argos {ARGOS}

Automatic Regression for Governing Equations (ARGOS)

Description

This function performs sparse regression on a data set to identify the governing equations of the system. It takes a list of data from 'build_design_matrix' then applies the Lasso or Adaptive Lasso for variable selection.

Usage

argos(
  design_matrix,
  library_type = c("poly", "four", "poly_four"),
  state_var_deriv = 1,
  alpha_level = 0.05,
  num_samples = 2000,
  sr_method = c("lasso", "alasso"),
  weights_method = NULL,
  ols_ps = TRUE,
  parallel = c("no", "multicore", "snow"),
  ncpus = NULL
)

Arguments

design_matrix

A list containing data frame, vector of predictor variable orders for 'theta', and derivative matrix.

library_type

A character vector (default: c("poly", "four", "poly_four")) specifying the type of library being used.

state_var_deriv

An integer. The index of the state variable for which the derivative is calculated. Default is 1.

alpha_level

A numeric scalar. The level of significance for confidence intervals. Default is 0.05.

num_samples

An integer. The number of bootstrap samples. Default is 2000.

sr_method

A character string. The sparse regression method to be used, either "lasso" or "alasso". Default is "lasso".

weights_method

A string or NULL. The method for calculating weights in the Adaptive Lasso. If NULL, ridge regression pilot estimates are used. Default is NULL.

ols_ps

A logical. If TRUE, post-selection OLS is performed after the Lasso or Adaptive Lasso. Default is TRUE.

parallel

A character string. The type of parallel computation to be used, either "no", "multicore" or "snow". Default is "no".

ncpus

An integer or NULL. The number of cores to be used in parallel computation. If NULL, the function will try to detect the number of cores. Default is NULL.

Value

A list with three elements: - point_estimates: a vector of point estimates for the coefficients. - ci: a matrix where each column represents the lower and upper bounds of the confidence interval for a coefficient. - identified_model: a matrix of coefficients of the identified model.

Examples

# Identify the x1 equation of the Duffing Oscillator with ARGOS.
# Output provides point estimates, confidence intervals, and identified model.
x_t <- duffing_oscillator(n=1000, dt = 0.01,
                          init_conditions = c(1, 0),
                          gamma_value = 0.1, kappa_value = 1,
                          epsilon_value = 5, snr = 49)
duffing_design_matrix <-
       build_design_matrix(x_t, dt = 0.01, sg_poly_order = 4,
                           library_degree = 5, library_type = "poly")
design_matrix <- duffing_design_matrix
state_var_deriv = 1 # Denotes first equation/derivative to be identified
alpha_level = 0.05
num_samples = 10
sr_method = "lasso"
weights_method = NULL
ols_ps = TRUE
parallel = "no"
ncpus = NULL
library_type <- "poly"
perform_argos <- argos(design_matrix = design_matrix,
                       library_type = library_type,
                       state_var_deriv = state_var_deriv,
                       alpha_level = alpha_level,
                       num_samples = num_samples,
                       sr_method = "lasso",
                       weights_method = NULL,
                       ols_ps = TRUE,
                       parallel = "no",
                       ncpus = NULL)
perform_argos$point_estimates
perform_argos$ci
perform_argos$identified_model