Exercise_08_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 8.1\n",
    "### Classification of magnetic phases using CNNs\n",
    "\n",
    "Imagine a 2-dimensional lattice arrangement of $n \\times n$ magnetic dipole moments (spins) that can be in one of two states ($+1$ or $−1$, Ising model).\n",
    "With interactions between spins being short ranged, each spin interacts only with its four neighbors.\n",
    "The probability to find a spin in one of the orientations is a function of temperature $T$ according to $p \\sim e^{−a/T},\\;a = \\mathrm{const.}$).\n",
    "\n",
    "At extremely low temperatures $T \\rightarrow 0$, neighboring spins have a very low probability of different orientations, so that a uniform overall state (ferromagnetic state) is adopted, characterized by $+1$ or $−1$.\n",
    "At very high temperatures $T \\rightarrow \\infty$, a paramagnetic phase with random spin alignment results, yielding $50\\%$ of $+1$ and $0%$ of $−1$ orientations.\n",
    "Below a critical temperature $0 < T < T_c$, stable ferromagnetic domains emerge, with both orientations being equally probable in the absence of an external magnetic field.\n",
    "The spin-spin correlation function diverges at $T_c$, whereas the correlation decays for $T > T_c$.\n",
    "\n",
    "The data for this task contain the $n \\times n$ dipole orientations on the lattice for different temperatures $T$.\n",
    "Classify the two magnetic phases (paramagnetic/ferromagnetic) using a convolutional neural network!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "keras 2.4.0\n"
     ]
    }
   ],
   "source": [
    "from tensorflow import keras\n",
    "import numpy as np\n",
    "callbacks = keras.callbacks\n",
    "layers = keras.layers\n",
    "\n",
    "print(\"keras\", keras.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load and prepare dataset\n",
    "See https://doi.org/10.1038/nphys4035 for more information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gdown\n",
    "url = \"https://drive.google.com/u/0/uc?export=download&confirm=HgGH&id=1Ihxt1hb3Kyv0IrjHlsYb9x9QY7l7n2Sl\"\n",
    "output = 'ising_data.npz'\n",
    "gdown.download(url, output, quiet=True)\n",
    "\n",
    "f = np.load(output, allow_pickle=True)\n",
    "n_train = 20000\n",
    "\n",
    "x_train, x_test = f[\"C\"][:n_train], f[\"C\"][n_train:]\n",
    "T_train, T_test = f[\"T\"][:n_train], f[\"T\"][n_train:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "for i,j in enumerate(np.random.choice(n_train, 6)):\n",
    "    plt.subplot(2,3,i+1)\n",
    "    image = x_train[j]\n",
    "    plot = plt.imshow(image)\n",
    "    plt.title(\"T: %.2f\" % T_train[j])\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'frequency')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(T_test)\n",
    "plt.xlabel(\"T\")\n",
    "plt.ylabel(\"frequency\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set up training data - define magnetic phases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "Tc = 2.27\n",
    "y_train, y_test = T_train > Tc, T_test > Tc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### Task\n",
    "\n",
    " - evaluate the test accuracy for a convolutional network,\n",
    " - plot the test accuracy vs. temperature.\n",
    " - compare to the results obtained using a fully-connected network (Exercise 7.1)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}