windowed_sindy {sindyr}

Run SINDy over time windows

Description

Run SINDy on raw data with a sliding window approach

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.)

fit.its

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

B.expected

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

window.size

Size of window to segment raw data as separate time series; defaults to deciles

window.shift

Step sizes across windows, permitting overlap; defaults to deciles

Details

A convenience function for extracting a list of coefficients on segments of a time series. This facilitates using SINDy output as source of descriptive measures of dynamics.

Value

It returns a list of coefficients Bs containing B coefficients at each window

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.