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    "id": "yRlBDWe_7mpz"
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   "source": [
    "# ANL11-A2 reactor: multigroup Neutron Diffusion\n",
    "\n",
    "**Aim of this notebook**: generate the parametric snapshots for the ANL11-A2 reactor (2D) from the [Argonne Code Center - Supplement 2](https://www.osti.gov/biblio/12030251).\n",
    "\n",
    "This notebook may took a while to run, consider converting it into a `.py` script."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "BzFeuQ9lhxyP"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import os\n",
    "from IPython.display import clear_output\n",
    "\n",
    "from pyforce.tools.functions_list import FunctionsList\n",
    "from pyforce.tools.backends import LoopProgress\n",
    "from pyforce.tools.write_read import StoreFunctionsList\n",
    "\n",
    "import pickle\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", category=DeprecationWarning) "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {
    "id": "PGMTWXdTbANs"
   },
   "source": [
    "### Importing geometry and meshing\n",
    "The geometry and the mesh can be either created with GMSH or imported from \"ANL11A2_octave.msh\", if available."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "fhLNwWrXa-fv",
    "outputId": "f1b501f2-3282-4e7a-dacd-33e65d5a9395"
   },
   "outputs": [],
   "source": [
    "from neutronics import create_anl11a2_mesh\n",
    "\n",
    "domain, ct, ft = create_anl11a2_mesh(use_msh=False, save_mesh=True)\n",
    "\n",
    "fuel1_marker    = 1\n",
    "fuel2_marker    = 2\n",
    "fuel_rod_marker = 3\n",
    "refl_marker     = 4\n",
    "\n",
    "void_marker     = 10\n",
    "sym_marker      = 20\n",
    "\n",
    "clear_output()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Definition of the physical parameters\n",
    "Since there are different subdomains in $\\Omega$, the values of the parameters changes according to the region. No thermal feedback effects are considered.\n",
    "\n",
    "The different values describe how the neutrons interact in the different regions of the domain."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "regions = [fuel1_marker, fuel2_marker, fuel_rod_marker, refl_marker]    \n",
    "\n",
    "neutronics_param = dict()\n",
    "\n",
    "neutronics_param['Energy Groups'] = 2\n",
    "\n",
    "neutronics_param['xs_a'] = [np.array([0.01,  0.01,   0.01,  0.]),\n",
    "                            np.array([0.085,  0.08,  0.13,  0.01])]\n",
    "neutronics_param['nu_xs_f'] = [np.array([0., 0., 0., 0.]),\n",
    "                               np.array([0.135, 0.135,  0.135, 0.])]\n",
    "neutronics_param['chi'] = [np.array([1,1,1,1]),\n",
    "                           np.array([0,0,0,0])]\n",
    "neutronics_param['B2z'] = [np.array([0.8e-4]*4),\n",
    "                           np.array([0.8e-4]*4)]\n",
    "neutronics_param['xs_s'] = [[np.array([0]*4), np.array([0.02,  0.02,   0.02,  0.04])],\n",
    "                            [np.array([0]*4), np.array([0]*4)]]\n",
    "\n",
    "# The values in the reflector regions are the one of the benchmark\n",
    "neutronics_param['D'] = [np.array([1.5, 1.5, 1.5, 2.]),\n",
    "                         np.array([0.4,   0.4,    0.4,   0.3])]\n",
    "\n",
    "# Normalisation parameters for the flux\n",
    "nu_value = 2.41 # Number of neutrons per fission\n",
    "Ef = 200e6 * 1.602e-19 # Energy of fission in Joules\n",
    "reactor_power = 1e9 # 1 GW\n",
    "\n",
    "# Void boundary conditions\n",
    "albedo = [0.4692] * 2"
   ]
  },
  {
   "attachments": {},
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   "metadata": {},
   "source": [
    "## Generation of the snapshots\n",
    "This section generates the snapshots employing a Finite Element solution. The PDEs are dependent of the parameters $D_1$ and $\\Sigma_{a,2}$, in the reflector (marker=4) and fuel+rod region (marker=3) respectively:\n",
    "\n",
    "\\begin{equation*}\n",
    "D_1^{\\text{refl}} \\in [0.45, 3.05] \\qquad \\qquad \\Sigma_{a,2}^{\\text{rod}} = [0.0775, 0.1525]\n",
    "\\end{equation*}\n",
    "\n",
    "The variational forms of the neutron diffusion equations are generated to prepare for the numerical solution and the subsequent generation of the snapshots. The class `steady_neutron_diff` implemented in `neutronics.py` is used to create the snapshots.\n",
