1
00:00:01,970 --> 00:00:06,200
After the training is finished, which took the first one.

2
00:00:06,200 --> 00:00:10,430
It took about 445 seconds.

3
00:00:10,670 --> 00:00:13,330
And this is the Adam part.

4
00:00:13,340 --> 00:00:22,460
And the other part, which is the lpg's part, took 767 seconds.

5
00:00:22,460 --> 00:00:30,020
So total about 1200 seconds, which is kind of considerable.

6
00:00:30,620 --> 00:00:33,950
And so let's see the results.

7
00:00:33,950 --> 00:00:35,390
So to do that.

8
00:00:37,200 --> 00:00:38,880
We need to make a sample.

9
00:00:39,570 --> 00:00:42,120
Samples equals GM.

10
00:00:43,810 --> 00:00:44,410
But.

11
00:00:46,130 --> 00:00:47,140
Random.

12
00:00:48,300 --> 00:00:49,090
Points.

13
00:00:49,200 --> 00:00:50,250
Points.

14
00:00:50,550 --> 00:00:56,410
And we need a lot of points, of course, because it's neural network.

15
00:00:56,430 --> 00:01:00,180
It's it's quite easy to solve.

16
00:01:00,210 --> 00:01:02,790
It's not like a numerical situation.

17
00:01:02,790 --> 00:01:10,410
We, of course, everything is numerical, but in typical numerical solution, what we have to to always

18
00:01:10,410 --> 00:01:17,980
do or is we have the mesh and we have to calculate all these points, but in neural network, things

19
00:01:17,980 --> 00:01:19,260
are happening much faster.

20
00:01:20,090 --> 00:01:25,760
But of course, this neural network only works with the same initial or not initial.

21
00:01:25,760 --> 00:01:30,500
In this case, we don't have initial with the same boundary condition that we trained it.

22
00:01:30,530 --> 00:01:33,170
It only know this small boundary condition.

23
00:01:33,170 --> 00:01:41,690
If you want a network that can serve for a different, uh, well, values, you have to engineer or

24
00:01:41,690 --> 00:01:47,600
you have to build a different neural network that can that can take into consideration different factors.

25
00:01:47,600 --> 00:01:52,580
So this is why this is only showing you how to apply it.

26
00:01:52,580 --> 00:01:58,550
But in order to build a really good network, you need to consider a network that can take on different

27
00:01:58,550 --> 00:02:03,650
initial conditions, different boundary conditions, different size of domain.

28
00:02:04,780 --> 00:02:08,820
It's not easy to build a network that can solve everything fast.

29
00:02:08,830 --> 00:02:09,760
So.

30
00:02:10,970 --> 00:02:19,190
The good thing is after the model is trained, any future solutions is much faster than using usual

31
00:02:19,190 --> 00:02:19,850
methods.

32
00:02:20,270 --> 00:02:25,580
So this is where things become not so simple.

33
00:02:26,640 --> 00:02:27,390
Predict.

34
00:02:27,390 --> 00:02:35,430
And of course you can use take the advantage of having or solving using neural networks.

35
00:02:35,760 --> 00:02:42,690
So the samples we took and we put the, the samples, which is x Y into the result, we now get the

36
00:02:42,690 --> 00:02:46,330
results and we need to plot.

37
00:02:46,350 --> 00:02:47,610
So color.

38
00:02:49,760 --> 00:02:51,050
Legend.

39
00:02:52,320 --> 00:02:53,040
Equals.

40
00:02:53,040 --> 00:02:54,180
This is just.

41
00:02:55,920 --> 00:03:03,540
Kind of boring just plotting my 4.30.3.

42
00:03:04,600 --> 00:03:06,280
And here.

43
00:03:06,310 --> 00:03:07,060
Zero.

44
00:03:08,100 --> 00:03:09,060
35.

45
00:03:11,700 --> 00:03:14,680
For in in.

46
00:03:15,530 --> 00:03:18,080
Index in.

