{ "cells": [ { "cell_type": "markdown", "id": "a1000001", "metadata": {}, "source": [ "# Global Sensitivity Analysis with `vplanet_inference`\n", "\n", "This tutorial demonstrates how to run a **Sobol variance-based global sensitivity analysis** using\n", "`vplanet_inference` and [SALib](https://salib.readthedocs.io/en/latest/).\n", "\n", "Global sensitivity analysis (GSA) answers the question:\n", "\n", "> *Which input parameters drive the most variance in the model outputs?*\n", "\n", "In this example we will show how to run similar analysis as [Birky et al. (2025)](https://iopscience.iop.org/article/10.3847/1538-4357/adf4cf/meta), but using a simplified model of binary evolution that only includes tides (but not stellar evolution or magnetic braking).\n", "\n", "### What we cover\n", "\n", "1. **Sobol sensitivity indices** — what S1 and ST mean\n", "2. **Setting up the VPLanet model** — a binary star system with tidal and stellar evolution\n", "3. **Running the sensitivity analysis** — using `SALib` directly with `VplanetModel`\n", "4. **Visualizing results** — heatmaps of first-order and total-order sensitivity\n", "5. **Using `AnalyzeVplanetModel`** — the YAML-driven convenience class\n", "\n", "---\n", "\n", "**Dependencies:** `vplanet_inference`, `SALib`, `numpy`, `matplotlib`, `astropy`\n", "\n", "**References:**\n", "- [SALib documentation](https://salib.readthedocs.io/en/latest/)\n", "- [Saltelli et al. (2010)](https://doi.org/10.1016/j.cpc.2009.09.018) — Variance-based sensitivity analysis\n", "- [VPLanet GitHub](https://github.com/VirtualPlanetaryLaboratory/vplanet)" ] }, { "cell_type": "code", "execution_count": null, "id": "a1000002", "metadata": {}, "outputs": [], "source": [ "import os\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib as mpl\n", "import pandas as pd\n", "import multiprocessing as mp\n", "import tqdm\n", "import astropy.units as u\n", "\n", "from SALib.sample import saltelli\n", "from SALib.analyze import sobol\n", "import seaborn as sn\n", "\n", "import vplanet_inference as vpi" ] }, { "cell_type": "markdown", "id": "a1000003", "metadata": {}, "source": [ "## 1. Sobol Sensitivity Indices\n", "\n", "The Sobol method decomposes the total variance of a model output $Y$ into contributions from\n", "each input parameter $X_i$ and their interactions.\n", "Two indices are commonly reported:\n", "\n", "| Index | Symbol | Meaning |\n", "|-------|--------|---------|\n", "| **First-order** | $S_1^i$ | Fraction of output variance explained by $X_i$ alone |\n", "| **Total-order** | $S_T^i$ | Fraction explained by $X_i$ including all its interactions with other parameters |\n", "\n", "Both indices lie in $[0, 1]$.\n", "If $S_T^i \\approx 0$, parameter $X_i$ has essentially no effect on output $Y$ — it can be fixed.\n", "If $S_T^i \\gg S_1^i$, parameter $X_i$ acts primarily through interactions with other parameters.