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Now we go for the.

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Evaluation and for actually seeing the results of this computation.

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So with.

4
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With the same as we do torch.

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The dot.

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No grad means gradient.

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Not grad.

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It's sometimes.

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Confusing mixed values.

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Torch.

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Torch.

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Dot line space.

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Line.

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Space.

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Actually no space like this.

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Starting point is zero.

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Ending point is one and we will take 100 points.

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We do this and do it again.

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And for why.

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Same, same, same thing.

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X.

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And why?

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Equals torch.

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We make a mesh grid.

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Mish grid.

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And we pass on these values.

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Of course, this time we do like the usual method, just a grid, and we evaluate this grid.

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And then.

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T value.

30
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Equals church.

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Dot ones.

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Like ones, correct?

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00:01:39,380 --> 00:01:44,060
Yeah, ones like X or Y is the same.

34
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Multiplied zero.

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Now we will.

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00:01:49,160 --> 00:01:57,290
Um, now this is basically the, uh, basically you're putting the time of the computation.

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00:01:57,290 --> 00:02:04,430
So if you put a zero, it means the initial condition one is the end condition or the final thing.

38
00:02:04,430 --> 00:02:06,050
So here, um.

39
00:02:07,680 --> 00:02:10,980
Uh, specify.

40
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The time.

41
00:02:15,920 --> 00:02:16,280
Time.

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Input data equals torch dot stack.

43
00:02:23,840 --> 00:02:25,190
We did this before.

44
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And.

45
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X.

46
00:02:30,970 --> 00:02:34,270
In Latin because we made a mesh from this one.

47
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Black.

48
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Ten.

49
00:02:41,780 --> 00:02:44,120
And we do the same with Latin.

50
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Why flatten?

51
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And.

52
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Actually in here.

53
00:02:56,730 --> 00:03:00,960
To value just to make sure it's flattened.

54
00:03:02,670 --> 00:03:04,860
Although I think it's already flat.

55
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Thine equals one.

56
00:03:18,200 --> 00:03:20,600
So this is the input data.

57
00:03:20,600 --> 00:03:23,150
And what we need is the solution.

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Solution equals.

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00:03:27,230 --> 00:03:27,980
Model.

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00:03:28,980 --> 00:03:30,030
Input data.

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00:03:32,860 --> 00:03:36,130
Dot reshape.

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And.

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And basically this shape.

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X shape.

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00:03:47,500 --> 00:03:52,780
And why the chip or even chip Same thing is okay, because it's a square.

66
00:03:54,620 --> 00:03:55,220
Okay.

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00:03:55,400 --> 00:03:57,380
This is the our solution.

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00:03:57,380 --> 00:04:00,080
Just we plt dot.

69
00:04:01,260 --> 00:04:01,980
Figure.

70
00:04:03,460 --> 00:04:04,780
Big size.

71
00:04:06,200 --> 00:04:10,670
And the fig size is eight six.

72
00:04:12,120 --> 00:04:14,790
It's an estate heat.

73
00:04:15,380 --> 00:04:18,000
Heat map.

74
00:04:18,870 --> 00:04:20,850
They pass on the solution.

75
00:04:23,380 --> 00:04:25,360
And we see map.

76
00:04:25,360 --> 00:04:27,760
The color map will be jet.

77
00:04:28,790 --> 00:04:29,430
Njit.

78
00:04:31,970 --> 00:04:32,270
A.

79
00:04:34,880 --> 00:04:38,420
BLT just to make it complete.

80
00:04:38,900 --> 00:04:41,090
Title to the.

81
00:04:42,500 --> 00:04:43,340
To the.

82
00:04:44,300 --> 00:04:45,010
It.

83
00:04:46,630 --> 00:04:49,090
Bayesian solution.

84
00:04:51,530 --> 00:04:51,890
And.

85
00:04:54,520 --> 00:04:56,740
Dot X label.

86
00:05:01,370 --> 00:05:02,030
X.

