Untitled2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:Calling GradientTape.gradient on a persistent tape inside its context is significantly less efficient than calling it outside the context (it causes the gradient ops to be recorded on the tape, leading to increased CPU and memory usage). Only call GradientTape.gradient inside the context if you actually want to trace the gradient in order to compute higher order derivatives.\n",
      "WARNING:tensorflow:Calling GradientTape.gradient on a persistent tape inside its context is significantly less efficient than calling it outside the context (it causes the gradient ops to be recorded on the tape, leading to increased CPU and memory usage). Only call GradientTape.gradient inside the context if you actually want to trace the gradient in order to compute higher order derivatives.\n",
      "WARNING:tensorflow:Calling GradientTape.gradient on a persistent tape inside its context is significantly less efficient than calling it outside the context (it causes the gradient ops to be recorded on the tape, leading to increased CPU and memory usage). Only call GradientTape.gradient inside the context if you actually want to trace the gradient in order to compute higher order derivatives.\n",
      "Epoch 1000: Loss=0.08016306161880493, MSE=0.0738634541630745\n",
      "Epoch 2000: Loss=0.055850811302661896, MSE=0.05254371464252472\n",
      "Epoch 3000: Loss=0.05539708957076073, MSE=0.052269820123910904\n",
      "Epoch 4000: Loss=0.055277612060308456, MSE=0.05233115702867508\n",
      "Epoch 5000: Loss=0.05490371212363243, MSE=0.05203092470765114\n",
      "Epoch 6000: Loss=0.05490649864077568, MSE=0.05207999050617218\n",
      "Epoch 7000: Loss=0.054578810930252075, MSE=0.05178729072213173\n",
      "Epoch 8000: Loss=0.054671529680490494, MSE=0.051771458238363266\n",
      "Epoch 9000: Loss=0.054375357925891876, MSE=0.05155792087316513\n",
      "Epoch 10000: Loss=0.054665036499500275, MSE=0.051896240562200546\n"
     ]
    },
    {
     "data": {
      "image/png": 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sMb3xxhvq3Lmz29d/Pp8KHPHx8SotLXUoKy0tlc1mczq7ITU+BdUhIly2COfLAAhMIe0jrW5Cq7QPtV24kpdrV+37+wDAfbz58vfIkBC1N+nJhTabzSFwuNuaNWt011136dVXX21wu4IZvO+iuCakpqYqLy/PoWzTpk1KTU21qEUAAACA7/jLX/6ijIwM/eUvf9GNN97okW1aGjiqqqq0c+dO7dy5U9J3j73duXOniouLJX13OdSECRPs9X/961/rwIEDevDBB7Vnzx49++yz+utf/6qZM2da0XwAAADAMq6OpVevXq0JEyboqaeeUkpKikpKSlRSUqKKigpT22lp4Ni+fbsGDx6swYMHS5KysrI0ePBg+2O5vvnmG3uHSVKPHj301ltvadOmTUpKStJTTz2lP//5z0pPT7ek/QAAAIBVXB1LP//88zp79qymTZumLl262F/Tp083tZ1e8zscnlJZWamoqCiVrv4t93AAcFDd6zKrm9Aqh0L7Wt2EVisq5aZxAN/dNH73DdGqqKgw9V6Gljg3lnwvZYjb7+GoOntWP91a4JX73Ro+dQ8HAJgpcn+h1U0AAMDvEDgAAF6B2Q0A8E8EDgAAAACmIXAAAAAAMA2BAwAAAIBpCBwAAAAATEPgAAAAAGAaAgcAAAAA0xA4AAAAAJiGwAEA5+HH/wAAcC8CBwDAcvzoHwD4LwIHAAAAANMQOAAAAACYhsABAAAAwDQEDgAAAACmIXAAAAAAMA2BAwAAAIBpCBwAAAAATEPgAAAAAGAaAgcA/AC/Nu5Z/OgfAPg3AgcAAAAA0xA4AAAAAJiGwAEAAADANAQOAAAAAKYhcAAAAAAwDYEDAAAAgGkIHAAAAABMQ+AAAAAAYBoCBwAAAADTEDgAwAl+bdwz+JVxAPB/BA4AAAAApmljdQMAX1VVsKPFy7YfMtiNLQEAAPBeBA6gmVoTMJpaF+EDAAD4MwIHcAHuDBpNrZ/gAQAA/BGBA3DC7JDR1DYJHgAAwJ8QOIDzWBE0GmsDwQMAAPgDnlIF/B9vCBvn87b2AAAAtAQzHAh43jywZ7YDAAD4OmY4ENC8OWycz1faCbiCH/0DgMBA4EBAqirY4XODeF9rrz/g18YBAGg9AgcCji8P3H257QAAIDAROBBQ/GHA7g/7AAAAAgeBAwHDnwbqvnhJGAAACEwEDgQEfx2c++t+AQAA/0HggF8LhJkAf98/AADg2wgc8FsMxAEAAKxH4IBfCrSwEWj7CwAAfAeBA34nUAffgbrfAAAEuqVLlyoxMVHh4eFKSUnRtm3bGq175swZzZs3T7169VJ4eLiSkpKUm5travsIHPArgT7oDvT9h+/gV8YBwD3Wrl2rrKwsZWdnq7CwUElJSUpPT1dZWZnT+o888oj+9Kc/acmSJfriiy/061//Wrfccot27DBvDEHggN9gsP0d+gEAAN9WWVnp8KqpqWm07uLFizVlyhRlZGSof//+WrZsmSIiIrRixQqn9V966SU99NBDGjVqlHr27KmpU6dq1KhReuqpp8zaHbUxbc2ABzHIdlRVsEPthwy2uhl+IXJ/oap7XWZ1MwAAXiZxRD91CAt16zpP1NRKWwuUkJDgUJ6dna2cnJwG9Wtra1VQUKA5c+bYy4KDg5WWlqb8/