\n", "\n", "### Workflow\n", "\n", "```\n", "Define problem → Saltelli sample → Evaluate model → Sobol analysis → Interpret\n", "```\n", "\n", "The **Saltelli sampler** generates $N_{\\rm sample} \\times (2 d + 2)$ parameter vectors,\n", "where $d$ is the number of input parameters and $N_{\\rm sample}$ is a base sample count\n", "(a power of 2 for best results). This is the sampling strategy required by the Sobol estimator." ] }, { "cell_type": "markdown", "id": "a1000004", "metadata": {}, "source": [ "## 2. Setting Up the VPLanet Model\n", "\n", "We model a **binary star system** with simultaneous stellar and tidal evolution,\n", "representative of a system like RUP 147. The two modules active on each body are:\n", "\n", "- `stellar` — tracks luminosity, radius, and rotation via magnetic braking\n", "- `eqtide` — computes tidal evolution of rotation period, orbital period, and eccentricity\n", " using the **Constant Time Lag (CTL)** model\n", "\n", "The template infiles are bundled with `vplanet_inference`:" ] }, { "cell_type": "code", "execution_count": 22, "id": "a1000005", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Infile directory: /home/jbirky/Tresorit/packages/vplanet_inference/infiles/eqtide/ctl\n", "Files: ['primary.in', 'secondary.in', 'vpl.in']\n" ] } ], "source": [ "INFILE_PATH = os.path.join(vpi.INFILE_DIR, \"eqtide/ctl\")\n", "print(f\"Infile directory: {INFILE_PATH}\")\n", "print(\"Files:\", os.listdir(INFILE_PATH))" ] }, { "cell_type": "markdown", "id": "a1000006", "metadata": {}, "source": [ "### 2.1 Declaring Input Parameters\n", "\n", "We vary **8 parameters** spanning stellar masses, initial rotation periods, tidal time lags, and orbital properties.\n", "The simulation stop time is **fixed** at 10 Myr — short enough for rapid evaluation during the sweep.\n", "\n", "The tidal time lag $\\tau$ controls the efficiency of tidal dissipation.\n", "We parameterise it in **dex(seconds)** so that the prior is logarithmically uniform,\n", "which is appropriate for a quantity that can span many orders of magnitude." ] }, { "cell_type": "code", "execution_count": 23, "id": "a1000007", "metadata": {}, "outputs": [], "source": [ "# Fixed parameters (not varied in sensitivity analysis)\n", "inparams_fix = {\n", " \"vpl.dStopTime\": u.Myr,\n", "}\n", "theta_fix = np.array([100.0]) # 100 Myr\n", "\n", "# Variable parameters (inputs to sensitivity analysis)\n", "inparams_var = {\n", " \"primary.dMass\": u.Msun,\n", " \"secondary.dMass\": u.Msun,\n", " \"primary.dRotPeriod\": u.day,\n", " \"secondary.dRotPeriod\": u.day,\n", " \"secondary.dEcc\": u.dimensionless_unscaled,\n", " \"secondary.dOrbPeriod\": u.day,\n", " \"primary.dTidalTau\": u.dex(u.s),\n", " \"secondary.dTidalTau\": u.dex(u.s),\n", "}\n", "\n", "# Parameter ranges for Sobol sampling\n", "bounds_var = [\n", " (0.6, 1.1), # primary mass [Msun]\n", " (0.6, 1.1), # secondary mass [Msun]\n", " (0.1, 6.0), # primary rot period [days]\n", " (0.1, 6.0), # secondary rot period [days]\n", " (0.0, 0.5), # eccentricity\n", " (0.1, 12.0), # orbital period [days]\n", " (-4.0, 1.0), # log(tau_1) [dex(s)]\n", " (-4.0, 1.0), # log(tau_2) [dex(s)]\n", "]\n", "\n", "# Human-readable labels for plots\n", "labels_var = [\n", " r\"$M_1\\,[M_\\odot]$\",\n", " r\"$M_2\\,[M_\\odot]$\",\n", " r\"$P_{\\rm rot,1}\\,[\\rm d]$\",\n", " r\"$P_{\\rm rot,2}\\,[\\rm d]$\",\n", " r\"$e_i$\",\n", " r\"$P_{\\rm orb,i}\\,[\\rm d]$\",\n", " r\"$\\log\\tau_1\\,[{\\rm dex}(s)]$\",\n", " r\"$\\log\\tau_2\\,[{\\rm dex}(s)]$\",\n", "]\n", "\n", "# Model outputs to analyze\n", "outparams = {\n", " \"final.primary.RotPer\": u.day,\n", " \"final.secondary.RotPer\": u.day,\n", " \"final.secondary.OrbPeriod\": u.day,\n", " \"final.secondary.Eccentricity\": u.dimensionless_unscaled,\n", "}\n", "\n", "labels_out = [\n", " r\"$P_{\\rm rot,1,f}\\,[\\rm d]$\",\n", " r\"$P_{\\rm rot,2,f}\\,[\\rm d]$\",\n", " r\"$P_{\\rm orb,f}\\,[\\rm d]$\",\n", " r\"$e_f$\",\n", "]" ] }, { "cell_type": "markdown", "id": "a1000008", "metadata": {}, "source": [ "### 2.2 Initializing `VplanetModel`\n", "\n", "We combine the fixed and variable parameters into one `inparams` dict.