87
00:05:03,150 --> 00:05:05,040
PLT dot y.

88
00:05:06,150 --> 00:05:13,110
Label just to know where x and where y and PLT dot show.

89
00:05:15,040 --> 00:05:15,370
Sean.

90
00:05:18,860 --> 00:05:22,960
Shift-enter And it's not a good thing, Fig.

91
00:05:30,360 --> 00:05:31,500
Thick size.

92
00:05:35,660 --> 00:05:35,870
Hm.

93
00:05:37,020 --> 00:05:38,400
There is no the equals.

94
00:05:39,510 --> 00:05:40,980
Okay, now we have it.

95
00:05:42,150 --> 00:05:43,200
Basically like this.

96
00:05:44,080 --> 00:05:47,050
So we have this circle.

97
00:05:47,050 --> 00:05:49,340
This is the sign thing, the sine wave.

98
00:05:49,360 --> 00:05:52,570
0 to 100 is actually the number of points.

99
00:05:52,570 --> 00:05:54,730
The actual value is zero to 4 to 1.

100
00:05:54,910 --> 00:06:05,260
And what we can see is here is, well, basically this high heat and it will like it should be with

101
00:06:05,260 --> 00:06:06,970
time, it should reduce.

102
00:06:06,970 --> 00:06:09,780
So, for example, at zero is like this.

103
00:06:09,790 --> 00:06:11,350
Let's keep let's take this one.

104
00:06:11,350 --> 00:06:18,550
And for example, consider at a 0.1 and shift enter.

105
00:06:18,580 --> 00:06:26,320
Basically we can see here is 0.08 and now is 0.012.

106
00:06:26,350 --> 00:06:28,480
It actually diffused a lot.

107
00:06:29,260 --> 00:06:32,560
It means like the energy is going like this.

108
00:06:32,770 --> 00:06:37,570
And how about if we increase it a bit?

109
00:06:37,570 --> 00:06:42,250
So 0.1, we add five and we shift enter.

110
00:06:42,280 --> 00:06:51,050
Now it's even farther diffused and we put it to.

111
00:06:52,040 --> 00:06:52,880
Shift.

112
00:06:53,620 --> 00:06:55,120
Now it's even more.

113
00:06:55,150 --> 00:07:03,880
It's diffusing and think this way like this will be there is a numerical explanation why it's happening

114
00:07:03,880 --> 00:07:04,270
like this.

115
00:07:04,270 --> 00:07:10,000
But think it it's all about the distance between the center and this.

116
00:07:11,560 --> 00:07:15,190
H So now it's more diffused.

117
00:07:15,190 --> 00:07:21,080
And then if we go zero five shift, enter more diffused.

118
00:07:21,100 --> 00:07:27,280
The reason is not Scimitar is it doesn't have symmetry because in our solution we used a lot of random

119
00:07:27,280 --> 00:07:27,910
things.

120
00:07:27,910 --> 00:07:35,530
So and actually the training, even if we didn't use random, the training, the computation of the

121
00:07:35,530 --> 00:07:41,530
neural networks always has some random variables as we have optimizers.

122
00:07:41,530 --> 00:07:46,330
And actually the optimizer we use is not so let's say strict.

123
00:07:47,580 --> 00:07:53,190
So if you want to have the one, we can see everything got diffused.

124
00:07:53,190 --> 00:07:59,490
But this value like this, of course, it's it's considered high value, but in reality it's not high

125
00:07:59,520 --> 00:08:07,790
0.008 And we start from 0.0.8 or maybe even about here, 0.9.

126
00:08:07,800 --> 00:08:11,610
So basically the value is very low.

127
00:08:11,610 --> 00:08:16,830
But you know, it it has to make this counter plot.

128
00:08:17,580 --> 00:08:21,090
This this legend and this counter plot.

129
00:08:21,870 --> 00:08:23,990
So that's it.

130
00:08:24,000 --> 00:08:32,820
This is how the results we get it and we see the results of solving a 2D heat equation.