1 00:00:00,500 --> 00:00:11,750 Now what we are going to do is to start the the major well class in which we will define the. 2 00:00:12,530 --> 00:00:18,170 Data even defined the loss, the loss method and even the function. 3 00:00:18,290 --> 00:00:24,170 But for now, what we need to do is start this class that will have everything. 4 00:00:24,170 --> 00:00:30,770 But what we will do is we will explain how to input the data. 5 00:00:30,770 --> 00:00:39,050 So we need to input the data, which is basically our the data is our boundary condition and the initial 6 00:00:39,050 --> 00:00:39,470 condition. 7 00:00:39,470 --> 00:00:45,380 So here we, I will start with class. 8 00:00:46,090 --> 00:00:49,180 And the class is called Net. 9 00:00:49,570 --> 00:00:58,150 And we first define the initial condition and it will have a self, self, self. 10 00:00:59,250 --> 00:01:00,690 And device. 11 00:01:01,400 --> 00:01:02,420 Will be. 12 00:01:05,280 --> 00:01:10,830 Torch dot device and the device will be cuda. 13 00:01:11,550 --> 00:01:13,530 Of course, if cuda exist. 14 00:01:13,650 --> 00:01:15,390 If torch. 15 00:01:17,000 --> 00:01:18,020 Dot cuda. 16 00:01:19,960 --> 00:01:20,950 Is. 17 00:01:22,440 --> 00:01:22,670 Uh. 18 00:01:24,160 --> 00:01:25,030 Valuable. 19 00:01:26,340 --> 00:01:27,060 Else. 20 00:01:28,460 --> 00:01:29,270 Well. 21 00:01:32,220 --> 00:01:36,870 And torch device will be. 22 00:01:40,070 --> 00:01:40,610 Sibiu. 23 00:01:43,540 --> 00:01:45,460 This is very common, of course. 24 00:01:45,460 --> 00:01:47,890 And with that. 25 00:01:51,050 --> 00:01:52,430 And divisive. 26 00:01:52,820 --> 00:01:53,470 Sorry. 27 00:01:57,400 --> 00:02:01,810 Here we basically define the computational. 28 00:02:04,290 --> 00:02:09,810 Network or the computational necessary Internet network, the device we need to calculate. 29 00:02:10,140 --> 00:02:14,070 Either it's going to be the GPU or it's going to be the CPU. 30 00:02:14,070 --> 00:02:21,510 In my case, I have a well GPU and I have everything is set up regarding cuda, so I will use GPU. 31 00:02:21,630 --> 00:02:24,240 But of course you can use CPU as well. 32 00:02:24,900 --> 00:02:26,700 And this model is not so big. 33 00:02:26,700 --> 00:02:32,700 And of course, our model, our our also network is not so not the network is not big. 34 00:02:32,700 --> 00:02:37,140 The actual problem, the points we need to calculate is also not so big. 35 00:02:37,140 --> 00:02:46,560 So I would say it will be like no problem regarding the use of cuda so you can use it. 36 00:02:46,560 --> 00:02:47,470 The cpu. 37 00:02:47,490 --> 00:02:48,870 So here self. 38 00:02:49,560 --> 00:02:51,720 We start by defining. 39 00:02:51,930 --> 00:02:53,580 Well, basically the. 40 00:02:55,330 --> 00:02:57,250 The computational domain. 41 00:02:57,400 --> 00:03:05,170 So we have X, which is we will have starting with a wave. 42 00:03:05,200 --> 00:03:09,790 So after this x, what we will do is we will. 43 00:03:11,960 --> 00:03:21,500 Basically from X, we have to also define the temperature, the time, and based on that, we will calculate 44 00:03:21,500 --> 00:03:27,260 the other like we will fill the U. 45 00:03:27,260 --> 00:03:29,030 That will be calculated. 46 00:03:29,030 --> 00:03:31,940 So first let's define something like mesh. 47 00:03:31,940 --> 00:03:36,560 Although the neural networks, we don't really need mesh. 48 00:03:36,640 --> 00:03:45,140 It's not the way the way we do this computation is not similar to our traditional way, so it's kind 49 00:03:45,140 --> 00:03:45,710 of meshless. 