Hyn26ipqVF4eLhDWbt27fTBBx+0fgcaQeAAAAAAvMjhw4dls9ns78PCwpzWO3bsmOrq6hQXF+dQHhcXpz179jhdJj09XYsXL9ZVV12lXr16KS8vT+vWrVNdXZ37duAHuKQKPo/ZDefoFwAAfJPNZnN4NRY4WuKZZ55R79691bdvX4WGhiozM1MZGRkKDjYvFhA44NMYVDeN/gEAwH/FxMQoJCREpaWlDuWlpaWKj493ukxsbKzWr1+v6upqff3119qzZ4/at2+vnj17mtZOAgd8FoPp5qGfAADwT6GhoRoyZIjy8vLsZfX19crLy1NqamqTy4aHh6tbt246e/as/va3v+nmm282rZ3cwwGfxCAaAABAysrK0sSJEzV06FANGzZMTz/9tKqrq5WRkSFJmjBhgrp166YFCxZIkrZu3aojR44oOTlZR44cUU5Ojurr6/Xggw+a1kYCB3wOYcN1PLUKgKt27Wn8MZyNGdDXfdeZA2iesWPH6ujRo5o7d65KSkqUnJys3Nxc+43kxcXFDvdnnD59Wo888ogOHDig9u3ba9SoUXrppZcUHR1tWhsJHPAphA0AME9LQkZjyxM+AM/JzMxUZmam08+2bNni8H7EiBH64osvPNCq7xE4gADBLAe8Bb8y7l1aGzKas17CBxDYuGkcPoPZjdajDwGcs2tPjWlhw8ptAfA+zHDAJzBQBgD3sHLgf27bzHgAgYUZDng9woZ70Z+ui9xfaHUTALfwllkGb2kHAM8gcAABiNABBBZvvKTJG9sEwBwEDng1BsYA0DrePqj39vYBaD0CB7wWYcNc9C/g/3xlMM9sB+DfCBzwSgyGAaB1fHEA74ttBnBhBA4ggBHsAP/j67MFvtx2AM4ROOB1GAQDQMv4y2Dd10MTAEcEDngVwobn0eeAf/DHAbo/7hMQiAgcAACPKSrtaHUT/JI/D8z9ed+AQEHggNfgTLt16HsA3ozQAfg2Age8AgNe6/EdAL4pUAbjgbKfgD8icAAA4KMCbRAeaPsL+AsCByzHmXXvwXfRuMj9hVY3AXAQqIPvQN1vwJcROGApBrgA4LpAH3QH+v4DvobAAcABIRDwbgy2v0M/AL6DwAHLMLAFALQGoQPwDQQOWIKwAQCuY4DdEH0CeD8CB4AGCISA92Fg3Tj6BvBuBA54HINZIDDxK+Mtx4AagC8jcABwimAIwJcQygDvZXngWLp0qRITExUeHq6UlBRt27atyfpPP/20+vTpo3bt2ikhIUEzZ87U6dOnPdRatBaDWABwDQPp5qOvAO9kaeBYu3atsrKylJ2drcLCQiUlJSk9PV1lZWVO669evVqzZ89Wdna2ioqK9MILL2jt2rV66KGHPNxytARhw/fwnQHWYgDtOvoM8D6WBo7FixdrypQpysjIUP/+/bVs2TJFRERoxYoVTut/9NFHuuKKK/SLX/xCiYmJuv766zVu3LgLzooAAIDAQegAvItlgaO2tlYFBQVKS0v7vjHBwUpLS1N+fr7TZYYPH66CggJ7wDhw4IA2bNigUaNGNbqdmpoaVVZWOrzgeZwp9118d4A1GDQD8BeWBY5jx46prq5OcXFxDuVxcXEqKSlxuswvfvELzZs3T1deeaXatm2rXr166eqrr27ykqoFCxYoKirK/kpISHDrfuDCGLDCX0TuL7S6CQCaicAGeA/Lbxp3xZYtW/TEE0/o2WefVWFhodatW6e33npL8+fPb3SZOXPmqKKiwv46fPiwB1sM+AdCI+BZDJbdg34EvEMbqzYcExOjkJAQlZaWOpSXlpYqPj7e6TKPPvqo7rzzTt11112SpIEDB6q6ulp33323Hn74YQUHN8xPYWFhCgsLc/8OoFkYqAKAaxgku9euPTUa0JdxAGAly2Y4QkNDNWTIEOXl5dnL6uvrlZeXp9TUVKfLnDx5skGoCAkJkSQZhmFeYwEAAAC0iKWXVGVlZWn58uV68cUXVVRUpKlTp6q6uloZGRmSpAkTJmjOnDn2+qNHj9Zzzz2nNWvW6ODBg9q0aZMeffRRjR492h484D2Y3fAvfJ+A+ZjdMAf9CljLskuqJGns2LE6evSo5s6dq5KSEiUnJys3N9d+I3lxcbHDjMYjjzyioKAgPfLIIzpy5IhiY2M1evRo/eY3v7FqFwAAgA/g0irAOkFGgF2LVFlZqaioKJWu/q1sEe2sbo7f4my4f2o/ZLDVTbBcda/LrG5Cow6F9rW6CY0qKu1odRO8HmfhPYPQ4RtOVVfq7huiVVFRIZvNZnVzHJwbSx548JfqEBbq1nWfqKlVz9++7JX73Ro+9ZQq+AbChv/iuwXMQdgA4M8IHAAAIGAQ7gDPI3DArTgD7v/4jgH3YgDsefQ54FkEDgAAAACmIXDAbTjzDQCu4Uy7deh7wHMIHABcFsjhMnJ/odVNAOAmhA7AMwgccItAHoACQEsw2AUQKAgcAFqEkAnAHxD8APMRONBqDDwBwDUMcr0L3wdgLgIHWoWwAQAAgKYQOAC0GIETzVFU2tHqJngVzqZ7J74XwDwEDrQYg00AgD8hdADmIHAAAOAhDGgBmGHp0qVKTExUeHi4UlJStG3btibrHz9+XNOmTVOXLl0UFhamSy65RBs2bDCtfQQOtAizGziHYwGAPyEUwtesXbtWWVlZys7OVmFhoZKSkpSenq6ysjKn9Wtra3Xdddfp0KFDeu2117R3714tX75c3bp1M62NbUxbMwAAAABTLV68WFOmTFFGRoYkadmyZXrrrbe0YsUKzZ49u0H9FStWqLy8XB999JHatm0rSUpMTDS1jcxwwGWc0QYA13Hm3HfwXcFqlZWVDq+aGufHZG1trQoKCpSWlmYvCw4OVlpamvLz850u8+abbyo1NVXTpk1TXFycBgwYoCeeeEJ1dXWm7IvEDAcAN6gq2KH2QwZb3QwAcJtde2o0oG+Y1c2AF4tMHqT2Ee3cus76k6ckSQkJCQ7l2dnZysnJaVD/2LFjqqurU1xcnEN5XFyc9uzZ43QbBw4c0Hvvvafx48drw4YN2rdvn+655x6dOXNG2dnZ7tmRHyBwwCXMbgBS5P5CVfe6zOpmwIdwxhyAKw4fPiybzWZ/HxbmvvBbX1+vzp076/nnn1dISIiGDBmiI0eO6He/+x2BAwAAwJOY5YBVbDabQ+BoTExMjEJCQlRaWupQXlpaqvj4eKfLdOnSRW3btlVISIi9rF+/fiopKVFtba1CQ0Nb13gnuIcDzcbsBprC8QE4x+wGALOEhoZqyJAhysvLs5fV19crLy9PqampTpe54oortG/fPtXX19vLvvzyS3Xp0sWUsCEROAAAABpFYIS3y8rK0vLly/Xiiy+qqKhIU6dOVXV1tf2pVRMmTNCcOXPs9adOnary8nJNnz5dX375pd566y098cQTmjZtmmlt5JIqNAtnrwEAgYpLq+DNxo4dq6NHj2ru3LkqKSlRcnKycnNz7TeSFxcXKzj4+zmGhIQEbdy4UTNnztSgQYPUrVs3TZ8+XbNmzTKtjQQOAG7D06rwQ0WlHa1ugqU4Ow7AEzIzM5WZmen0sy1btjQoS01N1ccff2xyq77HJVW4IGY3AACBjvAItByBAwAAEzBABYDvEDjQJGY34CqOGQD+ihAJtAyBAwAAAIBpCBxoFGeqAaBlOBPuv/huAdcROAC4HWEVAACcQ+CAUwwYAaBlOAPu//iOAdcQOACgBSL3F1rdBAAWInQAzUfgQAPMbsAdOI4AAIBE4AAAwG046x1Y+L6B