    "The details of the numerical solution are out of the scope of this notebook, interested readers can have a look at the Github repository [OFELIA](https://github.com/ERMETE-Lab/MP-OFELIA), developed within the ERMETE-Lab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from neutronics import steady_neutron_diff\n",
    "\n",
    "# The class is initialized with the mesh, the cell zones, the face tags, the parameters, the region and boundary markers \n",
    "# An option to used the albedo boundary condition is used\n",
    "neutr_steady_problem = steady_neutron_diff(domain, ct, ft, neutronics_param, regions, void_marker, \n",
    "                                           albedo = albedo)\n",
    "\n",
    "# The variational forms are assembled and the numerical solver is set up to be direct (LU factorization)\n",
    "neutr_steady_problem.assembleForm(direct=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Set\n",
    "The parameters and the `FunctionsList` used to store the snapshots are defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta_D1 = 0.05\n",
    "delta_xs_a2 = 0.02\n",
    "\n",
    "D_1_refl_train  = np.arange(0.5  - 0.1/2,   3.00 + 0.1/2,   delta_D1)\n",
    "xs_a2_rod_train = np.arange(0.08 - 0.005/2, 0.15 + 0.005/2, delta_xs_a2)\n",
    "\n",
    "# Number of training snapshots\n",
    "Ns = len(D_1_refl_train) * len(xs_a2_rod_train)\n",
    "\n",
    "# Create structures to save the data\n",
    "train_param = list()\n",
    "param_idx = 0\n",
    "phi_1_train = FunctionsList(neutr_steady_problem.V.sub(0).collapse()[0])\n",
    "phi_2_train = FunctionsList(neutr_steady_problem.V.sub(1).collapse()[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each parameter, the snapshots are generated and stored in the `FunctionsList`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating the training snapshots: 1.000 / 2.00 - 8.951 s/it\r"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ld: warning: duplicate -rpath '/Users/stefanoriva/miniconda3/envs/ml/lib' ignored\n",
      "ld: warning: duplicate -rpath '/Users/stefanoriva/miniconda3/envs/ml/lib' ignored\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating the training snapshots: 2.000 / 2.00 - 10.451 s/it\n"
     ]
    }
   ],
   "source": [
    "progress_bar = LoopProgress(msg='Generating the training snapshots', final = Ns)\n",
    "\n",
    "for ii in range(len(D_1_refl_train)):\n",
    "    for jj in range(len(xs_a2_rod_train)):\n",
    "        \n",
    "        # Update the diffusion coefficient in the reflector and fuel1 region (respectively)\n",
    "        neutr_steady_problem.phys_param['D'][0][3] = D_1_refl_train[ii]\n",
    "        neutr_steady_problem.phys_param['xs_a'][1][2] = xs_a2_rod_train[jj]\n",
    "        \n",
    "        # Solve the eigenvalue problem\n",
    "        res = neutr_steady_problem.solve(power = reactor_power, Ef=Ef, nu = nu_value, maxIter = 500, verbose=False)\n",
    "        \n",
    "        # Store the snapshots\n",
    "        phi_1_train.append(res[0][0].flatten())\n",
    "        phi_2_train.append(res[0][1].flatten())\n",
    "        \n",
    "        # Store parameters\n",
    "        train_param.append(dict())\n",
    "        train_param[param_idx]['D_1_refl']   = D_1_refl_train[ii]\n",
    "        train_param[param_idx]['xs_a_2_rod'] = xs_a2_rod_train[jj]\n",
    "        train_param[param_idx]['k_eff'] = res[1]\n",
    "        \n",
    "        # Update bar\n",
    "        param_idx += 1\n",
    "        progress_bar.update(1, percentage=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The neutron flux can reach very high values, which can lead to numerical instabilities. To avoid this, the snapshots are normalized using a min-max normalization, i.e.\n",
    "\n",
    "\\begin{equation*}\n",
    "\\tilde{\\phi}(\\cdot; \\boldsymbol{\\mu}) = \\frac{\\phi(\\cdot; \\boldsymbol{\\mu}) - \\min\\limits_{\\boldsymbol{\\mu}^*}(\\phi(\\cdot; \\boldsymbol{\\mu}^*))}{\\max\\limits_{\\boldsymbol{\\mu}^*}(\\phi(\\cdot; \\boldsymbol{\\mu}^*)) - \\min\\limits_{\\boldsymbol{\\mu}^*}(\\phi(\\cdot; \\boldsymbol{\\mu}^*))}\n",
    "\\end{equation*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`FunctionsList` comes with a method called `return_matrix` that returns the snapshots in a matrix format, that is as many rows as the spatial mesh and as many columns as the number of snapshots/parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi_1_train_rescaled = FunctionsList(phi_1_train.fun_space)\n",
    "phi_2_train_rescaled = FunctionsList(phi_2_train.fun_space)\n",
    "\n",
    "min_phi_1 = phi_1_train.return_matrix().min()\n",
    "max_phi_1 = phi_1_train.return_matrix().max()\n",