50 00:03:45,710 --> 00:03:53,060 But while computing using mesh is kind of easy to define, so we will do it. 51 00:03:53,270 --> 00:03:59,960 So here self H equals 0.1, which is the step size of. 52 00:04:02,440 --> 00:04:09,730 The step size of of x and K is the step size of t x equals. 53 00:04:10,440 --> 00:04:11,490 Torch. 54 00:04:12,310 --> 00:04:14,680 Dot range. 55 00:04:16,390 --> 00:04:21,520 From -1 to 1 plus self dot. 56 00:04:24,530 --> 00:04:27,160 And step size is self dot etch. 57 00:04:27,170 --> 00:04:32,120 We do the same but this time with t so t. 58 00:04:35,120 --> 00:04:36,140 And self-worth came. 59 00:04:37,310 --> 00:04:38,850 And self taught care. 60 00:04:39,750 --> 00:04:42,450 So how this things work? 61 00:04:42,450 --> 00:04:49,080 Well, first, let's let's define also the whole grid and here self dot x. 62 00:04:50,340 --> 00:04:53,340 Equals torch dot. 63 00:04:54,630 --> 00:04:55,650 Stack. 64 00:04:57,030 --> 00:04:57,930 Torch. 65 00:04:58,680 --> 00:04:59,270 Dot. 66 00:05:01,130 --> 00:05:02,630 Meshgrid. 67 00:05:03,850 --> 00:05:05,590 X and T. 68 00:05:05,920 --> 00:05:08,260 This has to be reshaped. 69 00:05:08,620 --> 00:05:09,820 Reshape. 70 00:05:10,650 --> 00:05:15,630 Two and minus one and it will be transposed. 71 00:05:16,670 --> 00:05:17,720 What does it mean? 72 00:05:17,840 --> 00:05:21,500 Let's let's let's start doing all of this. 73 00:05:21,920 --> 00:05:28,970 So basically, what we will do is let's consider it first these two. 74 00:05:37,080 --> 00:05:39,330 Or maybe this one is not needed. 75 00:05:39,360 --> 00:05:46,320 So x underscore test and T underscore. 76 00:05:47,290 --> 00:05:48,100 And test. 77 00:05:48,640 --> 00:05:50,650 And we want to print. 78 00:05:52,050 --> 00:05:53,310 And exist. 79 00:05:53,550 --> 00:05:54,990 And, of course. 80 00:05:55,950 --> 00:05:57,420 Print test. 81 00:05:59,250 --> 00:06:01,140 And see how these things change. 82 00:06:01,140 --> 00:06:04,200 So here we consider 0.1. 83 00:06:04,880 --> 00:06:06,020 And then here. 84 00:06:06,050 --> 00:06:07,130 0.1. 85 00:06:09,620 --> 00:06:10,340 And one. 86 00:06:11,640 --> 00:06:13,650 SIM goes here. 87 00:06:15,650 --> 00:06:20,870 With actually we have the time cannot be negative, so it has to be zero. 88 00:06:22,090 --> 00:06:22,720 This has to be. 89 00:06:24,870 --> 00:06:27,420 So this is how it works. 90 00:06:27,450 --> 00:06:37,530 You have the the torch that will is going to be from a -1 to 1 with a step size of 0.1. 91 00:06:37,530 --> 00:06:46,650 So we start from minus one and then minus well, minus 0.9 and then minus 0.8 and minus 0.7 and so on 92 00:06:46,650 --> 00:06:49,860 until it gets to a zero. 93 00:06:49,890 --> 00:06:51,420 This one is actually zero. 94 00:06:51,420 --> 00:06:56,490 And then it will be 10.1 until it will reach one. 95 00:06:57,090 --> 00:07:05,490 The reason we did from minus one to add plus or 0.1, because in Python it will not consider the last 96 00:07:06,240 --> 00:07:07,140 value. 97 00:07:07,140 --> 00:07:16,500 So it's it's important to add just one, one one step to get this answer and here the we do the same 98 00:07:16,500 --> 00:07:20,010 and but this time it's from zero to actually one. 99 00:07:20,970 --> 00:07:26,370 Okay but we have still left this one and let's understand how it works. 100 00:07:26,370 --> 00:07:32,640 So we this one is basically will give us a map of the whole domain. 101 00:07:32,640 --> 00:07:34,890 So let's just remove self. 102 00:07:34,890 --> 00:07:36,270 So torch stack. 