5iFwwAFnpQEAAOBOBA4AgCmKSjta3QTAdMxyABdG4IAdsxtwN44pBBIGngDgHIEDAACgFQibQNMIHJDEmWgAaA0GnADQOAIHAFMRZgEEAkIn0DgCBxgQAgAAwDQEDgAAWoEz2ziHYwFwjsABAAAAwDQEjgDH5VTwBI4zAIGCWQ6gIQIHAAAtxOASAC6MwBHAOOsMtE7k/kKrmwDACxFEAUcEDgAeQcAFACAwETgCFIM/AGgdzmKjKRwfwPcIHAAAtysq7Wh1EwAAXoLAEYCY3YBVOPYABBJmOYDvEDgAAHARA0kAaD4CR4DhDDMAAJ5DOAUIHAAAAABMROAIIMxuwBtwHMLXccYaruKYQaAjcAAAAAAwDYEDAADAZMxyIJAROAIEl7EAAADACgQOAB5HAIav4iw1WoPjB4GKwBEAGNwBAADAKgQOAGiFyP2FVjcBgA9hlgOBiMDh55jdAAD3YKAIAC1D4ABgCcKw/yoq7Wh1EwAAXoTA4ccY0AEA4H2YLUOgIXAAAHABDBABoOUIHAAAAB5GiEUgIXD4KS6ngi/gOAUAwP8ROAAAaAJnomEWji0ECgKHH+KsMQAAALwFgQMAAMAizHIgEBA4/AyzG/A1HLMAAPg3AgcAAI3g7DM8geMM/o7AAQAAAPiwpUuXKjExUeHh4UpJSdG2bdsarbtu3ToNHTpU0dHRioyMVHJysl566SVT20fg8CNcmgIAgG9ilgMttXbtWmVlZSk7O1uFhYVKSkpSenq6ysrKnNbv1KmTHn74YeXn5+uzzz5TRkaGMjIytHHjRtPaSOAAYDlfD8uR+wutbgIAIEAtXrxYU6ZMUUZGhvr3769ly5YpIiJCK1ascFr/6quv1i233KJ+/fqpV69emj59ugYNGqQPPvjAtDYSOPyErw/YAPiHotKOVjfBbTjjDMAqlZWVDq+aGud/j2pra1VQUKC0tDR7WXBwsNLS0pSfn3/B7RiGoby8PO3du1dXXXWV29r/Q21MWzMAAACabdeeGg3oG2Z1M9BMJ3skK6R9pHvXWVUtSUpISHAoz87OVk5OToP6x44dU11dneLi4hzK4+LitGfPnka3U1FRoW7duqmmpkYhISF69tlndd1117V+BxpB4PADzG4AAAD4j8OHD8tms9nfh4W5N4h26NBBO3fuVFVVlfLy8pSVlaWePXvq6quvdut2ziFwAAAAeAlmOSBJNpvNIXA0JiYmRiEhISotLXUoLy0tVXx8fKPLBQcH6+KLL5YkJScnq6ioSAsWLDAtcHAPBwCvwEwdvAn3bwDwBaGhoRoyZIjy8vLsZfX19crLy1Nqamqz11NfX9/ofSLuwAyHj2OQBgCAf2GWA67IysrSxIkTNXToUA0bNkxPP/20qqurlZGRIUmaMGGCunXrpgULFkiSFixYoKFDh6pXr16qqanRhg0b9NJLL+m5554zrY0EDgAAAMBHjR07VkePHtXcuXNVUlKi5ORk5ebm2m8kLy4uVnDw9xc1VVdX65577tG//vUvtWvXTn379tXLL7+ssWPHmtZGAocPY3YDANyPy6kA+JrMzExlZmY6/WzLli0O7x9//HE9/vjjHmjV97iHA4DXIEQDwHcIvvAnlgeOpUuXKjExUeHh4UpJSdG2bduarH/8+HFNmzZNXbp0UVhYmC655BJt2LDBQ631HgzMAAAA4AssDRxr165VVlaWsrOzVVhYqKSkJKWnp6usrMxp/draWl133XU6dOiQXnvtNe3du1fLly9Xt27dPNxyAAAAczHLAX9h6T0cixcv1pQpU+x30S9btkxvvfWWVqxYodmzZzeov2LFCpWXl+ujjz5S27ZtJUmJiYmebDIAwI8xwAMA97NshqO2tlYFBQVKS0v7vjHBwUpLS1N+fr7TZd58802lpqZq2rRpiouL04ABA/TEE0+orq6u0e3U1NSosrLS4eXruJwKAIDAQAiGP7AscBw7dkx1dXX2R3adExcXp5KSEqfLHDhwQK+99prq6uq0YcMGPfroo3rqqaeavNN+wYIFioqKsr8SEhLcuh8A3ItADQCAf7H8pnFX1NfXq3Pnznr++ec1ZMgQjR07Vg8//LCWLVvW6DJz5sxRRUWF/XX48GEPttj9GIwB3ilyf6HVTbBcUWlHq5sAAPBClt3DERMTo5CQEJWWljqUl5aWKj4+3ukyXbp0Udu2bRUSEmIv69evn0pKSlRbW6vQ0NAGy4SFhSksjF/rBAA0jUtX4K345XH4OstmOEJDQzVkyBDl5eXZy+rr65WXl6fU1FSny1xxxRXat2+f6uvr7WVffvmlunTp4jRsAAAAALCWpZdUZWVlafny5XrxxRdVVFSkqVOnqrq62v7UqgkTJmjOnDn2+lOnTlV5ebmmT5+uL7/8Um+99ZaeeOIJTZs2zapd8Cgup0Kg4FgHAEfMwMGXWfpY3LFjx+ro0aOaO3euSkpKlJycrNzcXPuN5MXFxQoO/j4TJSQkaOPGjZo5c6YGDRqkbt26afr06Zo1a5ZVuwAAAACgCZYGDknKzMxUZmam08+2bNnSoCw1NVUff/yxya3yPpzxBQDzcPYYvoB7OeCrfOopVQAAAAB8C4HDBzC7AQAAAF9F4ADglQjaANAQl//BFxE4AAABjQEcAJiLwOHlOMsLAADOR0iGryFwAAAAADANgcOLMbsBAACcYZYDvoTAAcBrEbphNgZtAGA+AgcAAAAA0xA4vBRndgHfE7m/0OomWKaotKPVTQACDjN08BUEDgAAAACmIXB4IWY3gO/x7wEAGscsB3wBgQMAEJAYqAGAZxA4AAAAAJiGwOFluHwEAAC4gtk6eDsCBwAAAADTEDi8CLMbAOAZnBGGv+GYhjcjcADweoRxAAB8F4EDAAAAgGkIHF6CM7gAAKA1uKwK3orAAQAIKAzKAMCzCBxegNkNAADgDgRqeCMCBwCfQDAHAMA3ETgAAAAAmIbAYTHO2gLwdUWlHa1uAoDzcFkVvA2BAwDcKHJ/odVNQBMYiAGA5xE4LMTsBgAAMAPhGt6EwAHAZxDSAQDwPQQOAAAAAKYhcFiEM7UAAMBMXFYFb0HgAAAEBAZfAGANAocFmN0AAACeQNCGNyBwAPApBHYAAHwLgQMAAACAaQgcHsbZWQAA4ElcVgWrETgAAH6PARcAf7Z06VIlJiYqPDxcKSkp2rZtW5P1X331VfXt21fh4eEaOHCgNmzYYGr7CBwAAAB+jtDtv9auXausrCxlZ2ersLBQSUlJSk9PV1lZmdP6H330kcaNG6fJkydrx44dGjNmjMaMGaNdu3aZ1kaXA0dxcbEMw2hQbhiGiouL3dIof8XlVAAAAHCnxYsXa8qUKcrIyFD//v21bNkyRUREaMWKFU7rP/PMMxo5cqQeeOAB9evXT/Pnz9dll12mP/7xj6a10eXA0aNHDx09erRBeXl5uXr06OGWRgFAUwjvAAB/VllZ6fCqqXE+Q1VbW6uCggKlpaXZy4KDg5WWlqb8/Hyny+Tn5zvUl6T09PRG67tDG1cXMAxDQUFBDcqrqqoUHh7ulkb5IwZIAADASrv21GhA3zCrm+E3vg7trfahNreusyq0UpKUkJDgUJ6dna2cnJwG9Y8dO6a6ujrFxcU5lMfFxWnPnj1Ot1FSUuK0fklJSSta3rRmB46srCxJUlBQkB599FFFRETYP6urq9PWrVuVnJzs9gYCALxXUWlHq5twQVy7DsDXHD58WDbb92EmLMy3g2KzA8eOHd+doTcMQ59//rlCQ0Ptn4WGhiopKUn333+/+1sIAAAAt2CWwzfYbDaHwNGYmJgYhYSEqLS01KG8tLRU8fHxTpeJj493qb47NDtwbN68WZKUkZGhZ555plmdgO9wORUQWCL3F6q612VWNwMA4OdCQ0M1ZMgQ5eXlacyYMZKk+vp65eXlKTMz0+kyqampysvL04wZM+xlmzZtUmpqqmntdPmm8ZUrVxI2AFiOIA8AwHe3PSxfvlwvvviiioqKNHXqVFVXVysjI0OSNGHCBM2ZM8def/r06crNzdVTTz2lPXv2KCcnR9u3b280oLiDyzeNwzUMigAAgDfhsir/MnbsWB09elRz585VSUmJkpOTlZuba78xvLi4WMHB388xDB8+XKtXr9Yjjzyihx56SL1799b69es1YMAA09pI4AAA+C1uGAcQCDIzMxudodiyZUuDsttuu0233Xabya36Hr80DgAAEGAI4/AkAoeJuJwKAAAAgY7AAQAAAMA0BA6TMLsBmI9/ZwDQclxWBU8hcAAA/BKDKQDwDgQOAACAAEUwhycQOEzAZR4AAADAdwgcAAAAAExD4AAAAAhgXFYFsxE43IzLqQDP4t8cnGEABQDeg8ABAGiRotKOVjcBAOADCBxuxJlWAADgi5gVhJkIHAAAAABMQ+AAABNE7i+0ugkA4BJmOWAWAoebcDkVAAAA0BCBA4DPI/DjfJylBQDvQuAAAACAJAI7zEHgcAPOrgIAAADOETgAAABgxywH3I3A0UrMbgAAAACNI3AAAPwGZ2YBwPsQOAD4BWYbAcB9CO9wJwJHKzDAAQAAAJpG4AAAAEADzHLAXQgcLcTsBgAAAHBhBA4AAAAApiFwAAD8Apd/AO7Hvyu4A4GjBbicCvBO/Nv0nKLSjlY3AQDgIwgcAAAAAExD4AAAAECjuKwKrUXgcBGXbABorsj9hVY3AQAAyxE4AAAA0CRmOdAaBA4XMLsBAN6JwRAAeC8CBwC/wokBAAC8C4EDAAAAF8RMIlrKKwLH0qVLlZiYqPDwcKWkpGjbtm3NWm7NmjUKCgrSmDFjzG2gOGsKAAAAtITlgWPt2rXKyspSdna2CgsLlZSUpPT0dJWVlTW53KFDh3T//ffrJz/5iYdaCgAAENiY5UBLWB44Fi9erClTpigjI0P9+/fXsmXLFBERoRUrVjS6TF1dncaPH6/HHntMPXv29GBrAQDehgEQAHg3SwNHbW2tCgoKlJaWZi8LDg5WWlqa8vPzG11u3rx56ty5syZPnnzBbdTU1KiystLh5SoupwIAAABaxtLAcezYMdXV1SkuLs6hPC4uTiUlJU6X+eCDD/TCCy9o+fLlzdrGggULFBUVZX8lJCS0ut0AAACBillFuMryS6pcceLECd15551avny5YmJimrXMnDlzVFFRYX8dPnzYpW0yuwH4Hv7dAgDgPdpYufGYmBiFhISotLTUoby0tFTx8fEN6u/fv1+HDh3S6NGj7WX19fWSpDZt2mjv3r3q1auXwzJhYWEKCwszofUAAAAALsTSGY7Q0FANGTJEeXl59rL6+nrl5eUpNTW1Qf2+ffvq888/186dO+2vm266Sddcc4127tzJ5VIAAAAewGVVcIWlMxySlJWVpYkTJ2ro0KEaNmyYnn76aVVXVysjI0OSNGHCBHXr1k0LFixQeHi4BgwY4LB8dHS0JDUodwcuywAA78agBwC8n+WBY+zYsTp69Kjmzp2rkpISJScnKzc3134jeXFxsYKDfepWEwAAAL+3a0+NBvTlsnVcmOWBQ5IyMzOVmZnp9LMtW7Y0ueyqVavc3yAAAAAAbsHUQSO4nAoAnCsq7Wh1EwAAPoTAAcAvcdIAAMzHfVS+o7y8XOPHj5fNZlN0dLQmT56sqqqqJpf51a9+pV69eqldu3aKjY3VzTffrD179ri8bQKHEwxUALhL5P5Cq5sAAIDGjx+v3bt3a9OmTfrHP/6h999/X3fffXeTywwZMkQrV65UUVGRNm7cKMMwdP3116uurs6lbXvFPRwAAADwTdw87n6VlZUO71v7u3JFRUXKzc3VJ598oqFDh0qSlixZolGjRmnRokXq2rWr0+XODySJiYl6/PHHlZSUpEOHDjX47bumEDgAAD6JSzkAWOnLso5qV21z6zpPVYdIUoPflsvOzlZOTk6L15ufn6/o6Gh72JCktLQ0BQcHa+vWrbrlllsuuI7q6mqtXLlSPXr0cPm37wgcP8DlVAAAALDS4cOHZbN9H2ZaM7shSSUlJercubNDWZs2bdSpUyeVlJQ0ueyzzz6rBx98UNXV1erTp482bdqk0NBQl7bPPRwAAABoFWYc3ctmszm8Ggscs2fPVlBQUJOvltzkfb7x48drx44d+p//+R9dcskluv3223X69GmX1sEMx3mY3QAAAICvuO+++zRp0qQm6/Ts2VPx8fEqKytzKD979qzKy8sVHx/f5PJRUVGKiopS7969dfnll6tjx456/fXXNW7cuGa3k8ABwG9VFexQ+yGDrW4GAAQEbh73vNjYWMXGxl6wXmpqqo4fP66CggINGTJEkvTee++pvr5eKSkpzd6eYRgyDEM1Na7NaHFJFQAAAODH+vXrp5EjR2rKlCnatm2bPvzwQ2VmZuqOO+6wP6HqyJEj6tu3r7Zt2yZJOnDggBYsWKCCggIVFxfro48+0m233aZ27dpp1KhRLm2fwPF/uJwKAAAA/uqVV15R3759de2112rUqFG68sor9fzzz9s/P3PmjPbu3auTJ09KksLDw/XPf/5To0aN0sUXX6yxY8eqQ4cO+uijjxrcgH4hXFIFAPA53KAKeCcuq/JenTp10urVqxv9PDExUYZh2N937dpVGzZscMu2meEAAAAAYBoCh7icCgAAADALgQMAAABuwyWP+KGADxzMbgD+jX/jAABYK+ADBwAAANyLWQ6cj8ABAPApDGQAwLcEdODgUgsAAADAXAEdOAAArikq7Wh1EwD4CGYjcU7ABo7qnZ9Z3QQAASJyf6HVTQAAwDIBGzgAAABgLmY5IBE4AAQA7tcCAMA6BA4AAAAApiFwAAB8BpdnAL6Hf7cgcAAAAAAwDYEDAAAApmKWI7AROAAAAACYhsABAAAAwDQEDgABgUfjAoC1uKwqcBE4AAAAAJiGwAEA8AmcHQV8H/+OAxOBAwAAAIBpCBwAAAAATEPgAAAAgMdwWVXgIXAAAAAAMA2BA0DA4NG4AAB4HoEDAAAAHsVlVYGFwAEA8HoMTgDAdxE4AMADIvcXWt0EAPAqnEgIHAQOAECzFJV2tLoJAAAfROAAAAAAYBoCBwAAACzBZVWBgcABAAAAwDQEDgABhd/iAADvwiyH/yNwAAAAADANgQMA4NU4+wkAvo3AAQAAAEtxYsG/ETgAAAAAmIbAAQAAAMsxy+G/CBwAAAAATEPgAAAAAGAaAgeAgMNvcQCAd+KyKv/UxuoGAIHs4Hu7m123x08vNbElAAAA5iBwAB7iSri40PKEDwCAv9q1p0a9EqxuBdyJwAGYqLUhoznrJXzAn3F5BQD4PgIHYAKzgkZT2yJ4AAD8xRdfcrLBnxA4ADfyZNBobNsEDwAA4E14ShXgBgff221p2Dift7QDAAB4j/Lyco0fP142m03R0dGaPHmyqqqqLrhcfn6+fvrTnyoyMlI2m01XXXWVTp065dK2meEAWsFbB/fMdgAAgPONHz9e33zzjTZt2qQzZ84oIyNDd999t1avXt3oMvn5+Ro5cqTmzJmjJUuWqE2bNvr0008