diff --git a/pyproject.toml b/pyproject.toml
index 6e4c4d3..697e522 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -13,6 +13,11 @@ requires-python = ">=3.9"
 dependencies = [
     "numpy",
     "scipy",
+    "matplotlib",
+    "torch",
+    "gpytorch",
+    "pandas",
+    "sxs",
 ]
 
 [project.optional-dependencies]
diff --git a/src/SimulationSupport/EccentricityControl/Examples/GPRTutorial.ipynb b/src/SimulationSupport/EccentricityControl/Examples/GPRTutorial.ipynb
new file mode 100644
index 0000000..86a7373
--- /dev/null
+++ b/src/SimulationSupport/EccentricityControl/Examples/GPRTutorial.ipynb
@@ -0,0 +1,1113 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "c35987a6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "/resnick/groups/sxs/vtommasi/env311/bin/python\n"
+     ]
+    }
+   ],
+   "source": [
+    "import sys\n",
+    "print(sys.executable)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "61d427f4",
+   "metadata": {},
+   "source": [
+    "### Imports"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "e448800d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Device: cpu\n",
+      "SXS version: 2025.0.27\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "# Import GPR library\n",
+    "import SimulationSupport.gpr as gpr\n",
+    "from SimulationSupport.gpr.diagnostics import loo_crossval, plot_loo_crossval, plot_loo_residuals\n",
+    "from SimulationSupport.EccentricityControl.ZeroEccParamsFromPN import omegaAndAdot\n",
+    "\n",
+    "plt.style.use(\"plots.mplstyle\")\n",
+    "\n",
+    "import torch\n",
+    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
+    "print(f\"Device: {device}\")\n",
+    "\n",
+    "import sxs\n",
+    "print(f\"SXS version: {sxs.__version__}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "649beb2e",
+   "metadata": {},
+   "source": [
+    "### Read in your chosen training data\n",
+    "For this example, we use data from the q83dAligned simulation campaign in the SXS catalog, corresponding to SXS IDs: SXS:BBH:1419 – SXS:BBH:1509. These runs are non-precessing binaries with mass ratios 1 ≤ q ≤ 8 and spins aligned with the orbital angular momentum.\n",
+    "\n",
+    "We load the sxs catalog and filter to only keep the runs we want to train on"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "396caffa",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Loading SXS simulations using latest tag 'v3.0.0', published at 2025-05-14T18:17:30Z.\n",
+      "Total simulations: 91\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>deprecated</th>\n",
+       "      <th>reference_mass_ratio</th>\n",
+       "      <th>reference_chi_eff</th>\n",
+       "      <th>reference_chi1_perp</th>\n",
+       "      <th>reference_chi2_perp</th>\n",
+       "      <th>reference_eccentricity</th>\n",
+       "      <th>reference_eccentricity_bound</th>\n",
+       "      <th>reference_time</th>\n",
+       "      <th>reference_dimensionless_spin1_x</th>\n",
+       "      <th>reference_dimensionless_spin1_y</th>\n",
+       "      <th>...</th>\n",
+       "      <th>initial_position2</th>\n",
+       "      <th>number_of_orbits</th>\n",
+       "      <th>number_of_orbits_from_start</th>\n",
+       "      <th>number_of_orbits_from_reference_time</th>\n",
+       "      <th>DOI_versions</th>\n",
+       "      <th>keywords</th>\n",
+       "      <th>date_link_earliest</th>\n",
+       "      <th>date_run_earliest</th>\n",
+       "      <th>date_run_latest</th>\n",
+       "      <th>date_postprocessing</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS ID</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1419</th>\n",
+       "      <td>False</td>\n",
+       "      <td>7.997013</td>\n",
+       "      <td>-0.799840</td>\n",
+       "      <td>1.994280e-06</td>\n",
+       "      <td>1.064214e-06</td>\n",
+       "      <td>0.000536</td>\n",
+       "      <td>0.000536</td>\n",
+       "      <td>1206.5</td>\n",
+       "      <td>-1.829859e-06</td>\n",
+       "      <td>4.755456e-07</td>\n",
+       "      <td>...</td>\n",
+       "      <td>[-11.865584989436478, 0.0278223811293813, 6.54...</td>\n",
+       "      <td>16.646018</td>\n",
+       "      <td>16.646018</td>\n",
+       "      <td>12.870273</td>\n",
+       "      <td>[, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]</td>\n",
+       "      <td>[]</td>\n",
+       "      <td>2017-04-03 20:51:50</td>\n",
+       "      <td>2017-06-23 06:52:21</td>\n",
+       "      <td>2017-11-23 18:01:23</td>\n",
+       "      <td>2025-01-28 17:15:45.045642</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1420</th>\n",
+       "      <td>False</td>\n",
+       "      <td>7.996591</td>\n",
+       "      <td>-0.622382</td>\n",
+       "      <td>8.181529e-07</td>\n",
+       "      <td>7.183138e-07</td>\n",
+       "      <td>0.000241</td>\n",
+       "      <td>0.000241</td>\n",
+       "      <td>1100.0</td>\n",
+       "      <td>-2.639596e-07</td>\n",
+       "      <td>2.534627e-07</td>\n",
+       "      <td>...</td>\n",
+       "      <td>[-11.691524862832026, 0.0279035300942018, 2.70...</td>\n",
+       "      <td>17.281135</td>\n",