103 00:07:36,300 --> 00:07:39,240 Torch mesh grid mesh grid. 104 00:07:39,240 --> 00:07:40,580 What x? 105 00:07:41,750 --> 00:07:46,360 And T and then he would reshape it and transpose it. 106 00:07:46,370 --> 00:07:47,360 So. 107 00:07:47,630 --> 00:07:49,010 And let's print it. 108 00:07:51,720 --> 00:07:52,270 Printex. 109 00:07:54,470 --> 00:07:56,480 A mistake. 110 00:07:58,420 --> 00:07:58,950 Oh, sorry. 111 00:08:02,560 --> 00:08:02,920 This. 112 00:08:04,240 --> 00:08:13,750 So here we can see that this will yield to minus one the time of zero, minus one, the time of one 113 00:08:13,750 --> 00:08:16,000 minus one, the time of two. 114 00:08:16,030 --> 00:08:24,580 So it will make us a whole domain that what we need to solve, which is we need to solve X and T for 115 00:08:24,580 --> 00:08:27,250 U so the our mesh will look like this. 116 00:08:27,250 --> 00:08:31,000 Of course, it doesn't have to be a uniform mesh or whatever. 117 00:08:31,000 --> 00:08:32,920 Even we don't really need to use mesh. 118 00:08:32,920 --> 00:08:36,130 But of course using now mesh is kind of. 119 00:08:37,250 --> 00:08:44,330 Make our life simpler because it's easy to just uniformly compute the points. 120 00:08:44,750 --> 00:08:47,780 But of course, it's a neural network and you don't have to. 121 00:08:48,050 --> 00:08:51,140 We don't really care about real mesh. 122 00:08:51,470 --> 00:08:57,550 So here what we have is a basically the transpose. 123 00:08:57,560 --> 00:09:01,780 So let's, let's undo a little bit, understand how what's, what's happening. 124 00:09:01,790 --> 00:09:07,130 So for example, if we remove the transpose, what we will get is this way. 125 00:09:07,130 --> 00:09:17,540 So we will have this network which has to for like it will have two dimensions and this is not what 126 00:09:17,540 --> 00:09:20,090 we want, so we have to transpose it. 127 00:09:20,090 --> 00:09:28,190 So we will have here all of this X's and then again, the, the, the X's. 128 00:09:28,190 --> 00:09:31,850 So this is not what what actually we want. 129 00:09:31,850 --> 00:09:41,250 So what we will do or what we have to do is to transpose this from X and of course this is the first 130 00:09:41,250 --> 00:09:54,010 one is going to be the, the, the X points from -1 to 1 and the other one is going to be from 0 to 131 00:09:54,010 --> 00:09:55,740 1, which is the time. 132 00:09:55,980 --> 00:09:58,440 But we don't want that. 133 00:09:58,440 --> 00:10:07,410 So this is why when we put transpose, what will happen is we will actually have this like kind of, 134 00:10:07,950 --> 00:10:16,560 I would say, beautiful list or tensor that has this component and every component will correspond to 135 00:10:16,560 --> 00:10:18,480 X and T only. 136 00:10:19,290 --> 00:10:20,340 A mesh grid. 137 00:10:20,340 --> 00:10:25,290 Also, like if we want to see here, we can also see. 138 00:10:25,290 --> 00:10:32,100 It's always nice to play with these things, to just understand how like these things work. 139 00:10:32,100 --> 00:10:34,500 But let's just comment out this one. 140 00:10:42,100 --> 00:10:42,880 Maybe. 141 00:10:42,880 --> 00:10:43,450 Yeah. 142 00:10:43,690 --> 00:10:44,110 Okay. 143 00:10:44,110 --> 00:10:45,790 We can consider like this. 144 00:10:46,300 --> 00:10:56,380 So we will have X, we will have also the time and here we will have, of course, the Xs and Xs, and 145 00:10:56,560 --> 00:11:07,960 it will also give us a grid with the first one is the tensor of A of the X and the other one is tensor 146 00:11:07,960 --> 00:11:09,310 with the time. 147 00:11:09,310 --> 00:11:13,750 And then we have to reshape it or stack it. 148 00:11:13,780 --> 00:11:19,840 Basically these two tensor become one tensor and then reshape it and then transpose it. 149 00:11:19,840 --> 00:11:24,040 So this is what we did in all of this thing. 