{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "from torch.distributions.multivariate_normal import MultivariateNormal\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "T=10\n",
    "n=1000\n",
    "N=100\n",
    "dt = torch.tensor(T/n)\n",
    "\n",
    "f= torch.tensor([1,0])\n",
    "g= torch.eye(2)\n",
    "mean = torch.zeros(2)\n",
    "distrib1 = MultivariateNormal(mean,g)\n",
    "sigma=0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulation of ODE vs. SDE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "X = torch.zeros(n+1,2)\n",
    "X[0,:] = np.sqrt(sigma)*distrib1.sample([1])\n",
    "\n",
    "for i in range(n):\n",
    "    #X[i+1,:] = X[i,:] + f*dt\n",
    "    X[i+1,:] = X[i,:] + f*dt + distrib1.sample([1])@g*np.sqrt(dt)\n",
    "\n",
    "plt.plot(X[:,0],X[:,1],'g-')\n",
    "plt.xlim([-5, 20])\n",
    "plt.ylim([-10, 15])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forward and reverse simulation with particles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "id": "dgkTbjezQCk-"
   },
   "outputs": [],
   "source": [
    "z = np.sqrt(sigma)*distrib1.rsample([N])\n",
    "forward = torch.zeros(9,100,2)\n",
    "forward[0] = z\n",
    "\n",
    "# forward simulation of particles\n",
    "for k in range(n):\n",
    "    if (k+1) % 125 == 0:\n",
    "        forward[(k+1)//125] = z\n",
    "    z = z + dt*f + torch.sqrt(dt)*distrib1.rsample([N])\n",
    "\n",
    "# reverse simulation of particles\n",
    "# reverse 1 is incorrect time-reversal\n",
    "# reverse 2 is correct time-reversal\n",
    "x,y = z,z\n",
    "reverse_1,reverse_2 = torch.zeros(9,100,2),torch.zeros(9,100,2)\n",
    "reverse_1[0],reverse_2[0] = z,z\n",
    "\n",
    "for k in range(n):\n",
    "    if (k+1) %125 == 0:\n",
    "        reverse_1[(k+1)//125] = x\n",
    "        reverse_2[(k+1)//125] = y\n",
    "    x = x - dt*f - torch.sqrt(dt)*distrib1.rsample([N])\n",
    "    t = T-k*dt\n",
    "    s = -(y-t*f)/(sigma+t)\n",
    "    y = y - dt*(f - s) + torch.sqrt(dt)*distrib1.rsample([N])\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Forward simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8ARRT9cAxB5qoCH8AxVQ5cMwMpeg21d0AAC0xHDjevDn+wPG0Aw2CoucPoJgqB46ZoRQd4Q+guKqu0mWGUnSEP4BmYjmIqKLV/M1sr5m9YWYvDf7dHmtbAIByYvf8H3L3v468DQBAScz2AYAExQ7/+83sh2a2ZmaXT/sBM9ttZn0z6586dSpycwAAkmTuvvgvmz0n6SNTvvUlSd+X9I4kl7RP0jZ3/3ze+/V6Pe/3+wu3BwBSZGbH3L1X5neWqvm7+44iP2dmj0h6epltAQDCiTnbZ9vY0zslHY+1LQBAOTFn+/yVmd2krOzzuqR7I24LAFBCtPB398/Fem8AwHKY6gkACSL80T4bG9L+/dkjgIWwtg/apQvrvHOTEjQA4Y92qfKGIjF04eCFTqDsg3ap8oYiMXCTEjQEPX+0S9vXeecmJWgIwh/t0+Z13tt+8EJnEP5A1dp88EJnUPMHgAQR/kCduGYBNaHsA9SFaZ+oET1/NEOKPWCmfaJG9PxRv1R7wEz7RI0If9Sv7VftLoppn6gR4Y/6pdwDZtonakL4o370gJuJBeg6jfBHM9ADbpZUx2ESwmwfABdjJlLnEf4ALtb21VMxF2UfABdjHKbzCH8A0zEO02mUfQAgQYQ/ACSI8AeABBH+AJAgwh8AEkT4A0CCCH8ASBDhDwAJIvwBIEGEPwAkiPAHgAQR/gCQIMIfABJE+ANAgpYKfzP7rJm9bGbnzaw38b0Hzew1M/uJmf3hcs0EAIS07Hr+xyX9saSHx180s09IukvSb0j6ZUnPmdmvufu5JbcHAAhgqZ6/u7/i7j+Z8q07JD3u7mfd/b8kvSZp+zLbAgCEE+tOXldL+v7Y8xOD1y5iZrsl7R48PWtmxyO1qW0+LOmduhvREOyLEfbFCPti5ONlf2Fu+JvZc5I+MuVbX3L3b8/6tSmv+bQfdPeDkg4OttV39960n0sN+2KEfTHCvhhhX4yYWb/s78wNf3ffsUBbTki6Zuz5RyW9ucD7AAAiiDXV8ylJd5nZpWZ2naTrJf17pG0BAEpadqrnnWZ2QtKKpH8zs+9Kkru/LOmfJf1Y0nck3Vdwps/BZdrTMeyLEfbFCPtihH0xUnpfmPvUUjwAoMO4whcAEkT4A0CCGhf+ZrbXzN4ws5cG/26vu01VM7PbBstivGZmD9TdnjqZ2etm9qPBZ6H0dLY2M7M1Mzs5fu2LmX3IzJ41s1cHj5fX2caqzNgXSWaFmV1jZs+b2SuD5XX+bPB6qc9G48J/4CF3v2nw75m6G1MlM9ss6euS/kjSJyTdPVguI2U3Dz4Lqc3pflTSbROvPSDpsLtfL+nw4HkKHtXF+0JKMys+kPRFd/91Sb8n6b5BRpT6bDQ1/FO2XdJr7v5Td39f0uPKlstAYtz9qKR3J16+Q9L64Ot1SZ+utFE1mbEvkuTub7n7fwy+fk/SK8pWUCj12Whq+N9vZj8cnOolcVo75mpJPxt7PnNpjES4pO+Z2bHBUiCpu8rd35KyEJB0Zc3tqVvKWSEz+5ik35L0A5X8bNQS/mb2nJkdn/LvDkl/L+lXJd0k6S1Jf1NHG2tUeGmMRHzS3X9bWRnsPjP7g7obhMZIOivM7BclPSFpj7v/b9nfj7WwW66iS0aY2SOSno7cnKZhaYwx7v7m4PGkmT2prCx2tN5W1eptM9vm7m+Z2TZJJ+tuUF3c/e3h16llhZn9grLg/yd3/5fBy6U+G40r+wwaPXSnsnsGpORFSdeb2XVmdomy+yI8VXObamFml5nZLw2/lvQppfd5mPSUpF2Dr3dJmrW4YuelmhVmZpK+IekVd//bsW+V+mw07gpfM/tHZadxLul1SfcO61ipGExZOyBps6Q1d//LmptUCzP7FUlPDp5ukfStlPaFmT0maVXZ0sVvS/qKpH9VtnTKtZL+W9Jn3b3zA6Ez9sWqEswKM/t9SS9I+pGk84OX/1xZ3b/wZ6Nx4Q8AiK9xZR8AQHyEPwAkiPAHgAQR/gCQIMIfABJE+ANAggh/AEjQ/wGuGYlUnsfBrQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "for i in range(9):\n",
    "    plt.figure(i+1)\n",
    "    plt.plot(forward[i,:,0],forward[i,:,1],'r.')\n",
    "    plt.xlim([-5,20])\n",
    "    plt.ylim([-10,15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reverse-time simulation (incorrect)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "n39DnnvOeR7n",
    "outputId": "cf36fa24-89a6-4289-ee81-62daeedb7ba2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "for i in range(9):\n",
    "    plt.figure(i+1)\n",
    "    plt.plot(reverse_1[i,:,0],reverse_1[i,:,1],'g.')\n",
    "    plt.xlim([-5,20])\n",
    "    plt.ylim([-10,15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reverse time simulation (correct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "for i in range(9):\n",
    "    plt.figure(i+1)\n",
    "    plt.plot(reverse_2[i,:,0],reverse_2[i,:,1],'b.')\n",
    "    plt.xlim([-5,20])\n",
    "    plt.ylim([-10,15])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "provenance": []
  },
  "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}