    "\n",
    "min_phi_2 = phi_2_train.return_matrix().min()\n",
    "max_phi_2 = phi_2_train.return_matrix().max()\n",
    "\n",
    "for mu in range(len(phi_1_train)):\n",
    "    phi_1_train_rescaled.append((phi_1_train(mu) - min_phi_1) / (max_phi_1 - min_phi_1))\n",
    "    phi_2_train_rescaled.append((phi_2_train(mu) - min_phi_2) / (max_phi_2 - min_phi_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The train snapshots and the correspondent parameters are stored using `StoreFunctionsList` and `pickle`, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "path='./Snapshots/'\n",
    "if not os.path.exists(path):\n",
    "    os.makedirs(path)\n",
    "    \n",
    "StoreFunctionsList(neutr_steady_problem.domain, phi_1_train_rescaled, 'phi_1', path+'train_snap_phi_1')\n",
    "StoreFunctionsList(neutr_steady_problem.domain, phi_2_train_rescaled, 'phi_2', path+'train_snap_phi_2')\n",
    "\n",
    "with open(path+'train.param', 'wb') as f:\n",
    "    pickle.dump([train_param], f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test Set\n",
    "The parameters and the `FunctionsList` used to store the snapshots are defined."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "D_1_refl_test  = np.arange(0.50, 3.001, delta_D1)\n",
    "xs_a2_rod_test = np.arange(0.08, 0.151, delta_xs_a2)\n",
    "\n",
    "# Number of training snapshots\n",
    "Ns = len(D_1_refl_test) * len(xs_a2_rod_test)\n",
    "\n",
    "# Create structures to save the data\n",
    "test_param = list()\n",
    "param_idx = 0\n",
    "phi_1_test = FunctionsList(neutr_steady_problem.V.sub(0).collapse()[0])\n",
    "phi_2_test = FunctionsList(neutr_steady_problem.V.sub(1).collapse()[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each parameter, the snapshots are generated and stored in the `FunctionsList`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ld: warning: duplicate -rpath '/Users/stefanoriva/miniconda3/envs/ml/lib' ignored\n",
      "ld: warning: duplicate -rpath '/Users/stefanoriva/miniconda3/envs/ml/lib' ignored\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Generating the test snapshots: 52.000 / 52.00 - 20.585 s/it\n"
     ]
    }
   ],
   "source": [
    "progress_bar = LoopProgress(msg='Generating the test snapshots', final = Ns)\n",
    "\n",
    "for ii in range(len(D_1_refl_test)):\n",
    "    for jj in range(len(xs_a2_rod_test)):\n",
    "        \n",
    "        # Update the diffusion coefficient in the reflector and fuel2 region (respectively)\n",
    "        neutr_steady_problem.phys_param['D'][0][3] = D_1_refl_test[ii]\n",
    "        neutr_steady_problem.phys_param['xs_a'][1][2] = xs_a2_rod_test[jj]\n",
    "        \n",
    "        # Solve the eigenvalue problem\n",
    "        res = neutr_steady_problem.solve(power = reactor_power, Ef=Ef, nu = nu_value, maxIter = 500, verbose=False)\n",
    "        \n",
    "        # Store the snapshots\n",
    "        phi_1_test.append(res[0][0].flatten())\n",
    "        phi_2_test.append(res[0][1].flatten())\n",
    "        \n",
    "        # Store parameters\n",
    "        test_param.append(dict())\n",
    "        test_param[param_idx]['D_1_refl']   = D_1_refl_test[ii]\n",
    "        test_param[param_idx]['xs_a_2_rod'] = xs_a2_rod_test[jj]\n",
    "        test_param[param_idx]['k_eff'] = res[1]\n",
    "        \n",
    "        # Update bar\n",
    "        param_idx += 1\n",
    "        progress_bar.update(1, percentage=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us rescale also the test snapshots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi_1_test_rescaled = FunctionsList(phi_1_test.fun_space)\n",
    "phi_2_test_rescaled = FunctionsList(phi_2_test.fun_space)\n",
    "\n",
    "for mu in range(len(phi_1_test)):\n",
    "    phi_1_test_rescaled.append((phi_1_test(mu) - min_phi_1) / (max_phi_1 - min_phi_1))\n",
    "    phi_2_test_rescaled.append((phi_2_test(mu) - min_phi_2) / (max_phi_2 - min_phi_2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test snapshots and the correspondent parameters are stored using `StoreFunctionsList` and `pickle`, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "StoreFunctionsList(neutr_steady_problem.domain, phi_1_test_rescaled, 'phi_1', path+'test_snap_phi_1')\n",
    "StoreFunctionsList(neutr_steady_problem.domain, phi_2_test_rescaled, 'phi_2', path+'test_snap_phi_2')\n",
    "\n",
    "with open(path+'test.param', 'wb') as f:\n",
    "    pickle.dump([test_param], f)"
   ]
  }
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