150 00:11:25,000 --> 00:11:31,810 Of course there are many ways to do it, but what we at the end of at the end of the day, we need. 151 00:11:32,610 --> 00:11:35,370 Something that looks like this. 152 00:11:35,400 --> 00:11:38,660 We need X and T. 153 00:11:39,760 --> 00:11:46,990 X for all the components of x and then T with all the time steps we have to take. 154 00:11:47,110 --> 00:11:48,460 It's very important. 155 00:11:50,590 --> 00:11:54,790 Okay, so now we did that. 156 00:11:54,820 --> 00:11:56,320 What we have to do now. 157 00:11:57,250 --> 00:12:05,500 We have to start with basically or like continue assigning the the data. 158 00:12:05,500 --> 00:12:10,660 So all of this is basically, well, I will say computation domain. 159 00:12:10,930 --> 00:12:11,650 Domain. 160 00:12:11,650 --> 00:12:20,470 But but of course, we don't really need, um, really, you know, like actual mesh because we're dealing 161 00:12:20,470 --> 00:12:24,340 with neural network and train data. 162 00:12:24,550 --> 00:12:27,580 Well, we start defining them. 163 00:12:27,700 --> 00:12:28,180 Basically. 164 00:12:28,180 --> 00:12:31,330 This is the most important topic now. 165 00:12:31,330 --> 00:12:33,520 They have two boundary condition. 166 00:12:33,520 --> 00:12:35,710 One boundary is a. 167 00:12:36,740 --> 00:12:44,000 That will the left part of the X and the other boundary is the right part of X. 168 00:12:44,000 --> 00:12:46,430 And and of course, we have initial conditions. 169 00:12:46,430 --> 00:12:52,880 The way it works in here, what will have this is not really okay. 170 00:12:52,880 --> 00:13:03,830 So what what we will have is basically we will have X equals zero and then we will have a line and then 171 00:13:03,830 --> 00:13:08,900 you will have X equals a no, sorry. 172 00:13:08,900 --> 00:13:09,650 It's minus one. 173 00:13:09,650 --> 00:13:11,240 I think -1 to 1. 174 00:13:11,270 --> 00:13:11,840 Yeah. 175 00:13:12,420 --> 00:13:19,860 And then you will have a start from zero and then you will have a function, a sine function. 176 00:13:20,250 --> 00:13:28,650 So it will change from -1 to 1 and the sine function will have this u values. 177 00:13:29,720 --> 00:13:32,900 And as the computation progress. 178 00:13:32,900 --> 00:13:35,450 So this is the initial condition. 179 00:13:35,450 --> 00:13:42,200 Maybe put it, let's use another color actually as the solution progress. 180 00:13:42,230 --> 00:13:46,340 It will give us a shape that looks like this. 181 00:13:47,090 --> 00:13:50,450 This is what this is the the general solution of this burgers. 182 00:13:50,480 --> 00:13:58,460 Of course, here t t equals something like, I don't know, like we have from 0 to 1. 183 00:13:58,460 --> 00:13:59,810 We said so let's say one. 184 00:14:00,260 --> 00:14:01,070 So. 185 00:14:01,930 --> 00:14:03,480 As a solution progress. 186 00:14:03,490 --> 00:14:10,120 It will a little bit diffuse and it will have this wave well behavior. 187 00:14:10,210 --> 00:14:14,710 So this is basic burgers equation and it's just very common. 188 00:14:14,710 --> 00:14:16,760 And but we need to get it with neural network. 189 00:14:16,780 --> 00:14:18,010 Of course, this solution. 