47
00:03:19,370 --> 00:03:20,870
In range.

48
00:03:21,650 --> 00:03:22,490
Three.

49
00:03:24,460 --> 00:03:25,140
Fealty.

50
00:03:27,160 --> 00:03:28,070
Fig size.

51
00:03:28,180 --> 00:03:28,980
Size.

52
00:03:29,090 --> 00:03:29,920
Size.

53
00:03:33,650 --> 00:03:34,910
Fig size.

54
00:03:34,940 --> 00:03:38,150
Size equals.

55
00:03:39,950 --> 00:03:41,930
24.

56
00:03:42,590 --> 00:03:49,870
The idea is to build a scatter plot and every scatter plot, every point will take a be small.

57
00:03:49,880 --> 00:03:54,080
This is why we took very we took half million points every point.

58
00:03:54,080 --> 00:04:00,410
This small points will put it and put different colors so we will have a kind of the effect.

59
00:04:01,490 --> 00:04:02,150
We'll finish.

60
00:04:04,760 --> 00:04:06,420
Samples.

61
00:04:07,830 --> 00:04:09,090
The samples.

62
00:04:09,090 --> 00:04:10,080
Everything.

63
00:04:11,830 --> 00:04:13,040
This is the X.

64
00:04:14,530 --> 00:04:15,910
Samples.

65
00:04:17,630 --> 00:04:21,710
Watch this point and why.

66
00:04:23,840 --> 00:04:25,880
And see and see.

67
00:04:27,500 --> 00:04:32,360
And results or the color result.

68
00:04:33,410 --> 00:04:35,180
Will be everything.

69
00:04:36,240 --> 00:04:37,440
And index.

70
00:04:37,440 --> 00:04:49,230
So we'll do it three times zero one, two, one is for you, one is for V and one is for.

71
00:04:53,380 --> 00:04:53,760
P.

72
00:04:54,610 --> 00:05:01,750
Of course, here is just the color is jet and is equals to is the size of the point which is considered

73
00:05:01,750 --> 00:05:02,200
small.

74
00:05:03,190 --> 00:05:05,680
PLT dot color.

75
00:05:08,430 --> 00:05:10,050
Colour bar.

76
00:05:12,070 --> 00:05:15,160
PLT dot c limit.

77
00:05:16,450 --> 00:05:18,730
And just take the colored legend.

78
00:05:20,400 --> 00:05:23,280
And the index because we have three indexes.

79
00:05:23,790 --> 00:05:24,810
Take it.

80
00:05:25,700 --> 00:05:26,840
Put it here.

81
00:05:29,830 --> 00:05:32,260
PLT dot x limit.

82
00:05:33,930 --> 00:05:35,460
Is from.

83
00:05:36,920 --> 00:05:42,410
Zero minus l l over two.

84
00:05:46,920 --> 00:05:47,370
And.

85
00:05:49,200 --> 00:05:50,820
And to.

86
00:05:52,860 --> 00:05:54,810
Just take this sink.

87
00:05:58,320 --> 00:06:00,570
Replace it with Dee Dee.

88
00:06:01,470 --> 00:06:05,010
And the d plt dot.

89
00:06:06,430 --> 00:06:07,150
Died.

90
00:06:08,190 --> 00:06:09,330
Lay out.

91
00:06:10,960 --> 00:06:12,250
PLT dot show.

92
00:06:12,580 --> 00:06:13,180
Okay.

93
00:06:13,210 --> 00:06:15,490
Finally we finished shift enter.

94
00:06:16,690 --> 00:06:17,740
A fig size.

95
00:06:17,740 --> 00:06:18,520
Fig size.

96
00:06:20,610 --> 00:06:22,140
Since.

97
00:06:28,320 --> 00:06:29,010
Fig.

98
00:06:30,170 --> 00:06:30,620
Figure.

99
00:06:30,650 --> 00:06:31,160
Figure.

100
00:06:31,490 --> 00:06:32,270
Not Figure.

