scipy_tensorflow_interpolations.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "scipy_tensorflow_interpolations.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TYsQYCzlRbow",
        "colab_type": "text"
      },
      "source": [
        "# ***THIS NOTEBOOK COMPARES THE CUBIC INTERPOLATIONS OF SCIPY AND TENSORFLOW***\n",
        "---\n",
        "---\n",
        "---\n",
        "---\n",
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WRD_pzfZR7AW",
        "colab_type": "text"
      },
      "source": [
        "We begin by making a neural network reproduce the ground state of a harmonic oscillator. Then we compute the mean (over all points on the x axis) of the absolute value of the difference between the ground state and its reproduction. We do the same with the cubic interpolations.\n",
        "\n",
        "Note that there are 1003 points along x in the beginning but as Tensorflow removes 3 points (cubic spline), we compute a mean over 1000 points (same for SciPy even though it is not necessary)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T7XuioCoRbeW",
        "colab_type": "text"
      },
      "source": [
        "# IMPORTS AND GLOBAL VARIABLES (don't forget to install tensorflow_graphics)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_npL_2anRY9y",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "\n",
        "from keras import layers, models, optimizers\n",
        "\n",
        "#!pip install tensorflow_graphics\n",
        "import tensorflow as tf\n",
        "from tensorflow_graphics.math.interpolation import bspline\n",
        "\n",
        "from scipy import integrate\n",
        "from scipy import interpolate\n",
        "\n",
        "hbar = 1\n",
        "omega = 1\n",
        "m = 1\n",
        "a = -5\n",
        "b = 5"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G9ecdIwuS5KK",
        "colab_type": "text"
      },
      "source": [
        "# DATA GENERATION"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "grjz_q0P1PCn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 555
        },
        "outputId": "30ebe298-43a4-4244-c82f-a2c1401f5f0e"
      },
      "source": [
        "############\n",
        "#SECTION : OPENING FILES (writing the mean of the absolute value of the difference)\n",
        "############\n",
        "file1 = open(\"diff_nn.txt\", \"w\")\n",
        "file2 = open(\"diff_sp.txt\", \"w\")\n",
        "file3 = open(\"diff_tf.txt\", \"w\")\n",
        "\n",
        "\n",
        "\n",
        "############\n",
        "#SECTION : COMPUTING WAVE FUNCTION (1003 and 1000 points along x)\n",
        "############\n",
        "\n",
        "pts=1003\n",
        "h = 10/pts\n",
        "linx = np.linspace (a,b,pts) #x axis with 1003 points\n",
        "norm = np.zeros_like(linx, dtype=float) #1003 points wafe function\n",
        "x=-5.\n",
        "for i in range(0,pts):\n",
        "  norm[i] = pow(m*omega/(math.pi*hbar),0.25)*math.exp(-m*omega*(pow(x,2))/(2*hbar))\n",
        "  x+=h\n",
        "\n",
        "\n",
        "linx_1000 = np.linspace (a,b,pts-3) #x axis with 1000 points\n",
        "x=-5.\n",
        "norm_1000 = np.zeros_like(linx_1000, dtype=float) #1000 points wave function\n",
        "for i in range(0,pts-3):\n",
        "  norm_1000[i] = pow(m*omega/(math.pi*hbar),0.25)*math.exp(-m*omega*(pow(x,2))/(2*hbar))\n",
        "  x+=h\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "############\n",
        "#SECTION : COMPUTING THE MEANS\n",
        "############\n",
        "\n",
        "#number of runs we want\n",
        "runs = 30\n",
        "#arrays for mean of the absolute value of the difference\n",
        "diff_nn = np.zeros((runs,1)) #Neural network prediction\n",
        "diff_sp = np.zeros((runs,1)) #SciPy interp. of prediction\n",
        "diff_tf = np.zeros((runs,1)) #Tensorflow interp. of prediction\n",
        "\n",
        "for j in range(0,runs):\n",
        "  print('run #',j+1)\n",
        "\n",
        "  #INITIALIZATION OF NEURAL NETWORK\n",
        "  model = models.Sequential([\n",
        "    layers.Dense(200, input_shape=(1,), activation='relu'),\n",
        "    layers.Dense(200, input_shape=(1,), activation='relu'), \n",
        "    layers.Dense(1),\n",
        "  ])\n",
        "  #model.summary()\n",
        "  opt = optimizers.Adam(learning_rate=0.001)\n",
        "  model.compile(loss='mse',optimizer=opt)\n",
        "\n",
        "\n",
        "  #Loop to compute the interpolations and the means\n",
        "  for k in range(0,points):\n",
        "\n",
        "    #neural network training (45 epochs on each run) and prediction\n",
        "    model.fit(linx, norm, epochs=45, batch_size=50,verbose=0)\n",