190 00:14:19,430 --> 00:14:21,020 So let's define this. 191 00:14:21,050 --> 00:14:25,040 We have starting zero here and ending zero. 192 00:14:25,040 --> 00:14:29,390 And in between we need to assign a sign. 193 00:14:29,660 --> 00:14:36,230 We need to assign the initial condition to be sine like sine function. 194 00:14:36,650 --> 00:14:37,490 So. 195 00:14:38,580 --> 00:14:42,480 Boundary condition one is torch dot. 196 00:14:42,960 --> 00:14:44,700 Well, basically we will do the same. 197 00:14:44,700 --> 00:14:45,990 But anyway, let's write it. 198 00:14:45,990 --> 00:14:46,710 Let's write it. 199 00:14:46,740 --> 00:14:52,050 Dot stack, torch dot mesh grid. 200 00:14:53,120 --> 00:14:56,330 And here is X. 201 00:14:57,530 --> 00:15:00,440 Zero and T. 202 00:15:02,510 --> 00:15:02,750 Why? 203 00:15:02,750 --> 00:15:08,510 X0 because simply we we just interested in the the first component. 204 00:15:08,540 --> 00:15:10,160 This is boundary condition. 205 00:15:10,160 --> 00:15:14,990 So with time it has to remain the same boundary conditions. 206 00:15:15,020 --> 00:15:21,200 Of course we can change it if we want, but in this case what we our aim is the boundary condition will 207 00:15:21,200 --> 00:15:22,580 be zero all the way. 208 00:15:22,790 --> 00:15:26,420 So dot reshape. 209 00:15:27,280 --> 00:15:30,970 And this two minus one. 210 00:15:30,970 --> 00:15:31,840 Same shape. 211 00:15:31,990 --> 00:15:33,310 Same like. 212 00:15:33,310 --> 00:15:33,700 Same. 213 00:15:33,700 --> 00:15:34,300 Same. 214 00:15:36,120 --> 00:15:39,090 Same way of assigning this way. 215 00:15:40,290 --> 00:15:41,790 Boundary condition to. 216 00:15:43,060 --> 00:15:44,050 Same thing. 217 00:15:44,050 --> 00:15:48,400 But this one, what it has to be the last element. 218 00:15:48,400 --> 00:15:52,150 So minus one means it's of course it doesn't mean the value. 219 00:15:52,180 --> 00:15:56,320 It means the final element has to be this. 220 00:15:56,320 --> 00:16:04,570 So this this way is we're creating the tensor of the boundary condition if we want to see it. 221 00:16:04,570 --> 00:16:10,450 Just like quickly of like if we want, we can. 222 00:16:11,850 --> 00:16:12,720 Like, Of course. 223 00:16:12,720 --> 00:16:14,490 Here we already printed. 224 00:16:18,130 --> 00:16:20,310 Maybe this one just to make sure. 225 00:16:20,320 --> 00:16:21,100 Test. 226 00:16:21,830 --> 00:16:22,840 Test. 227 00:16:24,080 --> 00:16:24,910 Expressed. 228 00:16:27,500 --> 00:16:29,300 And print this thing. 229 00:16:34,330 --> 00:16:41,420 So we can see that the starting of this is minus one, minus one. 230 00:16:41,440 --> 00:16:50,410 And of course, the time progress, if we want the last one, the last element, we will just put here 231 00:16:50,410 --> 00:16:53,710 minus one and here minus one. 232 00:16:53,710 --> 00:16:59,290 And then you will get the last element and the evolution over the time. 233 00:17:00,600 --> 00:17:01,470 And that's it. 234 00:17:01,470 --> 00:17:04,200 So we continue. 235 00:17:07,910 --> 00:17:11,210 So now we have the boundary condition and. 236 00:17:11,970 --> 00:17:16,050 We we need also the initial condition with it's going to be. 237 00:17:16,990 --> 00:17:24,360 The same thing or the same concept, but we have to be careful about X. 238 00:17:25,610 --> 00:17:27,410 Is its initial condition. 239 00:17:27,410 --> 00:17:33,140 So all x but now the time will be only. 240 00:17:34,560 --> 00:17:38,760 Not the first The zero, which is the first time. 241 00:17:39,620 --> 00:17:40,310 And. 242 00:17:40,460 --> 00:17:42,680 Oh, and for all the excess. 