101
00:06:32,300 --> 00:06:32,810
Figure.

102
00:06:34,900 --> 00:06:35,500
This one.

103
00:06:35,530 --> 00:06:36,220
Sorry.

104
00:06:37,840 --> 00:06:38,540
We finished.

105
00:06:38,560 --> 00:06:39,400
We're done.

106
00:06:39,430 --> 00:06:41,230
It's just plotting is not.

107
00:06:41,230 --> 00:06:43,900
So you can see some here points.

108
00:06:43,900 --> 00:06:46,930
Maybe we put a little bit more points.

109
00:06:48,440 --> 00:06:53,330
If you can see some points, there are some spaces.

110
00:06:58,890 --> 00:07:02,040
This is a little bit strange.

111
00:07:02,040 --> 00:07:08,340
And I checked actually, we plotted from minus 0.4 to 0.4, which is not correct.

112
00:07:08,370 --> 00:07:11,130
What we need is I made a mistake here.

113
00:07:11,670 --> 00:07:13,050
It should be y lim.

114
00:07:13,320 --> 00:07:20,970
And now we plot and hopefully it's a it's no problem because it was like zooming in into a specific

115
00:07:20,970 --> 00:07:21,680
location.

116
00:07:21,690 --> 00:07:24,990
This is why we got a bad wheel.

117
00:07:24,990 --> 00:07:27,040
The result wasn't reasonable.

118
00:07:27,060 --> 00:07:33,750
Here we can see these points, the small points still, it's from this size is not a problem.

119
00:07:33,750 --> 00:07:37,410
And so basically this is you.

120
00:07:37,440 --> 00:07:47,670
You can see that the you start from a value of one and as it goes the flow because of its viscosity,

121
00:07:47,670 --> 00:07:56,220
it will have a boundary layer in here for V because the flow has start making viscosity.

122
00:07:56,220 --> 00:07:58,690
The flow is directing into the center.

123
00:07:58,690 --> 00:08:02,710
So here it will start gaining speed in the V direction.

124
00:08:02,710 --> 00:08:07,090
And here, of course in the lower like in the opposite direction.

125
00:08:07,090 --> 00:08:14,110
And the last thing is we have increase in pressure in this area, in this area, as the flow goes into

126
00:08:14,110 --> 00:08:23,350
the center part of the of the computation domain and of course has to be zero at the output of the flow.

127
00:08:23,350 --> 00:08:25,540
So basically, this is how.

128
00:08:26,510 --> 00:08:30,860
This thing can be computed and and hopefully.

129
00:08:31,890 --> 00:08:40,080
It will be interesting, like if you would like to see if you put something here in the in the flow,

130
00:08:40,110 --> 00:08:48,180
like you defined a boundary, let's say a kind of circle and see how it will it will be considered.

131
00:08:48,180 --> 00:08:58,500
So this is basically or but you have to be careful about, uh, like making this domain in this location

132
00:08:58,500 --> 00:09:02,340
as the domain points should not be allowed to be inside here.

133
00:09:02,340 --> 00:09:11,220
So it's not very also simple computation you have to do so this is basically the way to do or to solve

134
00:09:11,220 --> 00:09:12,630
Navier-Stokes equation.

135
00:09:13,050 --> 00:09:15,540
I hope it was a good course.

136
00:09:15,540 --> 00:09:20,460
And you, you, you, you knew something that you learn something new.

137
00:09:20,460 --> 00:09:30,360
And of course, this is set you into the path of doing work or research or, or actually solving problems

138
00:09:30,360 --> 00:09:31,960
with pins.

139
00:09:31,960 --> 00:09:39,490
And yeah, you will basically you have to train your network and hopefully you can get a good network

140
00:09:39,490 --> 00:09:45,670
that can work on different boundary conditions and initial conditions and then you can get your solution

141
00:09:45,670 --> 00:09:47,140
in a very quick.

142
00:09:47,590 --> 00:09:52,120
Uh, well, a very quick, quickly, basically.