+       "      <td>17.281135</td>\n",
+       "      <td>13.801105</td>\n",
+       "      <td>[, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]</td>\n",
+       "      <td>[]</td>\n",
+       "      <td>2017-03-31 00:21:56</td>\n",
+       "      <td>2017-06-09 06:29:04</td>\n",
+       "      <td>2017-10-15 19:06:49</td>\n",
+       "      <td>2025-01-28 17:52:02.384148</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1421</th>\n",
+       "      <td>False</td>\n",
+       "      <td>7.809083</td>\n",
+       "      <td>-0.448263</td>\n",
+       "      <td>1.468047e-06</td>\n",
+       "      <td>1.064243e-07</td>\n",
+       "      <td>0.000821</td>\n",
+       "      <td>0.000821</td>\n",
+       "      <td>798.5</td>\n",
+       "      <td>7.033512e-07</td>\n",
+       "      <td>1.097131e-06</td>\n",
+       "      <td>...</td>\n",
+       "      <td>[-11.523620524996687, 0.0267340786553965, -5.0...</td>\n",
+       "      <td>18.504210</td>\n",
+       "      <td>18.504210</td>\n",
+       "      <td>15.973983</td>\n",
+       "      <td>[, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]</td>\n",
+       "      <td>[]</td>\n",
+       "      <td>2017-04-03 20:51:50</td>\n",
+       "      <td>2017-07-14 07:17:00</td>\n",
+       "      <td>2017-11-25 14:59:49</td>\n",
+       "      <td>2025-01-28 17:56:35.354106</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1422</th>\n",
+       "      <td>False</td>\n",
+       "      <td>7.952937</td>\n",
+       "      <td>-0.762148</td>\n",
+       "      <td>8.604935e-07</td>\n",
+       "      <td>1.151197e-07</td>\n",
+       "      <td>0.000159</td>\n",
+       "      <td>0.000159</td>\n",
+       "      <td>1251.0</td>\n",
+       "      <td>6.023313e-07</td>\n",
+       "      <td>-7.544145e-08</td>\n",
+       "      <td>...</td>\n",
+       "      <td>[-11.832006041240176, 0.0275421838379813, -1.1...</td>\n",
+       "      <td>16.776896</td>\n",
+       "      <td>16.776896</td>\n",
+       "      <td>12.847602</td>\n",
+       "      <td>[, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]</td>\n",
+       "      <td>[]</td>\n",
+       "      <td>2017-04-03 20:51:50</td>\n",
+       "      <td>2017-04-27 14:26:28</td>\n",
+       "      <td>2017-06-14 18:53:34</td>\n",
+       "      <td>2025-01-28 17:52:33.309173</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1423</th>\n",
+       "      <td>False</td>\n",
+       "      <td>7.996735</td>\n",
+       "      <td>-0.620261</td>\n",
+       "      <td>9.824482e-07</td>\n",
+       "      <td>5.072383e-07</td>\n",
+       "      <td>0.000586</td>\n",
+       "      <td>0.000586</td>\n",
+       "      <td>1193.0</td>\n",
+       "      <td>-1.595184e-07</td>\n",
+       "      <td>-1.092014e-06</td>\n",
+       "      <td>...</td>\n",
+       "      <td>[-11.673766302509936, 0.0262858865567793, -4.1...</td>\n",
+       "      <td>17.909408</td>\n",
+       "      <td>17.909408</td>\n",
+       "      <td>14.108192</td>\n",
+       "      <td>[, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]</td>\n",
+       "      <td>[]</td>\n",
+       "      <td>2017-04-25 02:07:24</td>\n",
+       "      <td>2017-06-16 05:13:16</td>\n",
+       "      <td>2017-10-23 03:38:53</td>\n",
+       "      <td>2025-01-28 17:53:37.033045</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "<p>5 rows × 87 columns</p>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "              deprecated  reference_mass_ratio  reference_chi_eff  \\\n",
+       "SXS ID                                                              \n",
+       "SXS:BBH:1419       False              7.997013          -0.799840   \n",
+       "SXS:BBH:1420       False              7.996591          -0.622382   \n",
+       "SXS:BBH:1421       False              7.809083          -0.448263   \n",
+       "SXS:BBH:1422       False              7.952937          -0.762148   \n",
+       "SXS:BBH:1423       False              7.996735          -0.620261   \n",
+       "\n",
+       "              reference_chi1_perp  reference_chi2_perp  \\\n",
+       "SXS ID                                                   \n",
+       "SXS:BBH:1419         1.994280e-06         1.064214e-06   \n",
+       "SXS:BBH:1420         8.181529e-07         7.183138e-07   \n",
+       "SXS:BBH:1421         1.468047e-06         1.064243e-07   \n",
+       "SXS:BBH:1422         8.604935e-07         1.151197e-07   \n",
+       "SXS:BBH:1423         9.824482e-07         5.072383e-07   \n",
+       "\n",
+       "              reference_eccentricity  reference_eccentricity_bound  \\\n",
+       "SXS ID                                                               \n",
+       "SXS:BBH:1419                0.000536                      0.000536   \n",
+       "SXS:BBH:1420                0.000241                      0.000241   \n",
+       "SXS:BBH:1421                0.000821                      0.000821   \n",
+       "SXS:BBH:1422                0.000159                      0.000159   \n",
+       "SXS:BBH:1423                0.000586                      0.000586   \n",
+       "\n",
