Empirical Discovery of Differential Equations from Time Series Data
Create Analysis Summary
Analyze Bifurcations
Analyze Fixed Points
Annotate Hypotheses
ARCH-LM Test
Block Bootstrap Indices
Bootstrap Confidence Intervals for Parameters
Build Pareto Front from Results
Check Qualitative Behavior
Coefficient Change Between Equations
Generate Coefficient Table
Compare Differentiation Methods
Compare OLS and GLS Estimation
Compare Simulated and Observed Trajectories
Centered Finite Differences
Savitzky-Golay Derivative
Spectral (FFT) Differentiation
Smoothing Spline Derivative
Total Variation Regularized Differentiation
Compute Derivative of a Time Series
Compute Derivatives for Specified Variables
Compute Excess Kurtosis
Compute Residuals from Symbolic Equation
Compute Skewness
Construct Stochastic Differential Equation Model
Create Block Folds (for time series)
Create Random Folds
Create Rolling Folds (walk-forward validation)
Create Candidate Transformations
Cross-Validate Discovered Equation
Define Custom Operators
Data Frame to HTML Table
Data Frame to LaTeX Table
Data Frame to Markdown Table
Diagnose Sampling Frequency
Default ggplot2 Theme for EmpiricalDynamics
Automatic Initial Value Estimation
Iterative GLS Estimation for SDEs
Evaluate equation with modified coefficients
Visual Exploration of Dynamical Structure
Comprehensive Dynamics Exploration
Export Results to Multiple Formats
Find Knee Point in Pareto Front
Fit Residual Distribution
Fit Specified Equation
Fit Student's t Distribution
Fit Using General Optimization
Format Equation String
Format Equation for Display
Generate Analysis Report
Get Analysis Template
Get Full Pareto Set
List Available Example Datasets
Load Example Dataset
Generate Model Comparison Table
Model Conditional Variance
Output and Report Generation
Bivariate Scatter Plot
Plot Pareto Front
1D Phase Diagram
Plot Residual Diagnostics Panel
3D Response Surface
Time Series Plot
2D Trajectory Plot
Diagnostic Plot for TVR Differentiation
Plot Bifurcation Diagram
Plot CV Results
Plot Simulated Trajectories
Plot Method for TVR Derivative
Plot Validation Results
Predict from Variance Model
Preprocessing Functions for Time Series Data
Print Analysis Summary
Print CV Results
Print Qualitative Check Results
Print Residual Diagnostics
Print Method for TVR Derivative
Print Validation Results
Convert R Expression to LaTeX
Read Empirical Data from File
Residual Analysis and Stochastic Differential Equations
Comprehensive Residual Diagnostics
Runs Test for Randomness
Save Diagnostic Plots
Create Section Header
Select Equation from Pareto Front
Cross-Validation Selection of Lambda for TVR
Parameter Sensitivity Analysis
Setup Julia Backend
Simulate Trajectory from SDE
Specify Variable Types for Dynamical Analysis
Suggest Differentiation Method Based on Data Characteristics
Julia Backend for Symbolic Search
Exhaustive Search for Simple Equations
R-Native Genetic Algorithm for Symbolic Regression
Weighted Symbolic Search
Symbolic Regression and Equation Discovery
Simple JSON Conversion
Convert Equation to LaTeX
Utility Functions for EmpiricalDynamics
Comprehensive Model Validation
Validation of Discovered Equations
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.
Useful links