SMIB_Conventional.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4080b41d-caea-4212-ba53-8a9c3e38d312",
   "metadata": {},
   "source": [
    "# Conventional PINNs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "741d5da8-3646-480d-8191-c0ae5333fa83",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import packages\n",
    "using OrdinaryDiffEq      #Package use to create and solve ODEs.\n",
    "using NeuralPDE           #Package to create a PINNs.\n",
    "using Lux                 #Package to create a layer of PINNs.\n",
    "using OptimizationOptimJL #Package to create a optimazation problems and optimize the loss function. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31a1ab34-7ed4-4284-b1ff-8053d75ac07a",
   "metadata": {},
   "source": [
    "### Classical Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "79716406-58d8-41e3-bcd9-f47ac789f250",
   "metadata": {},
   "outputs": [],
   "source": [
    "function SMIB(du,u,p,t)             #Define the power system dynamics.\n",
    "    du[1] = u[2]\n",
    "    du[2] = 5- 10*sin(u[1])-1.7*u[2]\n",
    "end;\n",
    "u0 = [-1.0, 7.0]                    #Initial conditions.\n",
    "h = 0.01                            #Time steps.\n",
    "tspan = (0.0,10.0)                  #Duration simulation.\n",
    "prob = ODEProblem(SMIB,u0,tspan);   #Define the ODEs system which solved by ODE solvers.\n",
    "sol = solve(prob,Tsit5(),dt = h,adaptive = false);\n",
    "sol = transpose(sol);               #Using transpose function to plot results and save it to CSV file."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d59c7d3-3707-48df-973c-565a1592c559",
   "metadata": {},
   "source": [
    "### PINNs Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c97aec75-acec-40bd-bb52-a6195d360afd",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "SMIB_NN(u,p,t) = [u[2],5- 10*sin(u[1])-1.7*u[2]] #Define the set of equations of SMIB system.\n",
    "prob_NN = ODEProblem(SMIB_NN,u0,tspan);          #Create a ODEs system from a set of equations. \n",
    "\n",
    "func = Lux.tanh      #Define the activation function from Lux.jl package.\n",
    "N = 20               #Define the number neurons of hidden layers.\n",
    "\n",
    "#Create a network.\n",
    "#Chain: Collects multiple layers / functions to be called in sequence on a given input.\n",
    "#Dense: Create a traditional fully connected layer, whose forward pass is given by: y = activation.(weight * x .+ bias).\n",
    "#Reader can visit \"https://docs.juliahub.com/Lux/Jbrqh/0.4.24/autodocs/\" for more information.\n",
    "#The output size of a network equals to the length of state variables.\n",
    "\n",
    "chain = Lux.Chain(Lux.Dense(1, N, func), Lux.Dense(N, N, func), Lux.Dense(N, N, func),\n",
    "                    Lux.Dense(N, N, func), Lux.Dense(N, length(u0)))\n",
    "\n",
    "opt = OptimizationOptimJL.BFGS()                                        #Define the optimizer (BFGS).\n",
    "alg = NeuralPDE.NNODE(chain, opt, autodiff = false)                     #Define the algorithm for training the network.\n",
    "sol_NN = solve(prob_NN, alg, verbose=false, maxiters = 50000, saveat = 0.01);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0d542595-8ddb-48ab-90ef-3664b055b8da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chain(\n",
       "    layer_1 = Dense(1 => 20, tanh_fast),  \u001b[90m# 40 parameters\u001b[39m\n",
       "    layer_2 = Dense(20 => 20, tanh_fast),  \u001b[90m# 420 parameters\u001b[39m\n",
       "    layer_3 = Dense(20 => 20, tanh_fast),  \u001b[90m# 420 parameters\u001b[39m\n",
       "    layer_4 = Dense(20 => 20, tanh_fast),  \u001b[90m# 420 parameters\u001b[39m\n",
       "    layer_5 = Dense(20 => 2),           \u001b[90m# 42 parameters\u001b[39m\n",
       ") \u001b[90m        # Total: \u001b[39m1_342 parameters,\n",
       "\u001b[90m          #        plus \u001b[39m0 states."