+       "              reference_time  reference_dimensionless_spin1_x  \\\n",
+       "SXS ID                                                          \n",
+       "SXS:BBH:1419          1206.5                    -1.829859e-06   \n",
+       "SXS:BBH:1420          1100.0                    -2.639596e-07   \n",
+       "SXS:BBH:1421           798.5                     7.033512e-07   \n",
+       "SXS:BBH:1422          1251.0                     6.023313e-07   \n",
+       "SXS:BBH:1423          1193.0                    -1.595184e-07   \n",
+       "\n",
+       "              reference_dimensionless_spin1_y  ...  \\\n",
+       "SXS ID                                         ...   \n",
+       "SXS:BBH:1419                     4.755456e-07  ...   \n",
+       "SXS:BBH:1420                     2.534627e-07  ...   \n",
+       "SXS:BBH:1421                     1.097131e-06  ...   \n",
+       "SXS:BBH:1422                    -7.544145e-08  ...   \n",
+       "SXS:BBH:1423                    -1.092014e-06  ...   \n",
+       "\n",
+       "                                              initial_position2  \\\n",
+       "SXS ID                                                            \n",
+       "SXS:BBH:1419  [-11.865584989436478, 0.0278223811293813, 6.54...   \n",
+       "SXS:BBH:1420  [-11.691524862832026, 0.0279035300942018, 2.70...   \n",
+       "SXS:BBH:1421  [-11.523620524996687, 0.0267340786553965, -5.0...   \n",
+       "SXS:BBH:1422  [-11.832006041240176, 0.0275421838379813, -1.1...   \n",
+       "SXS:BBH:1423  [-11.673766302509936, 0.0262858865567793, -4.1...   \n",
+       "\n",
+       "              number_of_orbits number_of_orbits_from_start  \\\n",
+       "SXS ID                                                       \n",
+       "SXS:BBH:1419         16.646018                   16.646018   \n",
+       "SXS:BBH:1420         17.281135                   17.281135   \n",
+       "SXS:BBH:1421         18.504210                   18.504210   \n",
+       "SXS:BBH:1422         16.776896                   16.776896   \n",
+       "SXS:BBH:1423         17.909408                   17.909408   \n",
+       "\n",
+       "              number_of_orbits_from_reference_time  \\\n",
+       "SXS ID                                               \n",
+       "SXS:BBH:1419                             12.870273   \n",
+       "SXS:BBH:1420                             13.801105   \n",
+       "SXS:BBH:1421                             15.973983   \n",
+       "SXS:BBH:1422                             12.847602   \n",
+       "SXS:BBH:1423                             14.108192   \n",
+       "\n",
+       "                                              DOI_versions  keywords  \\\n",
+       "SXS ID                                                                 \n",
+       "SXS:BBH:1419  [, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]        []   \n",
+       "SXS:BBH:1420  [, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]        []   \n",
+       "SXS:BBH:1421  [, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]        []   \n",
+       "SXS:BBH:1422  [, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]        []   \n",
+       "SXS:BBH:1423  [, v1.1, v1.2, v1.3, v1.4, v1.5, v2.0, v3.0]        []   \n",
+       "\n",
+       "              date_link_earliest   date_run_earliest     date_run_latest  \\\n",
+       "SXS ID                                                                     \n",
+       "SXS:BBH:1419 2017-04-03 20:51:50 2017-06-23 06:52:21 2017-11-23 18:01:23   \n",
+       "SXS:BBH:1420 2017-03-31 00:21:56 2017-06-09 06:29:04 2017-10-15 19:06:49   \n",
+       "SXS:BBH:1421 2017-04-03 20:51:50 2017-07-14 07:17:00 2017-11-25 14:59:49   \n",
+       "SXS:BBH:1422 2017-04-03 20:51:50 2017-04-27 14:26:28 2017-06-14 18:53:34   \n",
+       "SXS:BBH:1423 2017-04-25 02:07:24 2017-06-16 05:13:16 2017-10-23 03:38:53   \n",
+       "\n",
+       "                    date_postprocessing  \n",
+       "SXS ID                                   \n",
+       "SXS:BBH:1419 2025-01-28 17:15:45.045642  \n",
+       "SXS:BBH:1420 2025-01-28 17:52:02.384148  \n",
+       "SXS:BBH:1421 2025-01-28 17:56:35.354106  \n",
+       "SXS:BBH:1422 2025-01-28 17:52:33.309173  \n",
+       "SXS:BBH:1423 2025-01-28 17:53:37.033045  \n",
+       "\n",
+       "[5 rows x 87 columns]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = sxs.load(\"dataframe\")\n",
+    "df = df[(df.index >= 'SXS:BBH:1419') & (df.index <= 'SXS:BBH:1509')]\n",
+    "\n",
+    "print(f\"Total simulations: {len(df)}\")\n",
+    "df.head(5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e667cb19",
+   "metadata": {},
+   "source": [
+    "For this example, we have 90 training points. We want to train the GPR to learn the values of the initial orbital frequency, Ω_0, and radial velocity, ˙a_0, that yield a BBH evolution with near-zero eccentricity. So we filter to keep only simulations with \"zero\" ending eccentricity. This number can be changed to fit your definition of 0 eccentricity. We utilize 1e-3 as our cutoff, and are left with 89 training points."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "cb0dbd3d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Total simulations: 90\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>initial_separation</th>\n",
