1 00:00:00,820 --> 00:00:07,450 Okay, so now what we need to do is to write the training function. 2 00:00:07,450 --> 00:00:13,390 So we start by Def Train Self. 3 00:00:14,140 --> 00:00:15,880 And then self. 4 00:00:15,880 --> 00:00:18,490 And of course the model is quite big. 5 00:00:18,520 --> 00:00:22,120 Or we we wrote a lot of code without actually running. 6 00:00:22,120 --> 00:00:25,750 So most likely we'll have some trouble. 7 00:00:27,440 --> 00:00:28,670 Or like debugging. 8 00:00:29,370 --> 00:00:36,180 So first one is to train the model and for I in range. 9 00:00:37,840 --> 00:00:40,480 Range 1000. 10 00:00:40,720 --> 00:00:43,810 We will do the Adam selfie. 11 00:00:43,960 --> 00:00:44,680 Adam. 12 00:00:45,800 --> 00:00:47,030 Step. 13 00:00:48,250 --> 00:00:51,100 Self dot loss. 14 00:00:52,060 --> 00:00:53,110 Function. 15 00:00:55,180 --> 00:00:57,280 Uh, loss function. 16 00:01:00,250 --> 00:01:05,650 And after that we will self dot. 17 00:01:06,980 --> 00:01:09,380 Basically optimizer. 18 00:01:15,610 --> 00:01:17,230 Dot step. 19 00:01:18,170 --> 00:01:20,630 And actually, this guy will do his own. 20 00:01:21,550 --> 00:01:22,570 The iteration. 21 00:01:23,830 --> 00:01:25,540 But we have to also. 22 00:01:26,360 --> 00:01:30,050 Thus the loss, which is always important. 23 00:01:30,860 --> 00:01:32,270 And then death. 24 00:01:33,580 --> 00:01:37,090 Evaluation eval uation. 25 00:01:38,850 --> 00:01:39,990 Self. 26 00:01:41,860 --> 00:01:43,440 And just a little. 27 00:01:45,320 --> 00:01:49,430 Self-taught mode eval. 28 00:01:52,350 --> 00:01:53,340 And. 29 00:01:54,200 --> 00:01:55,340 That's it. 30 00:01:56,000 --> 00:02:02,690 It seems fast, but of course, actually I didn't put. 31 00:02:05,650 --> 00:02:06,700 And it's just. 32 00:02:08,510 --> 00:02:09,500 Myself. 33 00:02:10,660 --> 00:02:14,380 We didn't put the model declared the model. 34 00:02:15,250 --> 00:02:16,510 Model equals. 35 00:02:16,540 --> 00:02:17,630 Neural network. 36 00:02:17,650 --> 00:02:18,310 This. 37 00:02:19,160 --> 00:02:20,000 Neural network. 38 00:02:20,000 --> 00:02:21,260 We didn't put it here. 39 00:02:24,490 --> 00:02:25,540 To device. 40 00:02:26,760 --> 00:02:27,870 Yeah, this is. 41 00:02:27,870 --> 00:02:29,880 We should put it just. 42 00:02:30,900 --> 00:02:31,300 Okay. 43 00:02:31,350 --> 00:02:33,050 Seems good. 44 00:02:33,060 --> 00:02:34,200 This one. 45 00:02:35,490 --> 00:02:38,430 This one, I change its location. 46 00:02:42,830 --> 00:02:43,580 And here. 47 00:02:49,410 --> 00:02:49,950 Okay. 48 00:02:49,950 --> 00:02:55,650 Now the moment of truth will be actual train. 49 00:02:57,030 --> 00:03:00,000 Three training. 50 00:03:01,210 --> 00:03:02,830 Net equals. 51 00:03:02,860 --> 00:03:03,760 Net. 52 00:03:06,100 --> 00:03:09,160 Basically the whole this. 53 00:03:10,680 --> 00:03:13,440 And train. 54 00:03:15,410 --> 00:03:18,320 Knit dot train. 55 00:03:19,910 --> 00:03:22,940 And shift enter and 56 00:03:24,890 --> 00:03:26,450 47. 57 00:03:29,730 --> 00:03:30,800 Let's just. 58 00:03:32,340 --> 00:03:33,420 Syntax. 59 00:03:36,390 --> 00:03:40,200 A trained self optimizer loss function. 60 00:03:41,910 --> 00:03:42,680 It. 61 00:03:42,750 --> 00:03:43,910 Adam, Step. 62 00:03:46,590 --> 00:03:48,990 97. 63 00:03:53,710 --> 00:03:55,060 Adam step. 64 00:03:56,620 --> 00:03:59,740 This seems no problem. 