\n", "The fixed values will be set the same way for every model run." ] }, { "cell_type": "code", "execution_count": null, "id": "a1000009", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input parameters : ['vpl.dStopTime', 'primary.dMass', 'secondary.dMass', 'primary.dRotPeriod', 'secondary.dRotPeriod', 'secondary.dEcc', 'secondary.dOrbPeriod', 'primary.dTidalTau', 'secondary.dTidalTau']\n", "Output parameters: ['final.primary.RotPer', 'final.secondary.Eccentricity', 'final.secondary.OrbPeriod', 'final.secondary.RotPer']\n" ] } ], "source": [ "# suppress annoying warning messages from vplanet\n", "import logging\n", "logging.getLogger(\"vplanet\").setLevel(logging.CRITICAL)\n", "\n", "# Merge fixed and variable parameter dicts (fixed first so theta ordering is predictable)\n", "inparams_all = {**inparams_fix, **inparams_var}\n", "\n", "vpm = vpi.VplanetModel(\n", " inparams=inparams_all,\n", " outparams=outparams,\n", " inpath=INFILE_PATH,\n", " outpath=\"output/sensitivity\",\n", " verbose=False,\n", ")\n", "\n", "print(\"Input parameters :\", vpm.inparams)\n", "print(\"Output parameters:\", vpm.outparams)" ] }, { "cell_type": "markdown", "id": "a1000010", "metadata": {}, "source": [ "### 2.3 Defining a Model Wrapper\n", "\n", "The Sobol sampler provides arrays of the **variable** parameters only.\n", "We write a small wrapper that prepends the fixed parameter values before passing\n", "the full `theta` vector to `run_model`." ] }, { "cell_type": "code", "execution_count": 32, "id": "a1000011", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Nominal output:\n", " final.primary.RotPer = 2.0000 [d]\n", " final.secondary.Eccentricity = 0.2000 []\n", " final.secondary.OrbPeriod = 6.0000 [d]\n", " final.secondary.RotPer = 2.0000 [d]\n" ] } ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\", message=\"Cannot interpret unit\")\n", "\n", "def run_model_var(theta_var):\n", " \"\"\"Run VPLanet with fixed params prepended to the variable-param vector.\"\"\"\n", " theta = np.concatenate([theta_fix, theta_var])\n", " try:\n", " return vpm.run_model(theta, remove=True)\n", " except Exception:\n", " return np.full(vpm.noutparam, np.nan)\n", "\n", "\n", "# Sanity check: single model run at nominal values\n", "theta_nominal = np.array([0.9, 0.9, 2.0, 2.0, 0.2, 6.0, -2.0, -2.0])\n", "result = run_model_var(theta_nominal)\n", "print(\"Nominal output:\")\n", "for name, val, unit in zip(vpm.outparams, result, vpm.out_units):\n", " print(f\" {name:<40s} = {val:.4f} [{unit}]\")" ] }, { "cell_type": "markdown", "id": "a1000012", "metadata": {}, "source": [ "## 3. Running the Sensitivity Analysis\n", "\n", "### 3.1 Generating the Saltelli Sample\n", "\n", "The Saltelli sampler creates the input matrix needed for Sobol estimation.\n", "For $d$ parameters and base sample size $N$, it generates $N(2d+2)$ total samples.