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chain   #Show the total parameters of networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "53825be3-5261-46e6-8fc6-a7a4295c3273",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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372.065,714.944 374.086,727.944 376.107,740.646 378.128,753.051 380.149,765.155 382.17,776.961 384.191,788.468 386.212,799.678 388.234,810.594 390.255,821.219 392.276,831.556 394.297,841.61 396.318,851.385 398.339,860.886 400.36,870.118 402.381,879.087 404.402,887.799 406.424,896.259 408.445,904.473 410.466,912.448 412.487,920.189 414.508,927.703 416.529,934.995 418.55,942.072 420.571,948.94 422.592,955.604 424.614,962.071 426.635,968.347 428.656,974.436 430.677,980.344 432.698,986.078 434.719,991.642 436.74,997.041 438.761,1002.28 440.783,1007.37 442.804,1012.3 444.825,1017.09 446.846,1021.75 448.867,1026.26 450.888,1030.65 452.909,1034.91 454.93,1039.04 456.951,1043.06 458.973,1046.97 460.994,1050.77 463.015,1054.46 465.036,1058.05 467.057,1061.54 469.078,1064.94 471.099,1068.26 473.12,1071.48 475.141,1074.62 477.163,1077.69 479.184,1080.67 481.205,1083.59 483.226,1086.44 485.247,1089.22 487.268,1091.94 489.289,1094.6 491.31,1097.21 493.331,1099.77 495.353,1102.27 497.374,1104.73 499.395,1107.15 501.416,1109.52 503.437,1111.86 505.458,1114.16 507.479,1116.43 509.5,1118.67 511.521,1120.88 513.543,1123.07 515.564,1125.23 517.585,1127.37 519.606,1129.5 521.627,1131.61 523.648,1133.7 525.669,1135.78 527.69,1137.85 529.712,1139.91 531.733,1141.97 533.754,1144.02 535.775,1146.07 537.796,1148.12 539.817,1150.17 541.838,1152.21 543.859,1154.27 545.88,1156.32 547.902,1158.38 549.923,1160.45 551.944,1162.53 553.965,1164.61 555.986,1166.71 558.007,1168.82 560.028,1170.94 562.049,1173.07 564.07,1175.22 566.092,1177.38 568.113,1179.55 570.134,1181.75 572.155,1183.96 574.176,1186.19 576.197,1188.43 578.218,1190.7 580.239,1192.98 582.26,1195.29 584.282,1197.61 586.303,1199.96 588.324,1202.32 590.345,1204.71 592.366,1207.12 594.387,1209.55 596.408,1212 598.429,1214.47 600.45,1216.96 602.472,1219.48 604.493,1222.02 606.514,1224.57 608.535,1227.15 610.556,1229.76 612.577,1232.38 614.598,1235.02 616.619,1237.68 618.641,1240.36 620.662,1243.06 622.683,1245.79 624.704,1248.52 626.725,1251.28 628.746,1254.06 630.767,1256.85 632.788,1259.65 634.809,1262.47 636.831,1265.31 638.852,1268.16 640.873,1271.02 642.894,1273.89 644.915,1276.78 646.936,1279.67 648.957,1282.57 650.978,1285.48 652.999,1288.39 655.021,1291.3 657.042,1294.22 659.063,1297.14 661.084,1300.05 663.105,1302.97 665.126,1305.87 667.147,1308.78 669.168,1311.67 671.189,1314.55 673.211,1317.42 675.232,1320.27 677.253,1323.11 679.274,1325.92 681.295,1328.71 683.316,1331.48 685.337,1334.22 687.358,1336.93 689.379,1339.6 691.401,1342.23 693.422,1344.83 695.443,1347.38 697.464,1349.88 699.485,1352.33 701.506,1354.73 703.527,1357.07 705.548,1359.35 707.57,1361.56 709.591,1363.71 711.612,1365.78 713.633,1367.77 715.654,1369.68 717.675,1371.51 719.696,1373.24 721.717,1374.89 723.738,1376.43 725.76,1377.87 727.781,1379.21 729.802,1380.43 731.823,1381.54 