65 00:04:03,350 --> 00:04:05,810 We go to the Adam part? 66 00:04:17,740 --> 00:04:19,000 Torch Optim. 67 00:04:20,580 --> 00:04:21,180 Adam. 68 00:04:30,290 --> 00:04:31,220 Okay. 69 00:04:41,520 --> 00:04:42,780 The Los. 70 00:04:44,470 --> 00:04:45,850 Modules are. 71 00:04:47,950 --> 00:04:49,450 Autograd. 72 00:04:49,480 --> 00:04:51,910 Not autograd gradient. 73 00:04:51,940 --> 00:04:52,990 Not grad. 74 00:04:53,860 --> 00:04:54,670 So. 75 00:04:56,390 --> 00:04:56,710 To. 76 00:04:59,190 --> 00:05:03,840 Grant just means we have another one because we could best it. 77 00:05:04,900 --> 00:05:07,000 The execs here. 78 00:05:07,000 --> 00:05:07,960 Also two grand. 79 00:05:07,980 --> 00:05:08,800 Total grand. 80 00:05:09,810 --> 00:05:10,770 Okay. 81 00:05:16,650 --> 00:05:18,380 Well, let's run it again. 82 00:05:18,390 --> 00:05:19,290 All of it. 83 00:05:27,130 --> 00:05:29,560 The first one is. 84 00:05:31,450 --> 00:05:36,700 The grad location, this auto grad, which is. 85 00:05:39,160 --> 00:05:39,540 Um. 86 00:05:39,940 --> 00:05:42,840 Do we already have this size? 87 00:05:42,850 --> 00:05:46,870 And this one's like, is different size. 88 00:05:46,870 --> 00:05:52,240 So we have to put it here and like this and this should match, so. 89 00:05:53,810 --> 00:05:57,010 Uh, we also have the error. 90 00:06:19,950 --> 00:06:22,230 And we have also. 91 00:06:23,290 --> 00:06:26,890 This size is not matching, so it's better. 92 00:06:27,880 --> 00:06:28,900 Move. 93 00:06:31,790 --> 00:06:34,100 We said we move this one here. 94 00:06:34,250 --> 00:06:36,040 We just keep it as is. 95 00:06:36,050 --> 00:06:39,710 So this side of the equation should be equal this side of the equation. 96 00:06:39,770 --> 00:06:40,800 It's, um. 97 00:06:41,180 --> 00:06:41,690 It's. 98 00:06:41,690 --> 00:06:48,500 This is better because this have as a tensor it will have a different size than the other one. 99 00:06:48,500 --> 00:06:52,040 So it's better to this one rather than minus. 100 00:06:52,040 --> 00:06:57,170 We just separate it like this and remove this zero. 101 00:06:59,140 --> 00:07:01,090 And this one just. 102 00:07:07,460 --> 00:07:09,050 Another issue here. 103 00:07:09,050 --> 00:07:13,160 I found that it's quite strange, actually. 104 00:07:13,160 --> 00:07:18,050 Here we have when we declare. 105 00:07:26,370 --> 00:07:26,970 The. 106 00:07:31,070 --> 00:07:33,980 And here at. 107 00:07:35,050 --> 00:07:38,350 This one has to be u X, not x train. 108 00:07:38,350 --> 00:07:40,180 So line 56. 109 00:07:41,130 --> 00:07:42,630 Line 56. 110 00:07:42,660 --> 00:07:44,940 It's strange that we use Xtrain. 111 00:07:44,950 --> 00:07:46,500 It's actually the whole domain. 112 00:07:46,500 --> 00:07:49,920 We need the you the value of U for the whole domain. 113 00:07:49,920 --> 00:07:53,460 So this is why it should be X, I think. 114 00:07:53,700 --> 00:07:55,920 I think now it will run. 115 00:07:57,780 --> 00:08:00,660 So just run it again. 116 00:08:07,720 --> 00:08:12,850 Yeah, now it's running and it will take some not so much time. 117 00:08:13,240 --> 00:08:20,110 And basically it's a lot of moving parts, a lot of coding. 118 00:08:20,650 --> 00:08:25,260 We have to be careful just as it runs. 119 00:08:25,270 --> 00:08:27,730 I will just summarize what we did so far. 120 00:08:27,760 --> 00:08:33,370 It's basically we have imported the libraries, we have defined the network. 