\n", "\n", "| $N$ | Samples ($d=8$) | Accuracy |\n", "|-----|-----------------|----------|\n", "| 64 | 1,152 | Rough (quick test) |\n", "| 256 | 4,608 | Moderate |\n", "| 1024| 18,432 | Good |\n", "\n", "We use $N = 64$ here for demonstration. Increase to 512–1024 for publication-quality results." ] }, { "cell_type": "code", "execution_count": 26, "id": "a1000013", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Total parameter samples: 640 (64 × (2×8 + 2))\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/tmp/ipykernel_938057/2473565497.py:9: DeprecationWarning: `salib.sample.saltelli` will be removed in SALib 1.5.1 Please use `salib.sample.sobol`\n", " param_values = saltelli.sample(problem, N_SAMPLE, calc_second_order=False)\n" ] } ], "source": [ "problem = {\n", " \"num_vars\": len(inparams_var),\n", " \"names\": list(inparams_var.keys()),\n", " \"bounds\": bounds_var,\n", "}\n", "\n", "N_SAMPLE = 64 # base sample count; increase to 512+ for production runs\n", "\n", "param_values = saltelli.sample(problem, N_SAMPLE, calc_second_order=False)\n", "print(f\"Total parameter samples: {param_values.shape[0]} ({N_SAMPLE} × (2×{len(inparams_var)} + 2))\")" ] }, { "cell_type": "markdown", "id": "a1000014", "metadata": {}, "source": [ "### 3.2 Evaluating the Model\n", "\n", "We evaluate the VPLanet forward model at every sample point.\n", "This is the most time-consuming step — we parallelise over CPU cores with `multiprocessing`." ] }, { "cell_type": "code", "execution_count": 27, "id": "a1000015", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Using 8 CPU cores\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Running VPLanet: 0%| | 0/640 [00:00" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_sensitivity_table(table, title):\n", " fig, ax = plt.subplots(figsize=(9, 6))\n", " sn.heatmap(\n", " table,\n", " ax=ax,\n", " annot=True,\n", " annot_kws={\"size\": 13},\n", " fmt=\".2f\",\n", " vmin=0,\n", " vmax=1,\n", " cmap=\"bone\",\n", " linewidths=0.5,\n", " linecolor=\"gray\",\n", " )\n", " ax.set_title(title, fontsize=14, pad=12)\n", " ax.set_xlabel(\"Final Condition\", fontsize=12)\n", " ax.set_ylabel(\"Initial Condition\", fontsize=12)\n", " ax.set_xticklabels(ax.get_xticklabels(), rotation=30, ha=\"right\", fontsize=11)\n", " ax.set_yticklabels(ax.get_yticklabels(), rotation=0, fontsize=11)\n", " plt.tight_layout()\n", " return fig\n", "\n", "\n", "fig_s1 = plot_sensitivity_table(table_s1, \"First-order Sobol index $S_1$\")\n", "fig_sT = plot_sensitivity_table(table_sT, \"Total-order Sobol index $S_T$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a1000020", "metadata": {}, "source": [ "### Interpreting the Results\n", "\n", "**Reading the heatmap:**\n", "\n", "- A value close to **1.0** (dark cell) means that parameter dominates the variance in that output.\n", "- A value close to **0.0** (light cell) means that parameter has little effect on that output.\n", "- Cells where $S_T \\gg S_1$ indicate strong parameter interactions.\n", "\n", "**Physical interpretation for this binary system:**\n", "\n", "- Final rotation periods ($P_{\\rm rot}$) are typically sensitive to **initial rotation period** and\n", " **tidal time lag** of the same body — magnetic braking and tidal torques compete.\n", "- Final orbital period ($P_{\\rm orb}$) is most sensitive to **initial orbital period** and **eccentricity**,\n", " since these set the tidal timescale.\n", "- Final eccentricity is sensitive to the **tidal time lag**, which governs dissipation efficiency.