243 00:17:44,320 --> 00:17:46,150 Okay, we're done. 244 00:17:47,270 --> 00:17:48,020 Not yet. 245 00:17:48,020 --> 00:17:49,370 Just a little bit more. 246 00:17:49,670 --> 00:17:55,190 So self dot x x train not. 247 00:17:55,310 --> 00:17:55,640 Yeah. 248 00:17:55,670 --> 00:17:57,860 X underscore train. 249 00:17:59,760 --> 00:18:07,620 Each train will equal torch dot concatenation for. 250 00:18:08,770 --> 00:18:10,380 BC1. 251 00:18:11,960 --> 00:18:13,310 BC2. 252 00:18:14,390 --> 00:18:16,910 And see which is the initial condition. 253 00:18:17,090 --> 00:18:19,370 This is what we defined. 254 00:18:19,400 --> 00:18:20,630 Only the x. 255 00:18:20,780 --> 00:18:26,900 These are the points that the boundary condition points and the initial condition points. 256 00:18:26,900 --> 00:18:31,460 What we need to consider now is the values of the Y. 257 00:18:31,700 --> 00:18:37,520 So y pc one equals sorry, not this way. 258 00:18:37,550 --> 00:18:43,910 Y underscore pc one equals torch dot. 259 00:18:45,160 --> 00:18:46,040 Zeros. 260 00:18:47,200 --> 00:18:49,090 Length of. 261 00:18:49,950 --> 00:18:50,690 A PC one. 262 00:18:51,740 --> 00:18:55,610 So we assign all the values of this to be. 263 00:18:56,550 --> 00:18:58,830 Basically zero or it is zero. 264 00:18:59,610 --> 00:19:01,370 We do the same too. 265 00:19:01,410 --> 00:19:02,880 We said it. 266 00:19:02,910 --> 00:19:04,770 It gets to zero. 267 00:19:05,790 --> 00:19:06,960 I'm not sure it's needed. 268 00:19:06,960 --> 00:19:14,910 But anyway, like, this way, you can see that from here all the way to here, it's always has to be 269 00:19:14,910 --> 00:19:15,450 zero. 270 00:19:15,660 --> 00:19:22,230 This one all the way to here, it's always has to zero and initial condition only the first part. 271 00:19:22,530 --> 00:19:29,190 So this is why we assign zero A, y, C equals. 272 00:19:30,350 --> 00:19:31,190 Torch. 273 00:19:31,220 --> 00:19:32,960 This one is a bit. 274 00:19:35,650 --> 00:19:37,810 A little bit harder, but. 275 00:19:40,140 --> 00:19:43,830 In this example, we need this start from positive. 276 00:19:43,830 --> 00:19:47,730 So let's say minus torch. 277 00:19:49,360 --> 00:19:50,180 Sign. 278 00:19:52,070 --> 00:19:53,030 Math. 279 00:19:54,110 --> 00:19:54,890 Dot pi. 280 00:19:56,350 --> 00:19:57,400 Multiplied. 281 00:19:57,430 --> 00:19:58,120 I see. 282 00:19:59,860 --> 00:20:00,640 But. 283 00:20:01,520 --> 00:20:01,960 I see. 284 00:20:01,970 --> 00:20:04,070 Of what only. 285 00:20:05,280 --> 00:20:07,790 Only the X elements. 286 00:20:07,800 --> 00:20:15,630 So we take the X elements, we take it from here, and then we multiply it with a Pi. 287 00:20:15,840 --> 00:20:26,700 This is actually useful because we said we took math though math pi dot c and we take the sine of the 288 00:20:26,700 --> 00:20:35,220 whole thing and we need minus just to well, draw this kind of starting from a positive. 289 00:20:35,430 --> 00:20:45,750 If you didn't put it it will maybe it will have a different um like picture rather than having the, 290 00:20:45,750 --> 00:20:49,140 the starting of sine like this, it will start like this. 291 00:20:49,140 --> 00:20:54,930 So anyway you have to put this, it's this y value. 292 00:20:55,680 --> 00:20:58,290 To measure the value you need. 293 00:20:58,590 --> 00:21:03,480 Okay, So after that, what we need to do, we need to self. 294 00:21:06,150 --> 00:21:07,270 Solve dot. 295 00:21:08,040 --> 00:21:13,470 Y train equals the same thing. 296 00:21:16,230 --> 00:21:16,970 For. 297 00:21:17,750 --> 00:21:20,250 Why boundary condition? 