+       "      <th>initial_orbital_frequency</th>\n",
+       "      <th>initial_adot</th>\n",
+       "      <th>initial_mass_ratio</th>\n",
+       "      <th>initial_dimensionless_spin1_x</th>\n",
+       "      <th>initial_dimensionless_spin1_y</th>\n",
+       "      <th>initial_dimensionless_spin1_z</th>\n",
+       "      <th>initial_dimensionless_spin2_x</th>\n",
+       "      <th>initial_dimensionless_spin2_y</th>\n",
+       "      <th>initial_dimensionless_spin2_z</th>\n",
+       "      <th>reference_eccentricity</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS ID</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1419</th>\n",
+       "      <td>13.378235</td>\n",
+       "      <td>0.018250</td>\n",
+       "      <td>-0.000379</td>\n",
+       "      <td>8.000000</td>\n",
+       "      <td>3.610000e-14</td>\n",
+       "      <td>-4.500000e-15</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>-1.121800e-12</td>\n",
+       "      <td>-3.820000e-14</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>0.000536</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1420</th>\n",
+       "      <td>13.187256</td>\n",
+       "      <td>0.018372</td>\n",
+       "      <td>0.000463</td>\n",
+       "      <td>8.000000</td>\n",
+       "      <td>6.840000e-14</td>\n",
+       "      <td>-3.440000e-14</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>8.601000e-13</td>\n",
+       "      <td>-2.375000e-13</td>\n",
+       "      <td>0.800000</td>\n",
+       "      <td>0.000241</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1421</th>\n",
+       "      <td>13.027527</td>\n",
+       "      <td>0.018658</td>\n",
+       "      <td>0.000492</td>\n",
+       "      <td>7.811462</td>\n",
+       "      <td>-4.020000e-14</td>\n",
+       "      <td>-7.500000e-15</td>\n",
+       "      <td>-0.608090</td>\n",
+       "      <td>1.972000e-13</td>\n",
+       "      <td>-2.946000e-13</td>\n",
+       "      <td>0.800000</td>\n",
+       "      <td>0.000821</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1422</th>\n",
+       "      <td>13.349915</td>\n",
+       "      <td>0.018733</td>\n",
+       "      <td>-0.000139</td>\n",
+       "      <td>7.954555</td>\n",
+       "      <td>1.073700e-12</td>\n",
+       "      <td>2.263000e-13</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>-3.911600e-12</td>\n",
+       "      <td>-1.355800e-12</td>\n",
+       "      <td>-0.459032</td>\n",
+       "      <td>0.000159</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1423</th>\n",
+       "      <td>13.156250</td>\n",
+       "      <td>0.018749</td>\n",
+       "      <td>-0.000303</td>\n",
+       "      <td>8.000000</td>\n",
+       "      <td>-1.980000e-14</td>\n",
+       "      <td>2.250000e-14</td>\n",
+       "      <td>-0.603515</td>\n",
+       "      <td>4.771000e-13</td>\n",
+       "      <td>1.125000e-13</td>\n",
+       "      <td>-0.753207</td>\n",
+       "      <td>0.000586</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "              initial_separation  initial_orbital_frequency  initial_adot  \\\n",
+       "SXS ID                                                                      \n",
+       "SXS:BBH:1419           13.378235                   0.018250     -0.000379   \n",
+       "SXS:BBH:1420           13.187256                   0.018372      0.000463   \n",
+       "SXS:BBH:1421           13.027527                   0.018658      0.000492   \n",
+       "SXS:BBH:1422           13.349915                   0.018733     -0.000139   \n",
+       "SXS:BBH:1423           13.156250                   0.018749     -0.000303   \n",
+       "\n",
+       "              initial_mass_ratio  initial_dimensionless_spin1_x  \\\n",
+       "SXS ID                                                            \n",
+       "SXS:BBH:1419            8.000000                   3.610000e-14   \n",
+       "SXS:BBH:1420            8.000000                   6.840000e-14   \n",
+       "SXS:BBH:1421            7.811462                  -4.020000e-14   \n",
+       "SXS:BBH:1422            7.954555                   1.073700e-12   \n",
+       "SXS:BBH:1423            8.000000                  -1.980000e-14   \n",
+       "\n",
+       "              initial_dimensionless_spin1_y  initial_dimensionless_spin1_z  \\\n",
+       "SXS ID                                                                       \n",
+       "SXS:BBH:1419                  -4.500000e-15                      -0.800000   \n",
+       "SXS:BBH:1420                  -3.440000e-14                      -0.800000   \n",
+       "SXS:BBH:1421                  -7.500000e-15                      -0.608090   \n",
+       "SXS:BBH:1422                   2.263000e-13                      -0.800000   \n",
+       "SXS:BBH:1423                   2.250000e-14                      -0.603515   \n",
+       "\n",
+       "              initial_dimensionless_spin2_x  initial_dimensionless_spin2_y  \\\n",
