Package: EmpiricalDynamics 0.1.14

EmpiricalDynamics: Empirical Discovery of Differential Equations from Time Series Data

A comprehensive toolkit for discovering differential and difference equations from empirical time series data using symbolic regression. The package implements a complete workflow from data preprocessing (including Total Variation Regularized differentiation for noisy economic data), visual exploration of dynamical structure, and symbolic equation discovery via genetic algorithms. It leverages a high-performance 'Julia' backend ('SymbolicRegression.jl') to provide industrial-grade robustness, physics-informed constraints, and rigorous out-of-sample validation. Designed for economists, physicists, and researchers studying dynamical systems from observational data.

Authors:José Mauricio Gómez Julián [aut, cre]

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manual.pdf |manual.html✨
DESCRIPTION |NEWS
card.svg |card.png
EmpiricalDynamics/json (API)

# Install 'EmpiricalDynamics' in R:

install.packages('EmpiricalDynamics', repos = c('https://isadorenabi.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/isadorenabi/empiricaldynamics/issues

On CRAN:

nonlinear-dynamics time-series

4.62 score 12 scripts 335 downloads 65 exports 43 dependencies

Last updated from:3f4ed02e4f. Checks:9 OK. Indexed: yes.

Target	Result	Time
linux-devel	OK	166
source / vignettes	OK	332
linux-release	OK	164
macos-release	OK	191
macos-oldrel	OK	216
windows-devel	OK	157
windows-release	OK	130
windows-oldrel	OK	123
wasm-release	OK	194

Exports:analysis_summary analyze_bifurcations analyze_fixed_points annotate_hypotheses bootstrap_parameters check_qualitative_behavior coefficient_table compare_differentiation_methods compare_estimation_methods compare_trajectories compute_derivative compute_derivative_fd compute_derivative_savgol compute_derivative_spectral compute_derivative_spline compute_derivative_tvr compute_derivatives compute_residuals construct_sde create_transformations cross_validate define_custom_operators diagnose_sampling_frequency ed_consensus_fixed_points ed_derivative_step ed_theme estimate_diffusion_qv estimate_initial_values estimate_sde_iterative explore_dynamics export_results fit_residual_distribution fit_specified_equation format_equation generate_report get_analysis_template get_pareto_set list_example_data load_example_data model_comparison_table model_conditional_variance parameterize_equation plot_bivariate plot_pareto_front plot_phase_1d plot_residual_diagnostics_panel plot_surface_3d plot_timeseries plot_trajectory_2d plot_tvr_diagnostic print_summary read_empirical_data residual_diagnostics save_plots select_equation select_lambda_cv_tvr sensitivity_analysis setup_julia_backend simulate_trajectory specify_variables suggest_differentiation_method symbolic_search symbolic_search_weighted to_latex validate_model

Dependencies:backports checkmate clarabel cli cpp11 curl CVXR farver ggplot2 glue gmp gridExtra gtable highs isoband jsonlite labeling lattice lifecycle lmtest MASS Matrix minpack.lm osqp quadprog quantmod R6 RColorBrewer Rcpp RcppEigen rlang S7 scales scs signal slam tseries TTR vctrs viridisLite withr xts zoo