733.844,1382.53 735.865,1383.4 737.886,1384.14 739.907,1384.75 741.928,1385.22 743.95,1385.56 745.971,1385.75 747.992,1385.8 750.013,1385.7 752.034,1385.45 754.055,1385.05 756.076,1384.49 758.097,1383.77 760.118,1382.89 762.14,1381.85 764.161,1380.65 766.182,1379.28 768.203,1377.75 770.224,1376.05 772.245,1374.19 774.266,1372.17 776.287,1369.98 778.308,1367.64 780.33,1365.13 782.351,1362.47 784.372,1359.65 786.393,1356.68 788.414,1353.56 790.435,1350.29 792.456,1346.88 794.477,1343.34 796.498,1339.66 798.52,1335.85 800.541,1331.92 802.562,1327.87 804.583,1323.7 806.604,1319.43 808.625,1315.05 810.646,1310.57 812.667,1306 814.689,1301.34 816.71,1296.6 818.731,1291.78 820.752,1286.88 822.773,1281.92 824.794,1276.9 826.815,1271.81 828.836,1266.67 830.857,1261.48 832.879,1256.25 834.9,1250.98 836.921,1245.67 838.942,1240.32 840.963,1234.95 842.984,1229.55 845.005,1224.14 847.026,1218.7 849.047,1213.26 851.069,1207.8 853.09,1202.35 855.111,1196.89 857.132,1191.43 859.153,1185.99 861.174,1180.55 863.195,1175.13 865.216,1169.74 867.237,1164.37 869.259,1159.03 871.28,1153.73 873.301,1148.47 875.322,1143.25 877.343,1138.08 879.364,1132.97 881.385,1127.92 883.406,1122.93 885.427,1118.01 887.449,1113.17 889.47,1108.4 891.491,1103.72 893.512,1099.13 895.533,1094.62 897.554,1090.21 899.575,1085.91 901.596,1081.7 903.618,1077.6 905.639,1073.61 907.66,1069.73 909.681,1065.96 911.702,1062.31 913.723,1058.78 915.744,1055.37 917.765,1052.09 919.786,1048.92 921.808,1045.89 923.829,1042.97 925.85,1040.19 927.871,1037.53 929.892,1035 931.913,1032.59 933.934,1030.31 935.955,1028.16 937.976,1026.13 939.998,1024.22 942.019,1022.44 944.04,1020.78 946.061,1019.24 948.082,1017.82 950.103,1016.52 952.124,1015.34 954.145,1014.26 956.166,1013.3 958.188,1012.45 960.209,1011.7 962.23,1011.06 964.251,1010.53 966.272,1010.09 968.293,1009.75 970.314,1009.51 972.335,1009.36 974.356,1009.3 976.378,1009.33 978.399,1009.44 980.42,1009.63 982.441,1009.91 984.462,1010.26 986.483,1010.69 988.504,1011.19 990.525,1011.76 992.547,1012.39 994.568,1013.09 996.589,1013.85 998.61,1014.67 1000.63,1015.54 1002.65,1016.47 1004.67,1017.45 1006.69,1018.48 1008.72,1019.56 1010.74,1020.68 1012.76,1021.84 1014.78,1023.04 1016.8,1024.28 1018.82,1025.56 1020.84,1026.86 1022.86,1028.2 1024.88,1029.57 1026.91,1030.96 1028.93,1032.38 1030.95,1033.82 1032.97,1035.28 1034.99,1036.76 1037.01,1038.25 1039.03,1039.77 1041.05,1041.29 1043.07,1042.83 1045.1,1044.38 1047.12,1045.94 1049.14,1047.5 1051.16,1049.07 1053.18,1050.65 1055.2,1052.22 1057.22,1053.8 1059.24,1055.38 1061.26,1056.96 1063.29,1058.54 1065.31,1060.11 1067.33,1061.68 1069.35,1063.24 1071.37,1064.8 1073.39,1066.35 1075.41,1067.89 1077.43,1069.42 1079.45,1070.94 1081.48,1072.45 1083.5,1073.95 1085.52,1075.43 1087.54,1076.9 1089.56,1078.36 1091.58,1079.8 1093.6,1081.23 1095.62,1082.64 1097.64,1084.04 1099.67,1085.41 1101.69,1086.77 1103.71,1088.11 1105.73,1089.44 1107.75,1090.74 1109.77,1092.02 1111.79,1093.29 1113.81,1094.53 1115.83,1095.76 1117.86,1096.96 1119.88,1098.14 1121.9,1099.31 1123.92,1100.45 1125.94,1101.56 1127.96,1102.66 1129.98,1103.74 1132,1104.79 1134.02,1105.82 1136.05,1106.83 