sindyr-package: Sparse Identification of Nonlinear Dynamics

In racdale/sindyr: Sparse Identification of Nonlinear Dynamics

Sparse Identification of Nonlinear Dynamics

Description

This implements the Brunton et al (2016; PNAS, doi: 10.1073/pnas.1517384113) sparse identification algorithm for finding ordinary differential equations for a measured system from raw data (SINDy). The package includes a set of additional tools for working with raw data, with an emphasis on cognitive science applications (Dale and Bhat, in press, doi: 10.1016/j.cogsys.2018.06.020).

Details

Package:	sindyr
Type:	Package
Version:	0.2.1
Date:	2018-09-10
License:	GPL >= 2

sindy: Main function to infer coefficient matrix for set of ODEs.

windowed_sindy: Sliding window function to obtain SINDy results across segments of a time series.

features: Function for generation feature space from measured variables.

finite_differences: Numerical differentiation over multiple columns.

sindy: Main function to infer coefficient matrix for set of ODEs.

windowed_sindy: Sliding window function to obtain SINDy results across segments of a time series.

features: Function for generation feature space from measured variables.

finite_differences: Numerical differentiation over multiple columns.

finite_difference: Numerical differential of a vector.

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.

For further examples and links to other materials see: https://github.com/racdale/sindyr

Examples

# example to reconstruct of 
# the Lorenz system

library(sindyr)

set.seed(666)
dt = .001
numsteps = 10000; dt = dt; sigma = 10; r = 28; b = 2.6;
xs = data.frame(lorenzattractor(numsteps, dt, sigma, r, b, plots=FALSE))
colnames(xs) = list('x','y','z')
xs = xs[2000:nrow(xs),] # cut out initialization

points3D(xs$x,xs$y,xs$z,type='l',col='black')
Theta = features(xs,3) # grid of features
par(mfrow=c(7,3),oma = c(2,0,0,0) + 0.1,mar = c(1,1,1,1) + 0.1)
for (i in 2:ncol(Theta)) {
  plot(Theta[,i],xlab='t',main=gsub(':','',colnames(Theta)[i]),type='l',xaxt='n',yaxt='n')
}

sindy.obj = sindy(xs=xs,dt=dt,lambda=.5) # let's reconstruct
sindy.obj$B # Lorenz equations

racdale/sindyr documentation built on Sept. 12, 2023, 12:20 p.m.