VHOzanAWBA2ghbw0b5zv43m5ChxeJ3F+o6l6XWd0MBJDd2w+6VP/SoT1MagkAKxUVFSk3N1effPKJhg4dKklasmSJRo0apUWLFqlr165Ol5s5c6buvfdezZ49217Wp08fl7fPJVWAi7zp8qnm8KW2ehI//gd/tHv7QYeXp5cH4B6VlZUOr5qa1t1En5+fr+joaHvYkKS0tDQFBwdr69atTpcpKyvT1q1b1blzZw0fPlxxcXEaMWKEPvjgA5e3zwwH4AJfHbwz0wH4N7PCwfnrZfYDcPTFlzUKa+fep2nVnPpufQkJjj9Ekp2drZycnBavt6SkRJ07d3Yoa9OmjTp16qSSkhKnyxw4cECSlJOTo0WLFik5OVn//d//rWuvvVa7du1S7969m719AgfQDL4aNM5H6ICv4Tc4LsyTsxDntkXwAMx3+PBh2Ww2+/uwsDCn9WbPnq0nn3yyyXUVFRW1qA319fWSpF/96lfKyMiQJA0ePFh5eXlasWKFFixY0Ox1ETiAC/CHsHEON5MD/sHKy50IHoD5bDabQ+BozH333adJkyY1Wadnz56Kj49XWVmZQ/nZs2dVXl6u+Ph4p8t16dJFktS/f3+H8n79+qm4uPiCbTsfgQNogj+FDaA1iko7Wt0E/B9vubeC4AFYLzY2VrGxsResl5qaquPHj6ugoEBDhgyRJL333nuqr69XSkqK02USExPVtWtX7d2716H8yy+/1A033OBSO7lpHGiEP4cNf943wJ95S9g4HzeYA96vX79+GjlypKZMmaJt27bpww8/VGZmpu644w77E6qOHDmivn37atu2bZKkoKAgPfDAA/rDH/6g1157Tfv27dOjjz6qPXv2aPLkyS5tnxkO4AcCZTDOPR2A7/CFAf3u7QeZ7QC82CuvvKLMzExde+21Cg4O1q233qo//OEP9s/PnDmjvXv36uTJk/ayGTNm6PTp05o5c6bKy8uVlJSkTZs2qVevXi5tm8ABnCdQwsY5hA7A+/lC2DiHy6wA79WpU6cmf+QvMTFRhmE0KJ89e7bD73C0BJdUAf8n0MLGOYG63xK/xQHv50th43y+2m4A5iBwAArsQbfE/gPeyNcH7dzbAeAcAgcCHoNtAN7Gnwbq/rQvAFqGwIGARtj4Hn0BbxLIP/rnjwN0f9wnAM1H4EDAYoDdEH0CWMufB+ZcYgUELgIHAhIDawDeJlAG44GynwC+R+BAwCFsNI3+ATwv0Abhgba/QKAjcCCgMJhuHvoJgNkIHUDgIHAgYDCIBuCNAnngHcj7DgQSAgcCAmHDdYHSZ/z4H6zEgJs+AAIBgQN+L1AGzmag7wB4Ak+wAvwbgQN+jQEzAG/FALsh+gTwT14ROJYuXarExESFh4crJSVF27Zta7Tu8uXL9ZOf/EQdO3ZUx44dlZaW1mR9BC7ChnvQj4D7MbBuHH0D+B/LA8fatWuVlZWl7OxsFRYWKikpSenp6SorK3Naf8uWLRo3bpw2b96s/Px8JSQk6Prrr9eRI0c83HJ4MwbJ8FaR+wutboLXC+RfGcd3CB2Af7E8cCxevFhTpkxRRkaG+vfvr2XLlikiIkIrVqxwWv+VV17RPffco+TkZPXt21d//vOfVV9fr7y8PA+3HN6KsOF+9CngPgymm4d+AvyHpYGjtrZWBQUFSktLs5cFBwcrLS1N+fn5zVrHyZMndebMGXXq1Mnp5zU1NaqsrHR4wX8xMAbgzRhEu4b+AvyDpYHj2LFjqqurU1xcnEN5XFycSkpKmrWOWbNmqWvXrg6h5XwLFixQVFSU/ZWQkNDqdsM7ETbMRf8CsAKhA/B9ll9S1RoLFy7UmjVr9Prrrys8PNxpnTlz5qiiosL+Onz4sIdbCU9gMAzA2zFwbjn6DvBtlgaOmJgYhYSEqLS01KG8tLRU8fHxTS67aNEiLVy4UO+8844GDRrUaL2wsDDZbDaHF/wLYcNz/LWv+fE/wPsROgDfZWngCA0N1ZAhQxxu+D53A3hqamqjy/32t7/V/PnzlZubq6FDh3qiqQAAtBiDZfegHwHfZPklVVlZWVq+fLlefPFFFRUVaerUqaqurlZGRoYkacKECZozZ469/pNPPqlHH31UK1asUGJiokpKSlRSUqKqqiqrdgEW8tcz7t6MPgdgJUIH4HvaWN2AsWPH6ujRo5o7d65KSkqUnJys3Nxc+43kxcXFCg7+Phc999xzqq2t1c9//nOH9WRnZysnJ8eTTYfFGPgC8AUMkN1v9/aDunRoD6ubAaCZLA8ckpSZmanMzEynn23ZssXh/aFDh8xvELweYcNaB9/brR4/vdTqZgBej7ABAF5wSRXgKsIG4L/4lXE0F2EO8B0EDvgUwob34LsAmsaA2Hz0MeAbCBwAAMBnEToA70fggM/gjLr34TsBnGMQ7Fn0N+DdCBzwCQxsAQBNIXQA3ovAAa9H2PBufD8AvAWhA/BOBA54NQaz8JSqgh1WN8FrFZV2tLoJPoVBr7Xof8D7EDgAAIBfIXQA3oXAAa/F7Ibv4LsCvsNA13vwXQDeg8ABr8QAFgAAwD8QOOB1CBsAfBFn1L0P3wngHQgc8CqEDd/FdwfAGxE6AOsROAAAXmHXnhqrmwA/RegArEXggNfgDLnv4ztEoGJA6/34jgDrEDjgFRioIpBE7i+0uglAQCJ0ANYgcMByhA0AAAD/ReAA4FYESAQazpr7Fr4vwPMIHLAUg1N4k6qCHVY3AYAHEDoAzyJwwDKEDQC+joGr7+K7AzyHwAFLEDb8G98vAF9A6AA8g8ABAH4isXaP1U0AAKABAgc8jrPfAPwBZ8f9A98jYD4CBzyKsBE4+K4B+ApCB2AuAgc8hgEoAMBbEToA8xA4AABwEYNT/8T3Cn9WXl6u8ePHy2azKTo6WpMnT1ZVVVWTy+zfv1+33HKLYmNjZbPZdPvtt6u0tNTlbRM44BHMbgQmvncAALzD+PHjtXv3bm3atEn/+Mc/9P777+vuu+9utH51dbWuv/56BQUF6b333tOHH36o2tpajR49WvX19S5tu01rGw9cCINOAICv2L39oC4d2sPqZgBuVVRUpNzcXH3yyScaOnSoJGnJkiUaNWqUFi1apK5duzZY5sMPP9ShQ4e0Y8cO2Ww2SdKLL76ojh076r333lNaWlqzt88MB0xF2ADQHLv21FjdBMCOS6tgtcrKSodXTU3r/kbm5+crOjraHjYkKS0tTcHBwdq6davTZWpqahQUFKSwsDB7WXh4uIKDg/XBBx+4tH1mOACY6uB7u9Xjp5da3QzAbRiMBgZmOnAhRTu+VtvQ9m5d55na7+6pSEhIcCjPzs5WTk5Oi9dbUlKizp07O5S1adNGnTp1UklJidNlLr/8ckVGRmrWrFl64oknZBiGZs+erbq6On3zzTcubZ8ZDpiG2Q34oqqCHVY3AYCXIFzCKocPH1ZFRYX9NWfOHKf1Zs+eraCgoCZfe/a07EdhY2Nj9eqrr+rvf/+72rdvr6ioKB0/flyXXXaZgoNdixDMcMAUhA0AAICWsdls9vsmmnLfffdp0qRJTdbp2bOn4uPjVVZW5lB+9uxZlZeXKz4+vtFlr7/+eu3fv1/Hjh1TmzZtFB0drfj4ePXs2bNZ+3EOgQNuR9gA4K844x14uLQK3iw2NlaxsbEXrJeamqrjx4+roKBAQ4YMkSS99957qq+vV0pKygWXj4mJsS9TVlamm266yaV2ckkVANMRQgH4MoImfF2/fv00cuRITZkyRdu2bdOHH36ozMxM3XHHHfYnVB05ckR9+/bVtm3b7MutXLlSH3/8sfbv36+XX35Zt912m2bOnKk+ffq4tH1mOOBWDCwBAP6ImQ74uldeeUWZmZm69tprFRwcrFtvvVV/+MMf7J+fOXNGe/fu1cmTJ+1le/fu1Zw5c1ReXq7ExEQ9/PDDmjlzpsvbJnDAbQgbAAAA3qlTp05avXp1o58nJibKMAyHsoULF2rhwoWt3jaXVMEtCBsA/B2X1YBjAGgZAgcAjyCUAvAHhA7AdQQOtBoDSQBAICF0AK4hcKBVCBsAAgEDTPwQxwTQfAQOAB5DQAUAIPAQONBiDB4BAIGMWQ6geQgcaBHCBgAAhA6gOQgccBlhA2i9yP2FVjcBzcSAEhfCMQI0jcABwKN8IbBWFeywugkAAPgNAgdc4guDRQAAPI1ZDqBxBA40G2EDAIDGEToA5wgcAABL7dpTY3UTAAAmInCgWZjdABCIOGMNV3HMAA0ROHBBhA24G8cUAH9G6AAcETgAAADcjNABfI/AgSZxJhoAAACtQeBAowgbAAC0HLMcwHcIHAAAOMFgEe7AcQQQONAIZjdgNo4xAIGC0IFAR+BAAwwEAQAA4C4EDjggbAAA4H7MciCQETgAAAA8gNCBQEXggB2zGwDwHQaGMAvHFgIRgQOSCBuwBscdAAD+j8ABAADgQcxyINAQOMBZZsCJqoIdVjcBgB8jdCCQEDgCHGEDAAAAZiJwAAAAWIBZDgQKAkcAY3YDABpiEAhP4nhDICBwBCjCBrwFxyKAQEfogL8jcAAAAAAwDYEjAHFGGQAA78IsB/wZgSPAEDYAAPBOhA74KwIHAAAAANMQOAIIsxvwVhybAPAdZjngjwgcAYIBHQBcGIM9eAOOQ/gbAgcAAAAA0xA4AgCzGwAA+BZmOeBPCBx+jrABAIBvInTAXxA4/BhhAwAA30bogD8gcAAAAAAwDYHDTzG7AV/DMQsAzjHLAV9H4PBDDNwAwHUM6uDNOD7hywgcAAAAAExD4PAzzG4AAOCfmOWAryJw+BHCBgAA/o3QAV9E4AAAAABgGq8IHEuXLlViYqLCw8OVkpKibdu2NVn/1VdfVd++fRUeHq6BAwdqw4YNHmqp92J2AwCAwMAsB1riN7/5jYYPH66IiAhFR0dfsP6ZM2c0a9YsDRw4UJGRkeratasmTJigf//73y5v2/LAsXbtWmVlZSk7O1uFhYVKSkpSenq6ysrKnNb/6KOPNG7cOE2ePFk7duzQmDFjNGbMGO3atcvDLfcehA0AAAILoQOuqq2t1W233aapU6c2q/7JkydVWFioRx99VIWFhVq3bp327t2rm266yeVtWx44Fi9erClTpigjI0P9+/fXsmXLFBERoRUrVjit/8wzz2jkyJF64IEH1K9fP82fP1+XXXaZ/vjHP3q45QDcjfAMAIA5HnvsMc2cOVMDBw5sVv2oqCht2rRJt99+u/r06aPLL79cf/zjH1VQUKDi4mKXtt2mJQ12l9raWhUUFGjOnDn2suDgYKWlpSk/P9/pMvn5+crKynIoS09P1/r1653Wr6mpUU1Njf19RUWFJOlETW0rW+8dDv1PkdVNANzKm/5t1p88Zer6T1ZVu32dVaGVbl/nqeoQt6/zfDWnai5cyQPO1FZZ3QTAJTs/+lz9Bne3uhmmqDl9QpJkGIbFLWncWRP+ZpxbZ2Wl49/ysLAwhYWFuX17rqqoqFBQUFCzLsk6n6WB49ixY6qrq1NcXJxDeVxcnPbs2eN0mZKSEqf1S0pKnNZfsGCBHnvssQblSc/8tYWtBmCqrQVWtwAAfMbGVVa3wFzffvutoqKirG6Gg9DQUMXHxytv9U9NWX/79u2VkJDgUJadna2cnBxTttdcp0+f1qxZszRu3DjZbDaXlrU0cHjCnDlzHGZEjh8/ru7du6u4uNjrDmBvVllZqYSEBB0+fNjlgyxQ0WctQ7+5jj5rGfrNdfRZy9BvrquoqNBFF12kTp06Wd2UBsLDw3Xw4EHV1pozI28YhoKCghzKGpvdmD17tp588skm11dUVKS+ffu2qk1nzpzR7bffLsMw9Nxzz7m8vKWBIyYmRiEhISotLXUoLy0tVXx8vNNl4uPjXarf2BRUVFQU/+hbwGaz0W8uos9ahn5zHX3WMvSb6+izlqHfXBccbPntxk6Fh4crPDzc6mbovvvu06RJk5qs07Nnz1Zt41zY+Prrr/Xee++16Bi2NHCEhoZqyJAhysvL05gxYyRJ9fX1ysvLU2ZmptNlUlNTlZeXpxkzZtjLNm3apNTUVA+0GAAAAPAOsbGxio2NNW3958LGV199pc2bN+tHP/pRi9ZjeWzMysrS8uXL9eKLL6qoqEhTp05VdXW1MjIyJEkTJkxwuKl8+vTpys3N1VNPPaU9e/YoJydH27dvbzSgAAAAAIGuuLhYO3fuVHFxserq6rRz507t3LlTVVXf3/zet29fvf7665K+Cxs///nPtX37dr3yyiuqq6tTSUmJSkpKXL6czPJ7OMaOHaujR49q7ty5KikpUXJysnJzc+03hhcXFztMpw0fPlyrV6/WI488ooceeki9e/fW+vXrNWDAgGZtLywsTNnZ2V5xp78vod9cR5+1DP3mOvqsZeg319FnLUO/uY4+c7+5c+fqxRdftL8fPHiwJGnz5s26+uqrJUl79+61P9H1yJEjevPNNyVJycnJDus6f5nmCDK8+XljAAAAAHya5ZdUAQAAAPBfBA4AAAAApiFwAAAAADANgQMAAACAafwycPzmN7/R8OHDFRERoejo6GYtYxiG5s6dqy5duqhdu3ZKS0vTV1995VCnvLxc48ePl81mU3R0tCZPnuzwKDFf5uq+HTp0SEFBQU5fr776qr2es8/XrFnjiV3yiJYcE1dffXWDPvn1r3/tUKe4uFg33nijIiIi1LlzZz3wwAM6e/asmbviMa72WXl5uf7rv/5Lffr0Ubt27XTRRRfp3nvvtT9F4xx/O9aWLl2qxMREhYeHKyUlRdu2bWuy/quvvqq+ffsqPDxcAwcO1IYNGxw+b87fOF/nSp8tX75cP/nJT9SxY0d17NhRaWlpDepPmjSpwTE1cuRIs3fD41zpt1WrVjXokx/++BnHmiNnf/ODgoJ044032uv4+7H2/vvva/To0eratauCgoK0fv36Cy6zZcsWXXbZZQoLC9PFF1+sVatWNajj6t9JWMjwQ3PnzjUWL15sZGVlGVFRUc1aZuHChUZUVJSxfv1649NPPzVuuukmo0ePHsapU6fsdUaOHGkkJSUZH3/8sfHPf/7TuPjii41x48aZtBee5eq+nT171vjmm28cXo899pjRvn1748SJE/Z6koyVK1c61Du/T31dS46JESNGGFOmTHHok4qKCvvnZ8+eNQYMGGCkpaUZO3bsMDZs2GDExMQYc+bMMXt3PMLVPvv888+N//iP/zDefPNNY9++fUZeXp7Ru3dv49Zbb3Wo50/H2po1a4zQ0FBjxYoVxu7du40pU6YY0dHRRmlpqdP6H374oRESEmL89re/Nb744gvjkUceMdq2bWt8/vnn9jrN+Rvny1zts1/84hfG0qVLjR07dhhFRUXGpEmTjKioKONf//qXvc7EiRONkSNHOhxT5eXlntolj3C131auXGnYbDaHPikpKXGow7Hm6Ntvv3Xor127dhkhISHGypUr7XX8/VjbsGGD8fDDDxvr1q0zJBmvv/56k/UPHDhgREREGFlZWcYXX3xhLFmyxAgJCTFyc3PtdVz