1138.07,1107.82 1140.09,1108.78 1142.11,1109.73 1144.13,1110.65 1146.15,1111.55 1148.17,1112.42 1150.19,1113.28 1152.21,1114.11 1154.24,1114.92 1156.26,1115.71 1158.28,1116.47 1160.3,1117.22 1162.32,1117.94 1164.34,1118.64 1166.36,1119.32 1168.38,1119.98 1170.4,1120.61 1172.43,1121.23 1174.45,1121.83 1176.47,1122.4 1178.49,1122.96 1180.51,1123.49 1182.53,1124 1184.55,1124.5 1186.57,1124.97 1188.59,1125.43 1190.62,1125.86 1192.64,1126.28 1194.66,1126.68 1196.68,1127.06 1198.7,1127.42 1200.72,1127.76 1202.74,1128.09 1204.76,1128.4 1206.78,1128.69 1208.81,1128.97 1210.83,1129.22 1212.85,1129.46 1214.87,1129.69 1216.89,1129.9 1218.91,1130.09 1220.93,1130.27 1222.95,1130.43 1224.97,1130.58 1227,1130.72 1229.02,1130.84 1231.04,1130.94 1233.06,1131.04 1235.08,1131.11 1237.1,1131.18 1239.12,1131.23 1241.14,1131.27 1243.16,1131.3 1245.19,1131.32 1247.21,1131.32 1249.23,1131.31 1251.25,1131.29 1253.27,1131.26 1255.29,1131.22 1257.31,1131.17 1259.33,1131.11 1261.35,1131.04 1263.38,1130.96 1265.4,1130.87 1267.42,1130.77 1269.44,1130.66 1271.46,1130.54 1273.48,1130.41 1275.5,1130.28 1277.52,1130.14 1279.54,1129.99 1281.57,1129.83 1283.59,1129.66 1285.61,1129.49 1287.63,1129.31 1289.65,1129.13 1291.67,1128.93 1293.69,1128.74 1295.71,1128.53 1297.73,1128.32 1299.76,1128.1 1301.78,1127.88 1303.8,1127.66 1305.82,1127.43 1307.84,1127.19 1309.86,1126.95 1311.88,1126.7 1313.9,1126.45 1315.92,1126.2 1317.95,1125.94 1319.97,1125.68 1321.99,1125.42 1324.01,1125.15 1326.03,1124.88 1328.05,1124.6 1330.07,1124.32 1332.09,1124.04 1334.11,1123.76 1336.14,1123.48 1338.16,1123.19 1340.18,1122.9 1342.2,1122.61 1344.22,1122.32 1346.24,1122.02 1348.26,1121.72 1350.28,1121.43 1352.3,1121.13 1354.33,1120.83 1356.35,1120.52 1358.37,1120.22 1360.39,1119.92 1362.41,1119.62 1364.43,1119.31 1366.45,1119.01 1368.47,1118.7 1370.49,1118.39 1372.52,1118.09 1374.54,1117.78 1376.56,1117.48 1378.58,1117.17 1380.6,1116.87 1382.62,1116.56 1384.64,1116.26 1386.66,1115.95 1388.68,1115.65 1390.71,1115.35 1392.73,1115.04 1394.75,1114.74 1396.77,1114.44 1398.79,1114.14 1400.81,1113.84 1402.83,1113.54 1404.85,1113.25 1406.87,1112.95 1408.9,1112.66 1410.92,1112.37 1412.94,1112.08 1414.96,1111.79 1416.98,1111.5 1419,1111.21 1421.02,1110.93 1423.04,1110.64 1425.06,1110.36 1427.09,1110.08 1429.11,1109.8 1431.13,1109.53 1433.15,1109.25 1435.17,1108.98 1437.19,1108.71 1439.21,1108.44 1441.23,1108.18 1443.25,1107.91 1445.28,1107.65 1447.3,1107.39 1449.32,1107.13 1451.34,1106.88 1453.36,1106.63 1455.38,1106.38 1457.4,1106.13 1459.42,1105.88 1461.44,1105.64 1463.47,1105.4 1465.49,1105.16 1467.51,1104.92 1469.53,1104.69 1471.55,1104.45 1473.57,1104.22 1475.59,1104 1477.61,1103.77 1479.63,1103.55 1481.66,1103.33 1483.68,1103.12 1485.7,1102.9 1487.72,1102.69 1489.74,1102.48 1491.76,1102.27 1493.78,1102.07 1495.8,1101.87 1497.82,1101.67 1499.85,1101.47 1501.87,1101.28 1503.89,1101.09 1505.91,1100.9 1507.93,1100.72 1509.95,1100.53 1511.97,1100.35 1513.99,1100.17 1516.01,1100 1518.04,1099.83 1520.06,1099.66 1522.08,1099.49 1524.1,1099.32 1526.12,1099.16 1528.14,1099 1530.16,1098.85 1532.18,1098.69 1534.2,1098.54 1536.23,1098.39 1538.25,1098.24 