Empirical Discovery of Differential Equations from Time Series
Data
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Documentation for package ‘EmpiricalDynamics’ version 0.1.2
Help Pages
| analysis_summary | Create Analysis Summary |
| analyze_bifurcations | Analyze Bifurcations |
| analyze_fixed_points | Analyze Fixed Points |
| annotate_hypotheses | Annotate Hypotheses |
| bootstrap_parameters | Bootstrap Confidence Intervals for Parameters |
| check_qualitative_behavior | Check Qualitative Behavior |
| coefficient_table | Generate Coefficient Table |
| compare_differentiation_methods | Compare Differentiation Methods |
| compare_estimation_methods | Compare OLS and GLS Estimation |
| compare_trajectories | Compare Simulated and Observed Trajectories |
| compute_derivative | Compute Derivative of a Time Series |
| compute_derivatives | Compute Derivatives for Specified Variables |
| compute_derivative_fd | Centered Finite Differences |
| compute_derivative_savgol | Savitzky-Golay Derivative |
| compute_derivative_spectral | Spectral (FFT) Differentiation |
| compute_derivative_spline | Smoothing Spline Derivative |
| compute_derivative_tvr | Total Variation Regularized Differentiation |
| compute_residuals | Compute Residuals from Symbolic Equation |
| construct_sde | Construct Stochastic Differential Equation Model |
| create_transformations | Create Candidate Transformations |
| cross_validate | Cross-Validate Discovered Equation |
| define_custom_operators | Define Custom Operators |
| diagnose_sampling_frequency | Diagnose Sampling Frequency |
| ed_theme | Default ggplot2 Theme for EmpiricalDynamics |
| estimate_initial_values | Automatic Initial Value Estimation |
| estimate_sde_iterative | Iterative GLS Estimation for SDEs |
| exploration | Visual Exploration of Dynamical Structure |
| explore_dynamics | Comprehensive Dynamics Exploration |
| export_results | Export Results to Multiple Formats |
| fit_residual_distribution | Fit Residual Distribution |
| fit_specified_equation | Fit Specified Equation |
| format_equation | Format Equation for Display |
| generate_report | Generate Analysis Report |
| get_analysis_template | Get Analysis Template |
| get_pareto_set | Get Full Pareto Set |
| list_example_data | List Available Example Datasets |
| load_example_data | Load Example Dataset |
| model_comparison_table | Generate Model Comparison Table |
| model_conditional_variance | Model Conditional Variance |
| output | Output and Report Generation |
| plot.bifurcation_analysis | Plot Bifurcation Diagram |
| plot.cv_result | Plot CV Results |
| plot.trajectory_simulation | Plot Simulated Trajectories |
| plot.tvr_derivative | Plot Method for TVR Derivative |
| plot.validation_result | Plot Validation Results |
| plot_bivariate | Bivariate Scatter Plot |
| plot_pareto_front | Plot Pareto Front |
| plot_phase_1d | 1D Phase Diagram |
| plot_residual_diagnostics_panel | Plot Residual Diagnostics Panel |
| plot_surface_3d | 3D Response Surface |
| plot_timeseries | Time Series Plot |
| plot_trajectory_2d | 2D Trajectory Plot |
| plot_tvr_diagnostic | Diagnostic Plot for TVR Differentiation |
| predict.variance_model | Predict from Variance Model |
| preprocessing | Preprocessing Functions for Time Series Data |
| print.cv_result | Print CV Results |
| print.qualitative_check | Print Qualitative Check Results |
| print.residual_diagnostics | Print Residual Diagnostics |
| print.tvr_derivative | Print Method for TVR Derivative |
| print.validation_result | Print Validation Results |
| print_summary | Print Analysis Summary |
| read_empirical_data | Read Empirical Data from File |
| residual_analysis | Residual Analysis and Stochastic Differential Equations |
| residual_diagnostics | Comprehensive Residual Diagnostics |
| save_plots | Save Diagnostic Plots |
| select_equation | Select Equation from Pareto Front |
| select_lambda_cv_tvr | Cross-Validation Selection of Lambda for TVR |
| sensitivity_analysis | Parameter Sensitivity Analysis |
| setup_julia_backend | Setup Julia Backend |
| simulate_trajectory | Simulate Trajectory from SDE |
| specify_variables | Specify Variable Types for Dynamical Analysis |
| suggest_differentiation_method | Suggest Differentiation Method Based on Data Characteristics |
| symbolic_search | Symbolic Regression and Equation Discovery |
| symbolic_search_weighted | Weighted Symbolic Search |
| to_latex | Convert Equation to LaTeX |
| validate_model | Comprehensive Model Validation |
| validation | Validation of Discovered Equations |