From 5d4ee8f2930ff574ab597995278faa37db44d77b Mon Sep 17 00:00:00 2001 From: dfeen87 <158860247+dfeen87@users.noreply.github.com> Date: Sun, 3 May 2026 22:13:26 +0000 Subject: [PATCH] feat: Add Global Sensitivity Analysis (GSA) module MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Implements a parameter sweep across operators to calculate partial derivatives and identify the 'tipping point' of systemic coherence (Ψ). Includes generation of a Seaborn heatmap visualizing the sensitivity to Thermodynamic Stability (Θ) and Adaptive Gain (Γ). Co-authored-by: google-labs-jules[bot] <161369871+google-labs-jules[bot]@users.noreply.github.com> --- analysis/sensitivity.py | 263 +++++++++++++++++++++++++++ docs/figures/sensitivity_heatmap.png | Bin 0 -> 212431 bytes 2 files changed, 263 insertions(+) create mode 100644 analysis/sensitivity.py create mode 100644 docs/figures/sensitivity_heatmap.png diff --git a/analysis/sensitivity.py b/analysis/sensitivity.py new file mode 100644 index 0000000..89543ce --- /dev/null +++ b/analysis/sensitivity.py @@ -0,0 +1,263 @@ +""" +Global Sensitivity Analysis Module. + +MIT License + +Copyright (c) 2026 Don Michael Feeney Jr. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. + +This module performs Global Sensitivity Analysis (GSA) to identify critical +drivers of systemic collapse in the Neuro-Coherence Function (Ψ). The generated +heatmap allows researchers to identify which operator provides the most leverage +for therapeutic restoration, indicating where ΔΨ is maximized for a given change +in input. +""" + +import numpy as np +import pandas as pd +import seaborn as sns +import matplotlib.pyplot as plt +from typing import Tuple + +from simulations.core.neuro_coherence import NeuroCoherence +from simulations.core.operators import Operators + + +def perform_parameter_sweep( + resolution: int = 20, n_mc_samples: int = 100, phi: float = 1.0 +) -> Tuple[np.ndarray, np.ndarray, np.ndarray, np.ndarray]: + """ + Perform a parameter sweep across all four operators. + + Uses a grid for Θ (Thermodynamic Stability) and Γ (Adaptive Gain) + and Monte Carlo sampling for Δ (Connectivity Variance) and + Λ (Spatiotemporal Coherence). + + Args: + resolution: Grid resolution for Θ and Γ. + n_mc_samples: Number of Monte Carlo samples for Δ and Λ per grid point. + phi: Global modulation coefficient. + + Returns: + Tuple containing arrays for theta values, gamma values, + mean Ψ values, and mean partial derivative values w.r.t Θ and Γ. + """ + nc = NeuroCoherence(phi=phi) + ops = Operators() + + theta_vals = np.linspace(0.0, 1.0, resolution) + gamma_vals = np.linspace(0.0, 1.0, resolution) + + psi_grid = np.zeros((resolution, resolution)) + dpsi_dtheta_grid = np.zeros((resolution, resolution)) + dpsi_dgamma_grid = np.zeros((resolution, resolution)) + dpsi_ddelta_grid = np.zeros((resolution, resolution)) + dpsi_dlambda_grid = np.zeros((resolution, resolution)) + + # We use a small epsilon for finite differences + eps = 1e-4 + + for i, theta_param in enumerate(theta_vals): + for j, gamma_param in enumerate(gamma_vals): + psi_samples = np.zeros(n_mc_samples) + dpsi_dtheta_samples = np.zeros(n_mc_samples) + dpsi_dgamma_samples = np.zeros(n_mc_samples) + dpsi_ddelta_samples = np.zeros(n_mc_samples) + dpsi_dlambda_samples = np.zeros(n_mc_samples) + + for k in range(n_mc_samples): + # Monte Carlo sampling for delta and lambda + delta_param = np.random.uniform(0.0, 1.0) + lambda_param = np.random.uniform(0.0, 1.0) + + # Base operators + gamma_op = ops.adaptive_gain(plasticity=gamma_param) + theta_op = ops.thermodynamic_stability(homeostasis=theta_param) + delta_op = ops.connectivity_variance(sync_variance=delta_param) + lambda_op = ops.spatiotemporal_coherence(phase_alignment=lambda_param) + + base_psi = nc.calculate(gamma_op, theta_op, delta_op, lambda_op).psi + psi_samples[k] = base_psi + + # Perturb theta + theta_param_p = min(theta_param + eps, 1.0) + d_theta = theta_param_p - theta_param + if d_theta > 0: + theta_op_p = ops.thermodynamic_stability(homeostasis=theta_param_p) + psi_p = nc.calculate(gamma_op, theta_op_p, delta_op, lambda_op).psi + dpsi_dtheta_samples[k] = (psi_p - base_psi) / d_theta + + # Perturb gamma + gamma_param_p = min(gamma_param + eps, 1.0) + d_gamma = gamma_param_p - gamma_param + if d_gamma > 0: + gamma_op_p = ops.adaptive_gain(plasticity=gamma_param_p) + psi_p = nc.calculate(gamma_op_p, theta_op, delta_op, lambda_op).psi + dpsi_dgamma_samples[k] = (psi_p - base_psi) / d_gamma + + # Perturb delta + delta_param_p = min(delta_param + eps, 1.0) + d_delta = delta_param_p - delta_param + if d_delta > 0: + delta_op_p = ops.connectivity_variance(sync_variance=delta_param_p) + psi_p = nc.calculate(gamma_op, theta_op, delta_op_p, lambda_op).psi + dpsi_ddelta_samples[k] = (psi_p - base_psi) / d_delta + + # Perturb lambda + lambda_param_p = min(lambda_param + eps, 1.0) + d_lambda = lambda_param_p - lambda_param + if d_lambda > 0: + lambda_op_p = ops.spatiotemporal_coherence( + phase_alignment=lambda_param_p + ) + psi_p = nc.calculate(gamma_op, theta_op, delta_op, lambda_op_p).psi + dpsi_dlambda_samples[k] = (psi_p - base_psi) / d_lambda + + psi_grid[j, i] = np.mean( + psi_samples + ) # Note: y-axis is gamma (j), x-axis is theta (i) + dpsi_dtheta_grid[j, i] = np.mean(dpsi_dtheta_samples) + dpsi_dgamma_grid[j, i] = np.mean(dpsi_dgamma_samples) + dpsi_ddelta_grid[j, i] = np.mean(dpsi_ddelta_samples) + dpsi_dlambda_grid[j, i] = np.mean(dpsi_dlambda_samples) + + return ( + theta_vals, + gamma_vals, + psi_grid, + dpsi_dtheta_grid, + dpsi_dgamma_grid, + dpsi_ddelta_grid, + dpsi_dlambda_grid, + ) + + +def identify_tipping_points( + psi_grid: np.ndarray, threshold: float = 0.05 +) -> np.ndarray: + """ + Identify the 'tipping point' where Ψ approaches zero and the system + enters oscillatory divergence. + + Args: + psi_grid: The grid of Ψ values. + threshold: The threshold below which Ψ is considered near zero. + + Returns: + Boolean mask indicating the tipping point regions. + """ + # Find points where psi is below the threshold, indicating collapse + return psi_grid < threshold + + +def generate_sensitivity_heatmap( + theta_vals: np.ndarray, + gamma_vals: np.ndarray, + sensitivity_grid: np.ndarray, + tipping_points: np.ndarray, + output_path: str = "docs/figures/sensitivity_heatmap.png", +) -> None: + """ + Generate a high-resolution Seaborn Heatmap illustrating sensitivity. + + The heatmap displays the gradient magnitude (sensitivity) of Ψ with respect + to Θ and Γ. It also visually marks the tipping points. + + Args: + theta_vals: Array of Θ values (x-axis). + gamma_vals: Array of Γ values (y-axis). + sensitivity_grid: 2D array of sensitivity values to plot. + tipping_points: Boolean mask of tipping points. + output_path: Path to save the generated image. + """ + plt.figure(figsize=(10, 8)) + + # Create a DataFrame for seaborn + df = pd.DataFrame( + sensitivity_grid, index=np.round(gamma_vals, 2), columns=np.round(theta_vals, 2) + ) + + # Plot the heatmap + ax = sns.heatmap( + df, + cmap="viridis", + cbar_kws={"label": r"Sensitivity Magnitude ($||\nabla \Psi||$)"}, + linewidths=0.0, + ) + + # Optionally overlay tipping points + # Where tipping_points is True, overlay a marker or different color + y_idx, x_idx = np.where(tipping_points) + plt.scatter( + x_idx + 0.5, + y_idx + 0.5, + marker="x", + color="red", + s=20, + alpha=0.5, + label=r"Tipping Point ($\Psi \approx 0$)", + ) + + ax.invert_yaxis() # Ensure low Gamma is at the bottom + + plt.title( + "Sensitivity of Systemic Coherence (Ψ) to Operator Variance", + pad=20, + fontsize=14, + ) + plt.xlabel(r"Thermodynamic Stability ($\Theta$)", fontsize=12) + plt.ylabel(r"Adaptive Gain ($\Gamma$)", fontsize=12) + plt.legend(loc="upper left") + + plt.tight_layout() + plt.savefig(output_path, dpi=300, bbox_inches="tight") + plt.close() + + +def main(): + """Run the sensitivity analysis and generate the heatmap.""" + print("Running Global Sensitivity Analysis...") + resolution = 20 + n_samples = 50 # Lowered slightly for reasonable execution time + + results = perform_parameter_sweep(resolution=resolution, n_mc_samples=n_samples) + + theta_vals, gamma_vals, psi_grid, d_theta, d_gamma, d_delta, d_lambda = results + + # Calculate overall sensitivity (magnitude of gradient) + # The gradient vector is [dPsi/dGamma, dPsi/dTheta, dPsi/dDelta, dPsi/dLambda] + # We want to identify the total leverage at each point + sensitivity_grid = np.sqrt(d_theta**2 + d_gamma**2 + d_delta**2 + d_lambda**2) + + # Identify tipping points where Psi approaches 0 + tipping_points = identify_tipping_points(psi_grid, threshold=0.05) + + print("Generating visualization...") + generate_sensitivity_heatmap( + theta_vals=theta_vals, + gamma_vals=gamma_vals, + sensitivity_grid=sensitivity_grid, + tipping_points=tipping_points, + ) + print("GSA complete. Results saved to docs/figures/sensitivity_heatmap.png") + + +if __name__ == "__main__": + main() diff --git a/docs/figures/sensitivity_heatmap.png b/docs/figures/sensitivity_heatmap.png new file mode 100644 index 0000000000000000000000000000000000000000..93b933ae2eb6b07f7b16d187bef8e8318e313bcd GIT binary patch literal 212431 zcmeFZ^;?x`+cu07Iu?#&OX(;EDyWpSBPybV(#=RpcP&`pjDbNYNSBH%WKq%$Dk2gK z)J3OAxkx3Y-~IG{wr~5M`yY6Jd1u?E5b?UsIF7xJb@#H8+{Sgg*Rip&ZIr)oR)vji z-2xliTA|-o<0}#ist@olap!Yd&Z>51&Tdy7P1zK$I@?>@Ia^y8?Qu1Abh5Cs734p0 zoL}tdo@>s|_D7rYsV&fB(&{wNK=)Z2jfgZ>xS;b?)Au&z-j&z0Os$?_Z;e)jtgx z-&(Wvm-Qw4VlIrUQ^tS!N&Z4qH_zgyOD(M?R<2vR(udpDJGu_mN@Zm^(K?(0;;!zz zjX(W={q>#me%{aj>nr%5zXMDR|Lbcn3ZOwtvmkfYhSPIU-;?2z9xO||2^FQUXuT-EBAe6ad9!l;QkJQ z8CR{KXJ5WtOKy4Vx2t#b1*hw$m#di5Uihb-?`i>Yx3TEbxd9HB;U-04%ZAI}K38n} z;}4^pn5~B{zifZ*py4cqjybM2KoRS-ZpJ(U$>&uz|9+|W|ckU=G z-2Uh1H57@XfxCsSU8ePKT)&>#Q|?>BwVjRa_=hZW<>blmSSe3@16iU1t?T4)zl{3a z+neLidp<_o<>I$*-wN$}UQctF_4M@cU3q%5I!quv)3k=~`0@AcJwKg}b?mR+Rx&pb 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