+       "SXS ID                                                                       \n",
+       "SXS:BBH:1419                  -1.121800e-12                  -3.820000e-14   \n",
+       "SXS:BBH:1420                   8.601000e-13                  -2.375000e-13   \n",
+       "SXS:BBH:1421                   1.972000e-13                  -2.946000e-13   \n",
+       "SXS:BBH:1422                  -3.911600e-12                  -1.355800e-12   \n",
+       "SXS:BBH:1423                   4.771000e-13                   1.125000e-13   \n",
+       "\n",
+       "              initial_dimensionless_spin2_z  reference_eccentricity  \n",
+       "SXS ID                                                               \n",
+       "SXS:BBH:1419                      -0.800000                0.000536  \n",
+       "SXS:BBH:1420                       0.800000                0.000241  \n",
+       "SXS:BBH:1421                       0.800000                0.000821  \n",
+       "SXS:BBH:1422                      -0.459032                0.000159  \n",
+       "SXS:BBH:1423                      -0.753207                0.000586  "
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "ecc_threshold = 1e-3\n",
+    "df = df[df[\"reference_eccentricity\"] <= ecc_threshold]\n",
+    "\n",
+    "df = df[[\n",
+    "    'initial_separation',\n",
+    "    'initial_orbital_frequency',\n",
+    "    'initial_adot',\n",
+    "    'initial_mass_ratio',\n",
+    "    'initial_dimensionless_spin1_x', 'initial_dimensionless_spin1_y', 'initial_dimensionless_spin1_z',\n",
+    "    'initial_dimensionless_spin2_x', 'initial_dimensionless_spin2_y', 'initial_dimensionless_spin2_z',\n",
+    "    'reference_eccentricity',\n",
+    "]]\n",
+    "print(f\"Total simulations: {len(df)}\")\n",
+    "df.head(5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bd9f089f",
+   "metadata": {},
+   "source": [
+    "### Post-Newtonian predictions\n",
+    "We also calculate the corresponding Post-Newtonian predictions over the same parameter space. This is done with OmegaAndAdot, the current function utilized in SpEC."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "182e2134",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Total simulations: 90\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>initial_separation</th>\n",
+       "      <th>initial_orbital_frequency</th>\n",
+       "      <th>initial_adot</th>\n",
+       "      <th>initial_mass_ratio</th>\n",
+       "      <th>initial_dimensionless_spin1_x</th>\n",
+       "      <th>initial_dimensionless_spin1_y</th>\n",
+       "      <th>initial_dimensionless_spin1_z</th>\n",
+       "      <th>initial_dimensionless_spin2_x</th>\n",
+       "      <th>initial_dimensionless_spin2_y</th>\n",
+       "      <th>initial_dimensionless_spin2_z</th>\n",
+       "      <th>reference_eccentricity</th>\n",
+       "      <th>pn_guess_omega</th>\n",
+       "      <th>pn_guess_adot</th>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS ID</th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "      <th></th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1419</th>\n",
+       "      <td>13.378235</td>\n",
+       "      <td>0.018250</td>\n",
+       "      <td>-0.000379</td>\n",
+       "      <td>8.000000</td>\n",
+       "      <td>3.610000e-14</td>\n",
+       "      <td>-4.500000e-15</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>-1.121800e-12</td>\n",
+       "      <td>-3.820000e-14</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>0.000536</td>\n",
+       "      <td>0.018793</td>\n",
+       "      <td>-0.000041</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1420</th>\n",
+       "      <td>13.187256</td>\n",
+       "      <td>0.018372</td>\n",
+       "      <td>0.000463</td>\n",
+       "      <td>8.000000</td>\n",
+       "      <td>6.840000e-14</td>\n",
+       "      <td>-3.440000e-14</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>8.601000e-13</td>\n",
+       "      <td>-2.375000e-13</td>\n",
+       "      <td>0.800000</td>\n",
+       "      <td>0.000241</td>\n",
+       "      <td>0.019066</td>\n",
+       "      <td>-0.000042</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1421</th>\n",
+       "      <td>13.027527</td>\n",
+       "      <td>0.018658</td>\n",
+       "      <td>0.000492</td>\n",
+       "      <td>7.811462</td>\n",
+       "      <td>-4.020000e-14</td>\n",
+       "      <td>-7.500000e-15</td>\n",
+       "      <td>-0.608090</td>\n",
+       "      <td>1.972000e-13</td>\n",
+       "      <td>-2.946000e-13</td>\n",
+       "      <td>0.800000</td>\n",
+       "      <td>0.000821</td>\n",
+       "      <td>0.019335</td>\n",
+       "      <td>-0.000043</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1422</th>\n",
+       "      <td>13.349915</td>\n",
+       "      <td>0.018733</td>\n",
+       "      <td>-0.000139</td>\n",
+       "      <td>7.954555</td>\n",
+       "      <td>1.073700e-12</td>\n",
+       "      <td>2.263000e-13</td>\n",
+       "      <td>-0.800000</td>\n",
+       "      <td>-3.911600e-12</td>\n",
+       "      <td>-1.355800e-12</td>\n",