        "    predictions = model.predict(linx)\n",
        "    preds = predictions.reshape(-1)\n",
        "\n",
        "    \"\"\"\n",
        "    \"\"\"\n",
        "    #SCIPY interpolation of prediction - 1000 points\n",
        "    #cubic interpolation\n",
        "    tck_nn_sp = interpolate.splrep(linx, preds, k=3, s=0)\n",
        "    #spline 1000 points\n",
        "    spline_nn_sp = interpolate.splev(linx_1000, tck_nn_sp, der=0)\n",
        "    \n",
        "    \"\"\"\n",
        "    \"\"\"\n",
        "    #Tensorflow interpolation of prediction - 1000 points\n",
        "    degre = 3 #cubic spline\n",
        "    max_pos = pts-3 #tensorflow removes 3 points from the original array\n",
        "    # knots and position of knots\n",
        "    knots_nn = tf.constant((linx,preds))\n",
        "    positions = tf.expand_dims(tf.range(start=0.0, limit=max_pos, delta=1, dtype=knots_nn.dtype), axis=-1)\n",
        "    # interpolation\n",
        "    tck_nn_tf = bspline.interpolate(knots_nn, positions, cyclical=False, degree = degre)\n",
        "    #splines 1000 points\n",
        "    spline_nn_tf = tf.squeeze(tck_nn_tf, axis=1)\n",
        "\n",
        "    \"\"\"\n",
        "    \"\"\"\n",
        "    #Computing means of the absolute value of the difference between\n",
        "    #the ground state, the network prediction and the cubic interpolations of the prediction\n",
        "    diff_nn[j] = np.sum(np.abs(norm-preds))/1003\n",
        "    diff_sp[j] = np.sum(np.abs(norm_1000-spline_nn_sp))/1000\n",
        "    diff_tf[j] = np.sum(np.abs(norm_1000-spline_nn_tf[:,1]))/1000\n",
        "\n",
        "\n",
        "#Diff N.N.\n",
        "np.savetxt(file1, diff_nn, fmt='%.18e', delimiter='', newline='\\n')\n",
        "#Diff SciPy\n",
        "np.savetxt(file2, diff_sp, fmt='%.18e', delimiter='', newline='\\n')\n",
        "#Diff Tensorflow\n",
        "np.savetxt(file3, diff_tf, fmt='%.18e', delimiter='', newline='\\n')\n",
        "\n",
        "file1.close()\n",
        "file2.close()\n",
        "file3.close()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "run # 1\n",
            "run # 2\n",
            "run # 3\n",
            "run # 4\n",
            "run # 5\n",
            "run # 6\n",
            "run # 7\n",
            "run # 8\n",
            "run # 9\n",
            "run # 10\n",
            "run # 11\n",
            "run # 12\n",
            "run # 13\n",
            "run # 14\n",
            "run # 15\n",
            "run # 16\n",
            "run # 17\n",
            "run # 18\n",
            "run # 19\n",
            "run # 20\n",
            "run # 21\n",
            "run # 22\n",
            "run # 23\n",
            "run # 24\n",
            "run # 25\n",
            "run # 26\n",
            "run # 27\n",
            "run # 28\n",
            "run # 29\n",
            "run # 30\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sJvtMf68S_me",
        "colab_type": "text"
      },
      "source": [
        "# PLOT"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mO-zBcfGQ1sw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "outputId": "0a0a25e3-4100-4b30-b483-db53de25b46a"
      },
      "source": [
        "#OPENING FILES\n",
        "file1 = open(\"diff_nn.txt\", \"r\")\n",
        "file2 = open(\"diff_sp.txt\", \"r\")\n",
        "file3 = open(\"diff_tf.txt\", \"r\")\n",
        "\n",
        "with open('diff_nn.txt') as f:\n",
        "    lines1 = f.readlines()\n",
        "    diff_nn = np.array([float(line.split()[0]) for line in lines1])\n",
        "with open('diff_sp.txt') as f:\n",
        "    lines2 = f.readlines()\n",
        "    diff_sp = np.array([float(line.split()[0]) for line in lines2])\n",
        "with open('diff_tf.txt') as f:\n",
        "    lines3 = f.readlines()\n",
        "    diff_tf = np.array([float(line.split()[0]) for line in lines3])\n",
        "\n",
        "\n",
        "array_runs = np.arange(1,31)     #array of the number of runs (x axis on plot)\n",
        "\n",
        "#mavd stands for 'mean of the absolute value of the difference'\n",
        "plt.yscale('log')\n",
        "plt.plot(array_runs,diff_nn,marker='.',c='r', label='mavd Network')\n",
        "plt.plot(array_runs,diff_sp,marker='.',c='g', label='mavd SciPy')\n",
        "plt.plot(array_runs,diff_tf,marker='.',c='b', label='mavd Tensorflow')\n",
        "plt.ylabel('mavd')\n",
        "plt.xlabel('run')\n",
        "plt.legend(title = 'comparing cubic splines of SciPy - Tensorflow')\n",
        "plt.savefig('Tf_vs_SciPy_vs_NN.pdf')\n",
        "plt.show()\n",
        "plt.clf()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}