121 00:08:33,370 --> 00:08:38,230 After that, we set here the model to be a neural network. 122 00:08:38,230 --> 00:08:39,940 This is what we forgot before. 123 00:08:40,510 --> 00:08:49,540 And the first thing is here we after the setting the model, we start computing the we start creating 124 00:08:49,540 --> 00:08:58,150 the domain to actually create the data and define the initial condition and the boundary condition we 125 00:08:58,180 --> 00:08:58,930 set. 126 00:09:00,130 --> 00:09:06,030 The initial condition and boundary condition as we wish, which is in boundary condition, is zeros. 127 00:09:06,130 --> 00:09:10,060 And the initial condition is a sine wave. 128 00:09:11,100 --> 00:09:11,970 Uh, this is the. 129 00:09:11,970 --> 00:09:13,620 The values of all of this. 130 00:09:13,950 --> 00:09:20,520 We later after that, we define the optimizer functions, and then we define the method to calculate 131 00:09:20,520 --> 00:09:21,040 the loss. 132 00:09:21,060 --> 00:09:29,680 The loss means, uh, like when we have two, the two components we need to use the mean squared error. 133 00:09:29,700 --> 00:09:33,810 Now, the type of loss we need to calculate is basically. 134 00:09:34,870 --> 00:09:42,070 And the data loss, which we need to create a data, which is why predict and the loss of data is simply 135 00:09:42,070 --> 00:09:46,660 the difference between y predicted and Y train. 136 00:09:48,300 --> 00:10:01,380 And then we will calculate you and the X and the D and d, u d, t, and the second derivative of x 137 00:10:01,380 --> 00:10:03,960 with a with u. 138 00:10:03,960 --> 00:10:04,800 With x. 139 00:10:04,830 --> 00:10:12,330 All this has to be calculated in order to put into a loss, which is simply the whole equation. 140 00:10:12,330 --> 00:10:20,670 And here is this part D dt plus Udu has to equal this part. 141 00:10:22,640 --> 00:10:24,920 We can move it to this area here. 142 00:10:24,920 --> 00:10:33,860 But if we want to do that, we have to make sure that this side has the same tensor size as all of these 143 00:10:33,860 --> 00:10:34,190 data. 144 00:10:34,190 --> 00:10:42,740 So to avoid this, just keep the equation as is and put the right side to be this way. 145 00:10:42,860 --> 00:10:45,170 And then this is the loss. 146 00:10:45,740 --> 00:10:49,580 We calculate the whole loss based on that. 147 00:10:49,580 --> 00:10:59,030 And with that we already finished and the actual convergence has been achieved. 148 00:11:00,530 --> 00:11:09,200 A one thing I didn't note is basically this one why we put the zero and we just now test it here. 149 00:11:10,040 --> 00:11:11,630 Here and here. 150 00:11:13,710 --> 00:11:21,120 And just let's remove the zero and see how it looks without the zero and then how it looks with zero. 151 00:11:21,120 --> 00:11:24,210 So we shift enter and we run it. 152 00:11:24,300 --> 00:11:28,260 Of course it will blow up because it's simply. 153 00:11:30,470 --> 00:11:31,400 And not. 154 00:11:34,190 --> 00:11:39,440 Yeah, it's not the size is not compatible, but you can see here. 155 00:11:44,130 --> 00:11:51,300 That the tensor here will will be into a tuple and we don't want that. 156 00:11:51,300 --> 00:11:53,720 So we need to take this one out. 157 00:11:53,730 --> 00:12:02,700 And once we put this zero, the tensor here, we don't have this, um, this parentheses thing here. 158 00:12:02,700 --> 00:12:05,550 So this is why we put zero.