+       "      <td>-0.459032</td>\n",
+       "      <td>0.000159</td>\n",
+       "      <td>0.018827</td>\n",
+       "      <td>-0.000041</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>SXS:BBH:1423</th>\n",
+       "      <td>13.156250</td>\n",
+       "      <td>0.018749</td>\n",
+       "      <td>-0.000303</td>\n",
+       "      <td>8.000000</td>\n",
+       "      <td>-1.980000e-14</td>\n",
+       "      <td>2.250000e-14</td>\n",
+       "      <td>-0.603515</td>\n",
+       "      <td>4.771000e-13</td>\n",
+       "      <td>1.125000e-13</td>\n",
+       "      <td>-0.753207</td>\n",
+       "      <td>0.000586</td>\n",
+       "      <td>0.019174</td>\n",
+       "      <td>-0.000042</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "              initial_separation  initial_orbital_frequency  initial_adot  \\\n",
+       "SXS ID                                                                      \n",
+       "SXS:BBH:1419           13.378235                   0.018250     -0.000379   \n",
+       "SXS:BBH:1420           13.187256                   0.018372      0.000463   \n",
+       "SXS:BBH:1421           13.027527                   0.018658      0.000492   \n",
+       "SXS:BBH:1422           13.349915                   0.018733     -0.000139   \n",
+       "SXS:BBH:1423           13.156250                   0.018749     -0.000303   \n",
+       "\n",
+       "              initial_mass_ratio  initial_dimensionless_spin1_x  \\\n",
+       "SXS ID                                                            \n",
+       "SXS:BBH:1419            8.000000                   3.610000e-14   \n",
+       "SXS:BBH:1420            8.000000                   6.840000e-14   \n",
+       "SXS:BBH:1421            7.811462                  -4.020000e-14   \n",
+       "SXS:BBH:1422            7.954555                   1.073700e-12   \n",
+       "SXS:BBH:1423            8.000000                  -1.980000e-14   \n",
+       "\n",
+       "              initial_dimensionless_spin1_y  initial_dimensionless_spin1_z  \\\n",
+       "SXS ID                                                                       \n",
+       "SXS:BBH:1419                  -4.500000e-15                      -0.800000   \n",
+       "SXS:BBH:1420                  -3.440000e-14                      -0.800000   \n",
+       "SXS:BBH:1421                  -7.500000e-15                      -0.608090   \n",
+       "SXS:BBH:1422                   2.263000e-13                      -0.800000   \n",
+       "SXS:BBH:1423                   2.250000e-14                      -0.603515   \n",
+       "\n",
+       "              initial_dimensionless_spin2_x  initial_dimensionless_spin2_y  \\\n",
+       "SXS ID                                                                       \n",
+       "SXS:BBH:1419                  -1.121800e-12                  -3.820000e-14   \n",
+       "SXS:BBH:1420                   8.601000e-13                  -2.375000e-13   \n",
+       "SXS:BBH:1421                   1.972000e-13                  -2.946000e-13   \n",
+       "SXS:BBH:1422                  -3.911600e-12                  -1.355800e-12   \n",
+       "SXS:BBH:1423                   4.771000e-13                   1.125000e-13   \n",
+       "\n",
+       "              initial_dimensionless_spin2_z  reference_eccentricity  \\\n",
+       "SXS ID                                                                \n",
+       "SXS:BBH:1419                      -0.800000                0.000536   \n",
+       "SXS:BBH:1420                       0.800000                0.000241   \n",
+       "SXS:BBH:1421                       0.800000                0.000821   \n",
+       "SXS:BBH:1422                      -0.459032                0.000159   \n",
+       "SXS:BBH:1423                      -0.753207                0.000586   \n",
+       "\n",
+       "              pn_guess_omega  pn_guess_adot  \n",
+       "SXS ID                                       \n",
+       "SXS:BBH:1419        0.018793      -0.000041  \n",
+       "SXS:BBH:1420        0.019066      -0.000042  \n",
+       "SXS:BBH:1421        0.019335      -0.000043  \n",
+       "SXS:BBH:1422        0.018827      -0.000041  \n",
+       "SXS:BBH:1423        0.019174      -0.000042  "
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "rPrime0 = 1\n",
+    "\n",
+    "df[\"pn_guess_omega\"] = np.nan\n",
+    "df[\"pn_guess_adot\"]  = np.nan\n",
+    "\n",
+    "for idx, row in df.iterrows():\n",
+    "    q = row[\"initial_mass_ratio\"]\n",
+    "    r = row[\"initial_separation\"]\n",
+    "    S1x, S1y, S1z = row[\"initial_dimensionless_spin1_x\"], row[\"initial_dimensionless_spin1_y\"], row[\"initial_dimensionless_spin1_z\"]\n",
+    "    S2x, S2y, S2z = row[\"initial_dimensionless_spin2_x\"], row[\"initial_dimensionless_spin2_y\"], row[\"initial_dimensionless_spin2_z\"]\n",
+    "\n",
+    "    omega, adot = omegaAndAdot(r, q, np.array([S1x, S1y, S1z]), np.array([S2x, S2y, S2z]), rPrime0)\n",
+    "\n",
+    "    df.at[idx, \"pn_guess_omega\"] = omega\n",
+    "    df.at[idx, \"pn_guess_adot\"] = adot\n",
+    "\n",
+    "print(f\"Total simulations: {len(df)}\")\n",
