUE, prints an igraph plot of variables as a graph structure; default = FALSE

Details

Uses the "left-division" approach of Brunton et al. (2016), and implements least-squares sparsification, and outputs coefficients after iterations stabilize.

Value

Returns a matrix B of coefficients specifying the relationship between dx and Theta

Author(s)

Rick Dale and Harish S. Bhat

References

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.