\n", "\n", "Parameters with small $S_T$ across all outputs can be fixed at representative values in subsequent\n", "MCMC inference to reduce the dimensionality of the problem." ] }, { "cell_type": "markdown", "id": "a1000021", "metadata": {}, "source": [ "## 5. Bar Chart of Sensitivity by Parameter\n", "\n", "A bar chart makes it easy to rank parameters by their total influence on a specific output." ] }, { "cell_type": "code", "execution_count": 16, "id": "a1000022", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, len(labels_out), figsize=(14, 4), sharey=True)\n", "\n", "for ax, col in zip(axes, table_sT.columns):\n", " s1_vals = table_s1[col].values\n", " sT_vals = table_sT[col].values\n", " y = np.arange(len(labels_var))\n", "\n", " ax.barh(y, sT_vals, color=\"steelblue\", alpha=0.8, label=r\"$S_T$\")\n", " ax.barh(y, s1_vals, color=\"coral\", alpha=0.9, label=r\"$S_1$\")\n", " ax.set_xlim(0, 1)\n", " ax.set_title(col, fontsize=10)\n", " ax.set_xlabel(\"Sensitivity index\", fontsize=9)\n", " ax.axvline(0, color=\"k\", lw=0.5)\n", "\n", "axes[0].set_yticks(np.arange(len(labels_var)))\n", "axes[0].set_yticklabels(labels_var, fontsize=10)\n", "axes[0].legend(fontsize=9)\n", "\n", "fig.suptitle(\"Sobol Sensitivity Indices — Binary Star CTL Tidal Model\", fontsize=12)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a1000023", "metadata": {}, "source": [ "## 6. Using `AnalyzeVplanetModel` (YAML Workflow)\n", "\n", "For scripted workflows, `vplanet_inference` provides `AnalyzeVplanetModel`,\n", "which reads a YAML configuration file and wraps the entire sensitivity analysis.\n", "\n", "A YAML config file specifies the infile path, fixed and variable inputs,\n", "and outputs — matching the fields we defined manually above.\n", "The bundled example config is at `examples/sensitivity/config.yaml`." ] }, { "cell_type": "code", "execution_count": 17, "id": "a1000024", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "inpath: \"../../infiles/stellar_eqtide/ctl\"\n", "input_fix:\n", " \"vpl.dStopTime\":\n", " units: \"u.Myr\"\n", " true_value: 10\n", " label: r\"age [Myr]\"\n", "input_var:\n", " \"primary.dMass\":\n", " units: \"u.Msun\"\n", " bounds: (0.6, 1.1)\n", " label: r\"$\\rm M_1 [M_{\\odot}]$\"\n", " \"secondary.dMass\":\n", " units: \"u.Msun\"\n", " bounds: (0.6, 1.1)\n", " label: r\"$\\rm M_2 [M_{\\odot}]$\"\n", " \"primary.dRotPeriod\":\n", " units: \"u.day\"\n", " bounds: (0.1, 6.0)\n", " label: r\"$\\rm P_{rot1,i} [d]$\"\n", " \"secondary.dRotPeriod\":\n", " units: \"u.day\"\n", " bounds: (0.1, 6.0)\n", " label: r\"$\\rm P_{rot2,i} [d]$\"\n", " \"secondary.dEcc\": \n", " units: \"u.dimensionless_unscaled\"\n", " bounds: (0.0, 0.5)\n", " label: r\"$e_i$\"\n", " \"secondary.dOrbPeriod\":\n", " units: \"u.day\"\n", " bounds: (0.1, 12.0)\n", " label: r\"$\\rm P_{orb,i} [d]$\"\n", " \"primary.dTidalTau\":\n", " units: \"u.dex(u.s)\"\n", " bounds: (-4.0, 1.0)\n", " label: r\"$\\rm \\log\\tau_1$ [dex(s)]\"\n", " \"secondary.dTidalTau\":\n", " units: \"u.dex(u.s)\"\n", " bounds: (-4.0, 1.0)\n", " label: r\"$\\rm \\log\\tau_2$ [dex(s)]\"\n", "output:\n", " \"final.primary.RotPer\":\n", " units: \"u.day\"\n", " label: r\"$\\rm P_{rot1,f} [d]$\"\n", " \"final.secondary.RotPer\":\n", " units: \"u.day\"\n", " label: r\"$\\rm P_{rot2,f} [d]$\"\n", " \"final.secondary.OrbPeriod\":\n", " units: \"u.day\"\n", " label: r\"$\\rm P_{orb,f} [d]$\"\n", " \"final.secondary.Eccentricity\":\n", " units: \"u.dimensionless_unscaled\"\n", " label: r\"$e_f$\"\n", "\n" ] } ], "source": [ "# Show the example config file\n", "config_path = os.path.join(vpi.VPI_DIR, \"examples/sensitivity/config.yaml\")\n", "with open(config_path) as f:\n", " print(f.read())" ] }, { "cell_type": "code", "execution_count": 18, "id": "a1000025", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1152/1152 [01:46<00:00, 10.77it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "First-order table:\n", " final.primary.RotPer final.secondary.RotPer \\\n", "primary.dMass 0.02 0.00 \n", "secondary.dMass 0.00 0.01 \n", "primary.dRotPeriod 0.05 0.00 \n", "secondary.dRotPeriod 0.00 0.00 \n", "secondary.dEcc 0.11 0.11 \n", "secondary.dOrbPeriod 0.01 0.43 \n", "primary.dTidalTau 0.47 0.10 \n", "secondary.dTidalTau 0.00 0.07 \n", "\n", " final.secondary.OrbPeriod final.secondary.Eccentricity \n", "primary.dMass 0.00 0.00 \n", "secondary.dMass 0.00 0.00 \n", "primary.dRotPeriod 0.01 0.01 \n", "secondary.dRotPeriod 0.00 0.09 \n", "secondary.dEcc 0.00 0.01 \n", "secondary.dOrbPeriod 0.93 0.02 \n", "primary.dTidalTau 0.02 0.00 \n", "secondary.dTidalTau 0.00 0.56 \n" ] } ], "source": [ "# AnalyzeVplanetModel reads the config and automatically:\n", "# - initialises VplanetModel\n", "# - sets up the Saltelli problem\n", "# - builds tables and heatmaps\n", "\n", "synth = vpi.AnalyzeVplanetModel(\n", " config_path,\n", " outpath=\"output/sensitivity_yaml\",\n", " verbose=False,\n", " compute_true=False, # skip running the true-value model (no true_value in config)\n", " ncore=mp.cpu_count(),\n", ")\n", "\n", "# Run the sensitivity analysis — nsample should be 2^n (use 512-1024 for production)\n", "synth.variance_global_sensitivity(nsample=64, save=True)\n", "\n", "# Results are stored as attributes\n", "print(\"First-order table:\")\n", "print(synth.table_s1)" ] }, { "cell_type": "code", "execution_count": 21, "id": "b619c625", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig_s1 = plot_sensitivity_table(table_s1, \"First-order Sobol index $S_1$\")\n", "fig_sT = plot_sensitivity_table(table_sT, \"Total-order Sobol index $S_T$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a1000027", "metadata": {}, "source": [ "## Summary\n", "\n", "| Step | How |\n", "|------|-----|\n", "| Define variable parameters and bounds | `bounds_var = [...]` |\n", "| Generate Saltelli sample | `saltelli.sample(problem, N)` from SALib |\n", "| Evaluate VPLanet at each sample | `mp.Pool.imap(run_model_var, param_values)` |\n", "| Compute Sobol indices | `sobol.analyze(problem, Y_col)` from SALib |\n", "| Visualize | Heatmap via `seaborn.heatmap` or bar chart |\n", "| YAML shortcut | `AnalyzeVplanetModel(config, ...).variance_global_sensitivity(N)` |\n", "\n", "**Key takeaways:**\n", "\n", "- Use $N \\geq 512$ for reliable Sobol estimates (published results typically use 1024–2048)\n", "- Parameters with $S_T < 0.05$ across all outputs can usually be fixed\n", "- $S_T \\gg S_1$ signals that a parameter acts mainly through interactions\n", "- GSA is most useful when run on a **short simulation time** (10–100 Myr) to identify\n", " which parameters matter before running expensive long-period MCMC" ] } ], "metadata": { "kernelspec": { "display_name": "vpi", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.19" } }, "nbformat": 4, "nbformat_minor": 5 }