{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## gwModels kick velocity models\n", "\n", "- **gwModel_kick_q200** : aligned-spin analytical kick model trained on NR (SXS + RIT, $q \\leq 32$) and BHPT data ($q \\leq 200$). Valid for $1 \\leq q \\leq 1000$.\n", "- **gwModel_kick_q200_GPR** : aligned-spin GPR kick model trained on the same dataset. Provides both analytical and GPR predictions with uncertainty.\n", "- **gwModel_kick_prec_flow** : normalizing-flow model for precessing-spin kick distributions, trained on NR ($q \\leq 32$) and BHPT ($q \\leq 100$). Returns samples from the kick distribution marginalized over spin angles.\n", "\n", "All models from Islam & Wadekar (2025), https://arxiv.org/abs/2511.11536\n", "\n", "**Requirements for precessing model**: `torch`, `nflows` \n", "**Requirements for GPR model**: `scikit-learn`" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "lal.MSUN_SI != Msun\n" ] } ], "source": [ "import sys\n", "!{sys.executable} -m pip install -e ../ --no-deps --quiet\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib.lines import Line2D\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", \"Wswiglal-redir-stdio\")\n", "\n", "import gwModels\n", "gwModels.utils.set_rcparams()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. Aligned-spin kicks : gwModel_kick_q200" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Kick velocity: 128.97 +/- 4.29 km/s\n" ] } ], "source": [ "q = 2\n", "s1z = 0.6\n", "s2z = -0.7\n", "\n", "vk, vk_std = gwModels.remnants.gwModel_kick_q200(q, s1z, s2z, return_std=True)\n", "print(f'Kick velocity: {vk:.2f} +/- {vk_std:.2f} km/s')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_arr = np.linspace(1, 256, 5000)\n", "\n", "plt.figure(figsize=(8, 5))\n", "for chi1z, chi2z, label in [\n", " (0.9, -0.9, r'$[\\chi_1,\\chi_2]=[0.9,-0.9]$'),\n", " (0.0, 0.5, r'$[\\chi_1,\\chi_2]=[0.0,0.5]$'),\n", " (0.5, 0.0, r'$[\\chi_1,\\chi_2]=[0.5,0.0]$'),\n", " (-0.9, 0.5, r'$[\\chi_1,\\chi_2]=[-0.9,0.5]$'),\n", " (0.9, -0.3, r'$[\\chi_1,\\chi_2]=[0.9,-0.3]$'),\n", "]:\n", " vk = gwModels.remnants.gwModel_kick_q200(q_arr, chi1z, chi2z)\n", " plt.plot(np.log2(q_arr), vk, lw=2, alpha=0.8, label=label)\n", "\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.xticks([0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 4, 8, 16, 32, 64, 128, 256])\n", "plt.xlim([0, 8])\n", "plt.ylim([0, 500])\n", "plt.legend(frameon=False)\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. Aligned-spin GPR kicks : gwModel_kick_q200_GPR" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gwModel_kick_q200_GPR — GPR aligned-spin kick model\n", " Islam & Wadekar (2025), https://arxiv.org/abs/2511.11536\n", " Components : analytical (refitted RIT) + GPR\n", " GPR features: [log2(q), chi_hat, chi_a]\n", " Valid range : {'q': [1, 1000], 's1z': [-1, 1], 's2z': [-1, 1]}\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/tousifislam/miniforge3/envs/kitp-py310/lib/python3.10/site-packages/sklearn/base.py:442: InconsistentVersionWarning: Trying to unpickle estimator GaussianProcessRegressor from version 1.8.0 when using version 1.7.2. This might lead to breaking code or invalid results. Use at your own risk. For more info please refer to:\n", "https://scikit-learn.org/stable/model_persistence.html#security-maintainability-limitations\n", " warnings.warn(\n", "/Users/tousifislam/miniforge3/envs/kitp-py310/lib/python3.10/site-packages/sklearn/base.py:442: InconsistentVersionWarning: Trying to unpickle estimator StandardScaler from version 1.8.0 when using version 1.7.2. This might lead to breaking code or invalid results. Use at your own risk. For more info please refer to:\n", "https://scikit-learn.org/stable/model_persistence.html#security-maintainability-limitations\n", " warnings.warn(\n" ] } ], "source": [ "gpr_model = gwModels.remnants.gwModel_kick_q200_GPR('../gwModels/data/gwModel_kick_q200_GPR_aligned_spin.pkl')\n", "gpr_model.info()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Analytical: 129.43 km/s\n", "GPR: 132.81 +/- 5.52 km/s\n" ] } ], "source": [ "# Point evaluation\n", "vk_a = gpr_model.predict_analytical(q=2, s1z=0.6, s2z=-0.7)\n", "vk_g, vk_g_std = gpr_model.predict_gpr(q=2, s1z=0.6, s2z=-0.7)\n", "print(f'Analytical: {vk_a:.2f} km/s')\n", "print(f'GPR: {vk_g[0]:.2f} +/- {vk_g_std[0]:.2f} km/s')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Comparison: analytical vs GPR across mass ratios\n", "q_plot = np.linspace(1, 256, 2000)\n", "\n", "spin_cases = [\n", " (0.9, -0.9, 'C0'),\n", " (0.0, 0.5, 'C1'),\n", " (0.5, 0.0, 'C2'),\n", " (-0.9, 0.5, 'C3'),\n", " (0.9, -0.3, 'C4'),\n", "]\n", "\n", "plt.figure(figsize=(8, 5))\n", "for chi1z, chi2z, color in spin_cases:\n", " s1z_arr = np.full_like(q_plot, chi1z)\n", " s2z_arr = np.full_like(q_plot, chi2z)\n", " \n", " vk_a = gpr_model.predict_analytical(q_plot, s1z_arr, s2z_arr)\n", " vk_g, _ = gpr_model.predict_gpr(q_plot, s1z_arr, s2z_arr)\n", " \n", " label = f'$[\\\\chi_1,\\\\chi_2]=[{chi1z},{chi2z}]$'\n", " plt.plot(np.log2(q_plot), vk_a, c=color, lw=3, alpha=0.6, label=label)\n", " plt.plot(np.log2(q_plot), vk_g, c=color, lw=1.5, ls='--')\n", "\n", "legend1 = plt.legend(\n", " handles=[\n", " Line2D([0], [0], color='gray', lw=3, alpha=0.6, label='Analytical'),\n", " Line2D([0], [0], color='gray', lw=1.5, ls='--', label='GPR'),\n", " ],\n", " frameon=False, loc='upper left'\n", ")\n", "plt.gca().add_artist(legend1)\n", "plt.legend(frameon=False, loc='upper right')\n", "\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.xticks([0, 1, 2, 3, 4, 5, 6, 7, 8], [1, 2, 4, 8, 16, 32, 64, 128, 256])\n", "plt.xlim([0, 8])\n", "plt.ylim(bottom=0)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Non-spinning limit with uncertainty bands\n", "q_ns = np.logspace(0, 3, 500)\n", "zeros = np.zeros_like(q_ns)\n", "\n", "vk_a, vk_a_std = gpr_model.predict_analytical(q_ns, zeros, zeros, return_std=True)\n", "vk_g, vk_g_std = gpr_model.predict_gpr(q_ns, zeros, zeros)\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.fill_between(np.log2(q_ns), vk_a - 1.96*vk_a_std, vk_a + 1.96*vk_a_std,\n", " alpha=0.2, color='C0', label='Analytical 95% CI')\n", "plt.plot(np.log2(q_ns), vk_a, 'C0', lw=2.5, label='Analytical')\n", "plt.fill_between(np.log2(q_ns), vk_g - 1.96*vk_g_std, vk_g + 1.96*vk_g_std,\n", " alpha=0.2, color='C1', label='GPR 95% CI')\n", "plt.plot(np.log2(q_ns), vk_g, 'C1--', lw=2, label='GPR')\n", "\n", "plt.xlabel('$q$')\n", "plt.ylabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.xticks([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],\n", " [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024])\n", "plt.xlim([0, 10])\n", "plt.ylim(bottom=0)\n", "plt.legend(frameon=False)\n", "plt.title(r'Non-spinning limit ($\\chi_{1z}=\\chi_{2z}=0$)')\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. Precessing-spin kicks : gwModel_kick_prec_flow\n", "\n", "The flow model samples kick velocity distributions for given $(q, a_1, a_2)$, marginalizing over spin orientation angles." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "gwModel_kick_prec_flow — normalizing-flow kick model for precessing BBH\n", " Inputs : q, a1, a2 (spin angles marginalized)\n", " Flow config : d_in=1, d_hidden=8, d_context=3, n_layers=2\n" ] } ], "source": [ "flow_model = gwModels.remnants.gwModel_kick_prec_flow('../gwModels/data/')\n", "flow_model.info()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "samples = flow_model.sample(q=3, a1=0.5, a2=0.4, num_samples=5000)\n", "\n", "plt.figure(figsize=(6, 4))\n", "plt.hist(samples, bins=100, density=True, alpha=0.6)\n", "plt.xlabel(r'$v_{\\rm kick}$ [km/s]')\n", "plt.ylabel('Probability')\n", "plt.title(r'Kick distribution: $q=3$, $a_1=0.5$, $a_2=0.4$')\n", "plt.grid(alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mass_ratios = [1.0, 5.0, 10.0, 15.0]\n", "a1_test, a2_test = 0.5, 0.4\n", "\n", "all_samples = []\n", "for q_test in mass_ratios:\n", " s = flow_model.sample(q=q_test, a1=a1_test, a2=a2_test, num_samples=5000)\n", " all_samples.append(s)\n", "\n", "plt.figure(figsize=(7, 5))\n", "parts = plt.violinplot(all_samples, positions=range(len(mass_ratios)),\n", " widths=0.7, showmedians=True, showextrema=False)\n", "for pc in parts['bodies']:\n", " pc.set_alpha(0.6)\n", "plt.xticks(range(len(mass_ratios)), [f'$q={q}$' for q in mass_ratios])\n", "plt.xlabel('Mass Ratio')\n", "plt.ylabel('Kick Velocity [km/s]')\n", "plt.title(f'$a_1={a1_test}$, $a_2={a2_test}$')\n", "plt.grid(axis='y', alpha=0.3)\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "kitp-py310", "language": "python", "name": "kitp-py310" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.18" } }, "nbformat": 4, "nbformat_minor": 4 }