9HmAtvwwc56xcubJZgaO+vt6Ij483fve739nLjh8/boSFhRl/+ctfDMMwjC+++MKQZHzyySf2Om+//bYRFBRkHDlyxO1t9yR37VtycrLxn//5nw5lzfnD4qta2m8jRowwpk+f3ujnGzZsMIKDgx3+J/7cc88ZNpvNqKmpcUvbreKuY+2vf/2rERoaapw5c8Ze5k/H2rBhw4xp06bZ39fV1Rldu3Y1FixY4LT+7bffbtx4440OZSkpKcavfvUrwzCa9zfO17naZz909uxZo0OHDsaLL75oL5s4caJx8803u7upXsXVfrvQ/1c51i7s97//vdGhQwejqqrKXhYIx9o5zflb/eCDDxqXXnqpQ9nYsWON9PR0+/vWfg/wLL+8pMpVBw8eVElJidLS0uxlUVFRSklJUX5+viQpPz9f0dHRGjp0qL1OWlqagoODtXXrVo+32Z3csW8FBQXauXOnJk+e3OCzadOmKSYmRsOGDdOKFStk+MlPv7Sm31555RXFxMRowIABmjNnjk6ePOmw3oEDB9p//FKS0tPTVVlZqd27d7t/RzzIXf+OKioqZLPZ1KaN42+X+sOxVltbq4KCAoe/R8HBwUpLS7P/Pfqh/Px8h/rSd8fMufrN+Rvny1rSZz908uRJnTlzRp06dXIo37Jlizp37qw+ffpo6tSp+vbbb93adiu1tN+qqqrUvXt3JSQk6Oabb3b4u8SxdmEvvPCC7rjjDkVGRjqU+/Ox5qoL/U1zx/cAz7L8l8a9QUlJiSQ5DPDOvT/3WUlJiTp37uzweZs2bdSpUyd7HV/ljn174YUX1K9fPw0fPtyhfN68efrpT3+qiIgIvfPOO7rnnntUVVWle++9123tt0pL++0Xv/iFunfvrq5du+qzzz7TrFmztHfvXq1bt86+XmfH4rnPfJk7jrVjx45p/vz5uvvuux3K/eVYO3bsmOrq6pweA3v27HG6TGPHzPl/v86VNVbHl7Wkz35o1qxZ6tq1q8MAZuTIkfqP//gP9ejRQ/v379dDDz2kG264Qfn5+QoJCXHrPlihJf3Wp08frVixQoMGDVJFRYUWLVqk4cOHa/fu3frxj3/MsXYB27Zt065du/TCCy84lPv7seaqxv6mVVZW6tSpU/rf//3fVv+bh2f5TOCYPXu2nnzyySbrFBUVqW/fvh5qkfdrbp+11qlTp7R69Wo9+uijDT47v2zw4MGqrq7W7373O68eBJrdb+cPlAcOHKguXbro2muv1f79+9WrV68Wr9dKnjrWKisrdeONN6p///7Kyclx+MwXjzV4h4ULF2rNmjXasmWLww3Qd9xxh/2/Bw4cqEGDBqlXr17asmWLrr32WiuaarnU1FSlpqba3w8fPlz9+vXTn/70J82fP9/ClvmGF154QQMHDtSwYcMcyjnW4O98JnDcd999mjRpUpN1evbs2aJ1x8fHS5JKS0vVpUsXe3lpaamSk5PtdcrKyhyWO3v2rMrLy+3Le5vm9llr9+21117TyZMnNWHChAvWTUlJ0fz581VTU6OwsLAL1reCp/rtnJSUFEnSvn371KtXL8XHxzd40kZpaakkBfSxduLECY0cOVIdOnTQ66+/rrZt2zZZ3xeONWdiYmIUEhJi/87PKS0tbbSP4uPjm6zfnL9xvqwlfXbOokWLtHDhQr377rsaNGhQk3V79uypmJgY7du3zy8Gga3pt3Patm2rwYMHa9++fZI41ppSXV2tNWvWaN68eRfcjr8da65q7G+azWZTu3btFBIS0upjFx5m9U0kZnL1pvFFixbZyyoqKpzeNL59+3Z7nY0bN/rVTeMt3bcRI0Y0eGJQYx5//HGjY8eOLW6rN3HXMfHBBx8YkoxPP/3UMIzvbxo//0kbf/rTnwybzWacPn3afTtggZb2WUVFhXH55ZcbI0aMMKqrq5u1LV8+1oYNG2ZkZmba39fV1RndunVr8qbxn/3sZw5lqampDW4ab+pvnK9ztc8MwzCefPJJw2azGfn5+c3axuHDh42goCDjjTfeaHV7vUVL+u18Z8+eNfr06WPMnDnTMAyOtaasXLnSCAsLM44dO3bBbfjjsXaOmnnT+IABAxzKxo0b1+Cm8dYcu/AsvwwcX3/9tbFjxw77Y1p37Nhh7Nixw+FxrX369DHWrVtnf79w4UIjOjraeOONN4zPPvvMuPnmm50+Fnfw4MHG1q1bjQ8++MDo3bu3Xz0Wt6l9+9e//mX06dPH2Lp1q8NyX331lREUFGS8/fbbDdb55ptvGsuXLzc+//xz46uvvjKeffZZIyIiwpg7d67p++Mprvbbvn37jHnz5hnbt283Dh48aLzxxhtGz549jauuusq+zLnH4l5//fXGzp07jdzcXCM2NtavHovrSp9VVFQYKSkpxsCBA419+/Y5PDby7NmzhmH437G2Zs0aIywszFi1apXxxRdfGHfffbcRHR1tf3LZnXfeacyePdte/8MPPzTatGljLFq0yCgqKjKys7OdPhb3Qn/jfJmrfbZw4UIjNDTUeO211xyOqXP/nzhx4oRx//33G/n5+cbBgweNd99917jsssuM3r17+3zwP5+r/fbYY48ZGzduNPbv328UFBQYd9xxhxEeHm7s3r3bXodjzbHPzrnyyiuNsWPHNigPhGPtxIkT9rGYJGPx4sXGjh07jK+//towDMOYPXu2ceedd9rrn3ss7gMPPGAUFRUZS5cudfpY3Ka+B3gXvwwcEydONCQ1eG3evNleR//3zP5z6uvrjUcffdSIi4szwsLCjGuvvdbYu3evw3q//fZbY9y4cUb79u0Nm81mZGRkOIQYX3ahfTt48GCDPjQMw5gzZ46RkJBg1NXVNVjn22+/bSQnJxvt27c3IiMjjaSkJGPZsmVO6/oqV/utuLjYuOqqq4xOnToZYWFhxsUXX2w88MADDr/DYRiGcejQIeOGG24w2rVrZ8TExBj33XefwyNgfZmrfbZ582an/54lGQcPHjQMwz+PtSVLlhgXXXSRERoaagwbNsz4+OOP7Z+NGDHCmDhxokP9v/71r8Yll1xihIaGGpdeeqnx1ltvOXzenL9xvs6VPuvevbvTYyo7O9swDMM4efKkcf311xuxsbFG27Ztje7duxtTpkzxy8GMK/02Y8YMe924uDhj1KhRRmFhocP6ONYa/vvcs2ePIcl45513GqwrEI61xv6On+uniRMnGiNGjGiwTHJyshEaGmr07NnTYcx2TlPfA7xLkGH44HMjAQAAAPgEfocDAAAAgGkIHAAAAABMQ+AAAAAAYBoCBwAAAADTEDgAAAAAmIbAAQAAAMA0BA4AAAAApiFwAAAAADANgQMAAACAaQgcAAAAAExD4AAAAABgGgIHAPioo0ePKj4+Xk888YS97KOPPlJoaKjy8vIsbBkAAN8LMgzDsLoRAICW2bBhg8aMGaOPPvpIffr0UXJysm6++WYtXrzY6qYBACCJwAEAPm/atGl69913NXToUH3++ef65JNPFBYWZnWzAACQROAAAJ936tQpDRgwQIcPH1ZBQYEGDhxodZMAALDjHg4A8HH79+/Xv//9b9XX1+vQoUNWNwcAAAfMcACAD6utrdWwYcOUnJysPn366Omnn9bnn3+uzp07W900AAAkETgAwKc98MADeu211/Tpp5+qffv2GjFihKKiovSPf/zD6qYBACCJS6oAwGdt2bJFTz/9tF566SXZbDYFBwfrpZde0j//+U8999xzVjcPAABJzHAAAAAAMBEzHAAAAABMQ+AAAAAAYBoCBwAAAADTEDgAAAAAmIbAAQAAAMA0BA4AAAAApiFwAAAAADANgQMAAACAaQgcAAAAAExD4AAAAABgGgIHAAAAANP8f1acCy//j4ucAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#Set Global Seed\n",