298 00:21:20,270 --> 00:21:25,820 One Why Boundary condition two and why the initial condition? 299 00:21:27,380 --> 00:21:33,980 And the only thing we need to do is I will explain it a little bit more elaborately. 300 00:21:34,760 --> 00:21:40,790 It is basically is we need to have unsqueeze and. 301 00:21:42,660 --> 00:21:43,800 Squeeze. 302 00:21:45,910 --> 00:21:46,840 With one. 303 00:21:47,990 --> 00:21:49,490 So unsqueezed. 304 00:21:49,520 --> 00:21:50,960 What does it mean? 305 00:21:50,960 --> 00:21:52,310 Why we need it? 306 00:21:52,790 --> 00:21:56,480 We need it because you need all of this. 307 00:21:56,480 --> 00:21:58,310 Let's remove these prints. 308 00:22:03,240 --> 00:22:04,470 And let's. 309 00:22:04,560 --> 00:22:07,590 Let's keep it like this, okay? 310 00:22:07,770 --> 00:22:09,690 So let's let's do unsqueeze. 311 00:22:09,690 --> 00:22:13,080 So let's consider why train this one? 312 00:22:13,260 --> 00:22:16,980 And we call it test equals torch. 313 00:22:17,010 --> 00:22:21,780 Just give it a tensor tensors and it will have. 314 00:22:22,640 --> 00:22:24,680 A one, two, three, four. 315 00:22:25,350 --> 00:22:28,050 So when let's print it. 316 00:22:28,050 --> 00:22:29,460 Print this thing. 317 00:22:29,460 --> 00:22:30,390 And then. 318 00:22:32,500 --> 00:22:33,850 Do the Unsqueeze. 319 00:22:33,850 --> 00:22:36,820 Which is this one. 320 00:22:42,710 --> 00:22:45,530 And see how it will change the dimension. 321 00:22:58,860 --> 00:23:02,490 So you will have what is printing. 322 00:23:04,070 --> 00:23:05,480 There is a print statement. 323 00:23:05,480 --> 00:23:06,220 I don't want it. 324 00:23:06,230 --> 00:23:06,920 Yeah, this one. 325 00:23:06,920 --> 00:23:07,820 Just some of it. 326 00:23:08,120 --> 00:23:14,270 So here what we will have is we will have a tensor that has a list or a vector. 327 00:23:14,870 --> 00:23:16,910 It will have one, two, three. 328 00:23:16,910 --> 00:23:18,410 And this is not what we want. 329 00:23:18,590 --> 00:23:28,370 We want the whole thing to have the dimension of everyone will be a list by itself because all these 330 00:23:28,370 --> 00:23:31,470 work or let's say here we can see the X. 331 00:23:33,750 --> 00:23:35,760 Will have this dimension. 332 00:23:35,760 --> 00:23:41,820 So every, um, every row will represent one data point. 333 00:23:42,590 --> 00:23:44,630 So we needed to match this one. 334 00:23:44,630 --> 00:23:49,130 So this is why we did basically the Unsqueeze thing. 335 00:23:49,710 --> 00:23:51,150 To be like this. 336 00:23:51,840 --> 00:23:59,910 Anyway, this all code is going to be only for testing or just to show how things are defined. 337 00:23:59,910 --> 00:24:03,690 And I will keep it, but I will just comment it out. 338 00:24:03,900 --> 00:24:04,800 So. 339 00:24:05,480 --> 00:24:06,590 By this time. 340 00:24:06,590 --> 00:24:09,380 We already have the data. 341 00:24:10,370 --> 00:24:11,480 We already have. 342 00:24:12,550 --> 00:24:19,720 The X data which is made from the boundary condition and made from the initial condition. 343 00:24:19,720 --> 00:24:26,380 And then we have the Y data, which is also defining the boundary condition and the initial condition. 344 00:24:26,380 --> 00:24:33,470 This is Y, this is where we initialize it and this is in the in the in the when we're dealing with 345 00:24:33,490 --> 00:24:35,850 neural network, it will consider the training data. 346 00:24:35,860 --> 00:24:42,610 Next, we have to assign the other things like we'll talk about losses and optimizer and so on.