1540.27,1098.1 1542.29,1097.96 1544.31,1097.82 1546.33,1097.68 1548.35,1097.55 1550.37,1097.42 1552.39,1097.29 1554.42,1097.16 1556.44,1097.04 1558.46,1096.92 1560.48,1096.8 1562.5,1096.68 1564.52,1096.57 1566.54,1096.45 1568.56,1096.34 1570.58,1096.24 1572.61,1096.13 1574.63,1096.03 1576.65,1095.93 1578.67,1095.83 1580.69,1095.74 1582.71,1095.65 1584.73,1095.56 1586.75,1095.47 1588.77,1095.38 1590.8,1095.3 1592.82,1095.22 1594.84,1095.14 1596.86,1095.06 1598.88,1094.99 1600.9,1094.91 1602.92,1094.84 1604.94,1094.78 1606.97,1094.71 1608.99,1094.65 1611.01,1094.59 1613.03,1094.53 1615.05,1094.47 1617.07,1094.41 1619.09,1094.36 1621.11,1094.31 1623.13,1094.26 1625.16,1094.21 1627.18,1094.17 1629.2,1094.13 1631.22,1094.08 1633.24,1094.04 1635.26,1094.01 1637.28,1093.97 1639.3,1093.94 1641.32,1093.91 1643.35,1093.88 1645.37,1093.85 1647.39,1093.82 1649.41,1093.8 1651.43,1093.78 1653.45,1093.76 1655.47,1093.74 1657.49,1093.72 1659.51,1093.7 1661.54,1093.69 1663.56,1093.68 1665.58,1093.67 1667.6,1093.66 1669.62,1093.65 1671.64,1093.65 1673.66,1093.64 1675.68,1093.64 1677.7,1093.64 1679.73,1093.64 1681.75,1093.64 1683.77,1093.65 1685.79,1093.65 1687.81,1093.66 1689.83,1093.67 1691.85,1093.68 1693.87,1093.69 1695.89,1093.7 1697.92,1093.72 1699.94,1093.73 1701.96,1093.75 1703.98,1093.77 1706,1093.79 1708.02,1093.81 1710.04,1093.83 1712.06,1093.85 1714.08,1093.88 1716.11,1093.9 1718.13,1093.93 1720.15,1093.96 1722.17,1093.99 1724.19,1094.02 1726.21,1094.05 1728.23,1094.08 1730.25,1094.12 1732.27,1094.15 1734.3,1094.19 1736.32,1094.23 1738.34,1094.27 1740.36,1094.31 1742.38,1094.35 1744.4,1094.39 1746.42,1094.43 1748.44,1094.47 1750.46,1094.52 1752.49,1094.57 1754.51,1094.61 1756.53,1094.66 1758.55,1094.71 1760.57,1094.76 1762.59,1094.81 1764.61,1094.86 1766.63,1094.91 1768.65,1094.96 1770.68,1095.02 1772.7,1095.07 1774.72,1095.13 1776.74,1095.19 1778.76,1095.24 1780.78,1095.3 1782.8,1095.36 1784.82,1095.42 1786.84,1095.48 1788.87,1095.54 1790.89,1095.6 1792.91,1095.66 1794.93,1095.73 1796.95,1095.79 1798.97,1095.86 1800.99,1095.92 1803.01,1095.99 1805.03,1096.05 1807.06,1096.12 1809.08,1096.19 1811.1,1096.25 1813.12,1096.32 1815.14,1096.39 1817.16,1096.46 1819.18,1096.53 1821.2,1096.6 1823.22,1096.67 1825.25,1096.75 1827.27,1096.82 1829.29,1096.89 1831.31,1096.96 1833.33,1097.04 1835.35,1097.11 1837.37,1097.19 1839.39,1097.26 1841.41,1097.34 1843.44,1097.41 1845.46,1097.49 1847.48,1097.57 1849.5,1097.64 1851.52,1097.72 1853.54,1097.8 1855.56,1097.87 1857.58,1097.95 1859.6,1098.03 1861.63,1098.11 1863.65,1098.19 1865.67,1098.27 1867.69,1098.35 1869.71,1098.43 1871.73,1098.51 1873.75,1098.59 1875.77,1098.67 1877.79,1098.75 1879.82,1098.83 1881.84,1098.91 1883.86,1099 1885.88,1099.08 1887.9,1099.16 1889.92,1099.24 1891.94,1099.32 1893.96,1099.41 1895.98,1099.49 1898.01,1099.57 1900.03,1099.65 1902.05,1099.74 1904.07,1099.82 1906.09,1099.9 1908.11,1099.99 1910.13,1100.07 1912.15,1100.15 1914.17,1100.24 1916.2,1100.32 1918.22,1100.4 1920.24,1100.49 1922.26,1100.57 1924.28,1100.66 1926.3,1100.74 1928.32,1100.82 1930.34,1100.91 1932.36,1100.99 1934.39,1101.07 1936.41,1101.16 1938.43,1101.24 1940.45,1101.33 