Getting Started with EmpiricalDynamics

Rendered fromgetting-started.Rmdusingknitr::rmarkdown

Last update: 2026-01-21
Started: 2026-01-21

Help page	Topics
Create Analysis Summary	analysis_summary
Analyze Bifurcations	analyze_bifurcations
Analyze Fixed Points	analyze_fixed_points
Annotate Hypotheses	annotate_hypotheses
Bootstrap Confidence Intervals for Parameters	bootstrap_parameters
Check Qualitative Behavior	check_qualitative_behavior
Generate Coefficient Table	coefficient_table
Compare Differentiation Methods	compare_differentiation_methods
Compare OLS and GLS Estimation	compare_estimation_methods
Compare Simulated and Observed Trajectories	compare_trajectories
Compute Derivative of a Time Series	compute_derivative
Centered Finite Differences	compute_derivative_fd
Savitzky-Golay Derivative	compute_derivative_savgol
Spectral (FFT) Differentiation	compute_derivative_spectral
Smoothing Spline Derivative	compute_derivative_spline
Total Variation Regularized Differentiation	compute_derivative_tvr
Compute Derivatives for Specified Variables	compute_derivatives
Compute Residuals from Symbolic Equation	compute_residuals
Construct Stochastic Differential Equation Model	construct_sde
Create Candidate Transformations	create_transformations
Cross-Validate Discovered Equation	cross_validate
Define Custom Operators	define_custom_operators
Diagnose Sampling Frequency	diagnose_sampling_frequency
Reduce a Posterior of Fixed Points to Branches	ed_consensus_fixed_points
The step of the central difference this package differentiates with	ed_derivative_step
Default ggplot2 Theme for EmpiricalDynamics	ed_theme
Estimate Diffusion via Quadratic Variation	estimate_diffusion_qv
Automatic Initial Value Estimation	estimate_initial_values
Iterative GLS Estimation for SDEs	estimate_sde_iterative
Visual Exploration of Dynamical Structure	exploration
Comprehensive Dynamics Exploration	explore_dynamics
Export Results to Multiple Formats	export_results
Fit Residual Distribution	fit_residual_distribution
Fit Specified Equation	fit_specified_equation
Format Equation for Display	format_equation
Generate Analysis Report	generate_report
Get Analysis Template	get_analysis_template
Get Full Pareto Set	get_pareto_set
List Available Example Datasets	list_example_data
Load Example Dataset	load_example_data
Generate Model Comparison Table	model_comparison_table
Model Conditional Variance	model_conditional_variance
Output and Report Generation	output
Turn the Fitted Constants of a Discovered Equation into Free Parameters	parameterize_equation
Bivariate Scatter Plot	plot_bivariate
Plot Pareto Front	plot_pareto_front
1D Phase Diagram	plot_phase_1d
Plot Residual Diagnostics Panel	plot_residual_diagnostics_panel
3D Response Surface	plot_surface_3d
Time Series Plot	plot_timeseries
2D Trajectory Plot	plot_trajectory_2d
Diagnostic Plot for TVR Differentiation	plot_tvr_diagnostic
Plot Bifurcation Diagram	plot.bifurcation_analysis
Plot CV Results	plot.cv_result
Plot Simulated Trajectories	plot.trajectory_simulation
Plot Method for TVR Derivative	plot.tvr_derivative
Plot Validation Results	plot.validation_result
Predict from Variance Model	predict.variance_model
Preprocessing Functions for Time Series Data	preprocessing
Print Analysis Summary	print_summary
Print a Bifurcation Analysis	print.bifurcation_analysis
Print CV Results	print.cv_result
Print Qualitative Check Results	print.qualitative_check
Print Residual Diagnostics	print.residual_diagnostics
Print Method for TVR Derivative	print.tvr_derivative
Print Validation Results	print.validation_result
Read Empirical Data from File	read_empirical_data
Residual Analysis and Stochastic Differential Equations	residual_analysis
Comprehensive Residual Diagnostics	residual_diagnostics
Save Diagnostic Plots	save_plots
Select Equation from Pareto Front	select_equation
Cross-Validation Selection of Lambda for TVR	select_lambda_cv_tvr
Parameter Sensitivity Analysis	sensitivity_analysis
Setup Julia Backend	setup_julia_backend
Simulate Trajectory from SDE	simulate_trajectory
Specify Variable Types for Dynamical Analysis	specify_variables
Suggest Differentiation Method Based on Data Characteristics	suggest_differentiation_method
Symbolic Regression and Equation Discovery	symbolic_search
Weighted Symbolic Search	symbolic_search_weighted
Convert Equation to LaTeX	to_latex
Comprehensive Model Validation	validate_model
Validation of Discovered Equations	validation

Package: EmpiricalDynamics 0.1.14

EmpiricalDynamics: Empirical Discovery of Differential Equations from Time Series Data

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