+    "df.head(5)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bab861fb",
+   "metadata": {},
+   "source": [
+    "### GPR Training\n",
+    "We extract the training inputs for the GPR:\n",
+    "1. initial separation, D_0\n",
+    "2. mass ratio, q\n",
+    "3. and the spins of each black hole, S_1 and S_2 - for these aligned-spin cases, we only take S_z"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "fec0ffab",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Extract training inputs - same for omega and adot\n",
+    "features = [\n",
+    "    \"initial_separation\",\n",
+    "    \"initial_mass_ratio\",\n",
+    "    \"initial_dimensionless_spin1_z\",\n",
+    "    \"initial_dimensionless_spin2_z\"\n",
+    "]\n",
+    "\n",
+    "# Turn columns into numpy array\n",
+    "X = df[features].values"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dcf1f259",
+   "metadata": {},
+   "source": [
+    "We take the PN guesses as our baseline, and train two independent GPR models on the residuals between the final simulation values and this baseline."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "c3fb6efd",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/resnick/groups/sxs/vtommasi/env311/lib/python3.11/site-packages/gpytorch/models/exact_gp.py:299: GPInputWarning: The input matches the stored training data. Did you forget to call model.train()?\n",
+      "  warnings.warn(\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 2400x1800 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 2400x1800 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Omega\n",
+    "# Prepare target features Y\n",
+    "baseline_omega = \"pn_guess_omega\"\n",
+    "training_omega = \"initial_orbital_frequency\"\n",
+    "\n",
+    "# Prepare target difference,\n",
+    "# ie the difference between the output values from the simulations to the PN guesses for\n",
+    "# the initial values\n",
+    "Y_omega = df[training_omega].values - df[baseline_omega].values\n",
+    "# Run full GPR pipeline\n",
+    "model_omega, likelihood_omega, Y_pred_omega = gpr.run_gpr_pipeline(X, Y_omega, target_name=\"$\\Omega$\")\n",
+    "\n",
+    "# Adot\n",
+    "# Prepare target features Y\n",
+    "baseline_adot = \"pn_guess_adot\"\n",
+    "training_adot = \"initial_adot\"\n",
+    "\n",
+    "# Prepare target difference\n",
+    "Y_adot = df[training_adot].values - df[baseline_adot].values\n",
+    "# Run full GPR pipeline\n",
+    "model_adot, likelihood_adot, Y_pred_adot = gpr.run_gpr_pipeline(X, Y_adot, target_name = \"$\\dot{A}$\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a859789",
+   "metadata": {},
+   "source": [
+    "### Model Validation\n",
+    "To assess our model's performance, we utilize a leave-one-out cross-validation, in which each data point is withheld in turn from the training set and predicted by a GPR trained on the remaining data. We plot the results of this LOO and summary statistics to analyze how our model did. An unbiased model should yield LOO residuals centered around zero."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fe745fd4",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Prepare target feature Y\n",
+    "targets = [\n",
+    "    (\"pn_guess_omega\", \"initial_orbital_frequency\", \"omega\"),\n",
+    "    (\"pn_guess_adot\", \"initial_adot\", \"adot\")\n",
+    "]\n",
+    "\n",
+    "for baseline_col, final_col, name in targets:\n",
+    "    # Fit to the difference between the output omega values from the simulations to the\n",
+    "    # PN guesses for the initial values\n",
+    "    Y = df[final_col].values - df[baseline_col].values\n",
+    "\n",
+    "    preds_loo, stds_loo = loo_crossval(\n",
+    "        X,\n",
+    "        Y,\n",
+    "        target_name=name\n",
+    "    )\n",
+    "\n",
+    "    # Plot correlation and compute statistics\n",
+    "    rmse_loo, mae_loo, r2_loo = plot_loo_crossval(\n",
+    "        Y,\n",
+    "        preds_loo,\n",
+    "        target_name=name,\n",
+    "        plot=True\n",
+    "    )\n",
+    "\n",
+    "    # Plot residuals\n",
+    "    plot_loo_residuals(Y, preds_loo, target_name=name, show=False)\n",
+    "\n",
+    "    ax = plt.gca()  # get current axes\n",
+    "    ax.xaxis.get_offset_text().set_fontsize(14)\n",
+    "\n",
+    "    if name == \"omega\":\n",
+    "        ax.set_xlabel(r\"$\\Omega_0$ Residuals\")\n",
+    "    elif name == \"adot\":\n",
+    "        ax.set_xlabel(r\"$\\dot{a}_0$ Residuals\")\n",
+    "\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6d23b635",
+   "metadata": {},
+   "source": [
+    "### Saving the model\n",
+    "After training the model, we can save it to disk by storing the model parameters, likelihood, and metadata. This means you can evalute the GPR without having to retrain each time."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "31f7bbcd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Save both checkpoints\n",
+    "gpr.save_gpr_checkpoint(\n",
+    "    model_omega,likelihood_omega, features,\n",
+    "    output_name=\"omega\",\n",
+    "    run_col=\"initial_orbital_frequency\",\n",