1942.47,1101.41 1944.49,1101.49 1946.51,1101.58 1948.53,1101.66 1950.55,1101.74 1952.58,1101.83 1954.6,1101.91 1956.62,1101.99 1958.64,1102.08 1960.66,1102.16 1962.68,1102.24 1964.7,1102.33 1966.72,1102.41 1968.74,1102.49 1970.77,1102.57 1972.79,1102.66 1974.81,1102.74 1976.83,1102.82 1978.85,1102.9 1980.87,1102.98 1982.89,1103.07 1984.91,1103.15 1986.93,1103.23 1988.96,1103.31 1990.98,1103.39 1993,1103.47 1995.02,1103.55 1997.04,1103.63 1999.06,1103.71 2001.08,1103.79 2003.1,1103.87 2005.12,1103.95 2007.15,1104.03 2009.17,1104.11 2011.19,1104.19 2013.21,1104.27 2015.23,1104.35 2017.25,1104.43 2019.27,1104.5 2021.29,1104.58 2023.31,1104.66 2025.34,1104.74 2027.36,1104.81 2029.38,1104.89 2031.4,1104.97 2033.42,1105.04 2035.44,1105.12 2037.46,1105.19 2039.48,1105.27 2041.5,1105.34 2043.53,1105.42 2045.55,1105.49 2047.57,1105.57 2049.59,1105.64 2051.61,1105.71 2053.63,1105.79 2055.65,1105.86 2057.67,1105.93 2059.69,1106 2061.72,1106.07 2063.74,1106.15 2065.76,1106.22 2067.78,1106.29 2069.8,1106.36 2071.82,1106.43 2073.84,1106.5 2075.86,1106.57 2077.88,1106.64 2079.91,1106.7 2081.93,1106.77 2083.95,1106.84 2085.97,1106.91 2087.99,1106.97 2090.01,1107.04 2092.03,1107.11 2094.05,1107.17 2096.07,1107.24 2098.1,1107.3 2100.12,1107.37 2102.14,1107.43 2104.16,1107.5 2106.18,1107.56 2108.2,1107.62 2110.22,1107.69 2112.24,1107.75 2114.26,1107.81 2116.29,1107.87 2118.31,1107.93 2120.33,1107.99 2122.35,1108.05 2124.37,1108.11 2126.39,1108.17 2128.41,1108.23 2130.43,1108.29 2132.45,1108.35 2134.48,1108.41 2136.5,1108.46 2138.52,1108.52 2140.54,1108.58 2142.56,1108.63 2144.58,1108.69 2146.6,1108.74 2148.62,1108.8 2150.64,1108.85 2152.67,1108.91 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      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Plotting the results of transient speed.\n",
    "using Plots\n",
    "plot(u_predict[2,:], ls = :solid, lw = 3, label= \"Symbolic NN\", lc = :red)\n",
    "plot!(sol[:,2],ls = :dash, lw = 5, label = \"Classical ODE\", lc = :blue)\n",
    "title!(\"Transient speed\")\n",
    "xlabel!(\"t\")\n",
    "ylabel!(\"\\$ \\\\omega - \\\\omega_s \\$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1914e1be-54f1-4154-8da9-84859652257a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Plotting the results of rotor angle.\n",
    "plot(u_predict[1,:], ls = :solid, lw = 3, label= \"Conventional NN\", lc = :red)\n",
    "plot!(sol[:,1],ls = :dash, lw = 5, label = \"Classical ODE\", lc = :blue)\n",
    "title!(\"Rotor angle\")\n",
    "xlabel!(\"t\")\n",
    "ylabel!(\"\\$ \\\\delta \\$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "99d884bf-213e-4192-9f47-e4d72e28f918",
   "metadata": {},
   "outputs": [],
   "source": [
    "using DataFrames\n",
    "using CSV\n",
    "df = DataFrame(delta_NN = sol_NN[1,:], omega_NN = sol_NN[2,:], delta_ODE = sol[:,1], omega_ODE=sol[:,2]) #delta = -1, transient = 7\n",
    "CSV.write(\"filename.csv\", df; append = false) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fe2c6744-1fd7-4f40-948a-8e68ad951e5b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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