    "tf.random.set_seed(42)\n",
    "\n",
    "\n",
    "class BurgersPINN(tf.keras.Model):\n",
    "    def __init__(self):\n",
    "        super().__init__()  #Passes \n",
    "        \n",
    "        self.dense1 = tf.keras.layers.Dense(20, activation='tanh')\n",
    "        self.dense2 = tf.keras.layers.Dense(20, activation='tanh')\n",
    "        self.dense3 = tf.keras.layers.Dense(20, activation='tanh')\n",
    "        self.dense4 = tf.keras.layers.Dense(1, activation='linear')\n",
    "    \n",
    "    def call(self, inputs):\n",
    "        x, t = inputs\n",
    "        u = tf.concat([x, t], axis=1)\n",
    "        u = self.dense1(u)\n",
    "        u = self.dense2(u)\n",
    "        u = self.dense3(u)\n",
    "        u = self.dense4(u)\n",
    "        return u\n",
    "\n",
    "def BurgersPINN_loss(model, x, t, u_true):\n",
    "    with tf.GradientTape(persistent=True) as g:\n",
    "        g.watch(x)\n",
    "        g.watch(t)\n",
    "        u_pred = model([x, t])\n",
    "        u_x = g.gradient(u_pred, x)\n",
    "        u_t = g.gradient(u_pred, t)\n",
    "        f = u_t + u_pred*u_x - 0.05*np.pi*g.gradient(u_x, x)\n",
    "        mse = tf.reduce_mean(tf.square(u_true - u_pred))\n",
    "\n",
    "    f_mse = tf.reduce_mean(tf.square(f))\n",
    "    loss = mse + f_mse\n",
    "\n",
    "    return loss\n",
    "\n",
    "# Define the optimizer\n",
    "optimizer = tf.keras.optimizers.Adam(learning_rate=0.001)\n",
    "\n",
    "# Instantiate the model and set the loss and accuracy metrics\n",
    "model = BurgersPINN()\n",
    "train_loss = tf.keras.metrics.Mean(name='train_loss')\n",
    "train_mse = tf.keras.metrics.MeanSquaredError(name='train_mse')\n",
    "\n",
    "# Train the model\n",
    "for epoch in range(1, 10001):\n",
    "    with tf.GradientTape() as tape:\n",
    "        # Generate a batch of random inputs\n",
    "        x = tf.random.uniform(shape=(100,1), minval=-1, maxval=1)\n",
    "        t = tf.random.uniform(shape=(100,1), minval=0, maxval=1)\n",
    "\n",
    "        # Compute the loss\n",
    "        u_true = -tf.sin(np.pi*x)\n",
    "        loss = BurgersPINN_loss(model, x, t, u_true)\n",
    "\n",
    "    # Compute gradients and update the model\n",
    "    gradients = tape.gradient(loss, model.trainable_variables)\n",
    "    optimizer.apply_gradients(zip(gradients, model.trainable_variables))\n",
    "\n",
    "    # Update the metrics\n",
    "    train_loss(loss)\n",
    "    train_mse(u_true, model([x, t]))\n",
    "\n",
    "    # Print the metrics every 100 epochs\n",
    "    if epoch % 1000 == 0:\n",
    "        print(f\"Epoch {epoch}: Loss={train_loss.result()}, MSE={train_mse.result()}\")\n",
    "\n",
    "        # Reset the metrics for the next epoch\n",
    "        train_loss.reset_states()\n",
    "        train_mse.reset_states()\n",
    "# Generate a grid of points in the domain\n",
    "x = np.linspace(-1, 1, 101)\n",
    "t = np.linspace(0, 1, 101)\n",
    "x_grid, t_grid = np.meshgrid(x, t)\n",
    "\n",
    "# Flatten the grid and use the trained model to predict the velocity\n",
    "u_pred = model([x_grid.flatten()[:,None], t_grid.flatten()[:,None]])\n",
    "u_pred = np.reshape(u_pred, x_grid.shape)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.contourf(x_grid, t_grid, u_pred, cmap='coolwarm')\n",
    "plt.colorbar()\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('t')\n",
    "plt.title('Burgers\\' Equation')\n",
    "plt.show()\n"
   ]
  }
 ],
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