+    "    base_column=\"pn_guess_omega\",\n",
+    "    X=X, Y=Y_omega,\n",
+    "    path=\"gpr_model_omega.pth\"\n",
+    ")\n",
+    "\n",
+    "gpr.save_gpr_checkpoint(\n",
+    "    model_adot, likelihood_adot, features,\n",
+    "    output_name=\"adot\",\n",
+    "    run_col=\"initial_adot\",\n",
+    "    base_column=\"pn_guess_adot\",\n",
+    "    X=X, Y=Y_adot,\n",
+    "    path=\"gpr_model_adot.pth\"\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9cc57486",
+   "metadata": {},
+   "source": [
+    "### Example of how to load the pre-trained model and evaluate\n",
+    "Once the model is saved to disk, you can load it and correct new runs. For this example, we utilize SXS:BBH:1419 (which is also included in training, and is simply used as an example)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ccce0eee",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Load models from disk\n",
+    "model_omega, likelihood_omega, meta_omega = gpr.load_gpr_checkpoint(\"gpr_model_omega.pth\")\n",
+    "model_adot, likelihood_adot, meta_adot    = gpr.load_gpr_checkpoint(\"gpr_model_adot.pth\")\n",
+    "\n",
+    "# Define a single test point (must match the feature orders used during training)\n",
+    "sim_id = 'SXS:BBH:1419'\n",
+    "row = df.loc[sim_id]\n",
+    "\n",
+    "test_point = {\n",
+    "    \"initial_separation\": row[\"initial_separation\"],\n",
+    "    \"initial_mass_ratio\": row[\"initial_mass_ratio\"],\n",
+    "    \"initial_dimensionless_spin1_x\": row[\"initial_dimensionless_spin1_x\"],\n",
+    "    \"initial_dimensionless_spin1_y\": row[\"initial_dimensionless_spin1_y\"],\n",
+    "    \"initial_dimensionless_spin1_z\": row[\"initial_dimensionless_spin1_z\"],\n",
+    "    \"initial_dimensionless_spin2_x\": row[\"initial_dimensionless_spin2_x\"],\n",
+    "    \"initial_dimensionless_spin2_y\": row[\"initial_dimensionless_spin2_y\"],\n",
+    "    \"initial_dimensionless_spin2_z\": row[\"initial_dimensionless_spin2_z\"],\n",
+    "}\n",
+    "\n",
+    "# Convert to numpy array in the correct feature order\n",
+    "X_test = np.array([[test_point[f] for f in features]])\n",
+    "\n",
+    "# Get PN baseline for this point\n",
+    "omega_pn, adot_pn = omegaAndAdot(\n",
+    "    test_point[\"initial_separation\"],\n",
+    "    test_point[\"initial_mass_ratio\"],\n",
+    "    np.array([test_point[\"initial_dimensionless_spin1_x\"], test_point[\"initial_dimensionless_spin1_y\"], test_point[\"initial_dimensionless_spin1_z\"]]),\n",
+    "    np.array([test_point[\"initial_dimensionless_spin2_x\"], test_point[\"initial_dimensionless_spin2_y\"], test_point[\"initial_dimensionless_spin2_z\"]]),\n",
+    "    rPrime0\n",
+    ")\n",
+    "\n",
+    "# Make GPR prediction\n",
+    "delta_omega, sigma_omega = gpr.predict_with_gpr_model(X_test, model_omega, likelihood_omega)\n",
+    "delta_adot, sigma_adot   = gpr.predict_with_gpr_model(X_test, model_adot, likelihood_adot)\n",
+    "\n",
+    "# Final corrected values = PN baseline + GPR correction\n",
+    "omega_gpr_corrected = omega_pn + delta_omega[0]\n",
+    "adot_gpr_corrected  = adot_pn + delta_adot[0]\n",
+    "\n",
+    "# Past run simulation values for comparison\n",
+    "original_omega = float(row[\"initial_orbital_frequency\"])\n",
+    "original_adot  = float(row[\"initial_adot\"])\n",
+    "\n",
+    "print(f\"Results for {sim_id}:\")\n",
+    "print(f\"Original omega:       {original_omega:.15f}\")\n",
+    "print(f\"PN omega:             {omega_pn:.15f}\")\n",
+    "print(f\"GPR correction:       {delta_omega[0]:.15f} ± {sigma_omega[0]:.15f}\")\n",
+    "print(f\"GPR corrected omega:  {omega_gpr_corrected:.15f}\")\n",
+    "print()\n",
+    "print(f\"Original adot:        {original_adot:.15f}\")\n",
+    "print(f\"PN adot:              {adot_pn:.15f}\")\n",
+    "print(f\"GPR correction:       {delta_adot[0]:.15f} ± {sigma_adot[0]:.15f}\")\n",
+    "print(f\"GPR corrected adot:   {adot_gpr_corrected:.15f}\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "env311 (3.11.6)",
+   "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": "3.11.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/src/SimulationSupport/EccentricityControl/Examples/plots.mplstyle b/src/SimulationSupport/EccentricityControl/Examples/plots.mplstyle
new file mode 100644
index 0000000..615974c
--- /dev/null
+++ b/src/SimulationSupport/EccentricityControl/Examples/plots.mplstyle
@@ -0,0 +1,34 @@
+
+
+# ========= Figure / save =========
+figure.dpi: 300
+figure.autolayout: True
+savefig.bbox: tight
+
+# ========= Fonts =========
+text.usetex: False
+font.size: 9
+font.family: serif
+
+# ========= Lines =========
+lines.linewidth: 0.8
+
+# ========= Grid =========
+grid.linewidth: 0.5
+grid.color: black
+grid.alpha: 0.2
+
+# ========= Legends =========
+legend.fancybox: False
+legend.fontsize: 8
+legend.title_fontsize: 8
+
+# ========= Patches =========
+patch.linewidth: 0.5
+
+# ========= PDF / PS output =========
+pdf.fonttype: 42
+ps.fonttype: 42
+
+# ========= Color cycle =========
+axes.prop_cycle: cycler('color', ['4c72b0', '55a868', 'c44e52', 'da8bc3', '64b5cd'])
\ No newline at end of file