Now we go for the.
Evaluation and for actually seeing the results of this computation.
So with.
With the same as we do torch.
The dot.
No grad means gradient.
Not grad.
It's sometimes.
Confusing mixed values.
Torch.
Dot line space.
Line.
Space.
Actually no space like this.
Starting point is zero.
Ending point is one and we will take 100 points.
We do this and do it again.
And for why.
Same, same, same thing.
X.
And why?
Equals torch.
We make a mesh grid.
Mish grid.
And we pass on these values.
Of course, this time we do like the usual method, just a grid, and we evaluate this grid.
And then.
T value.
Equals church.
Dot ones.
Like ones, correct?
Yeah, ones like X or Y is the same.
Multiplied zero.
Now we will.
Um, now this is basically the, uh, basically you're putting the time of the computation.
So if you put a zero, it means the initial condition one is the end condition or the final thing.
So here, um.
Uh, specify.
The time.
Time.
Input data equals torch dot stack.
We did this before.
And.
X.
In Latin because we made a mesh from this one.
Black.
Ten.
And we do the same with Latin.
Why flatten?
And.
Actually in here.
To value just to make sure it's flattened.
Although I think it's already flat.
Thine equals one.
So this is the input data.
And what we need is the solution.
Solution equals.
Model.
Input data.
Dot reshape.
And.
And basically this shape.
X shape.
And why the chip or even chip Same thing is okay, because it's a square.
Okay.
This is the our solution.
Just we plt dot.
Figure.
Big size.
And the fig size is eight six.
It's an estate heat.
Heat map.
They pass on the solution.
And we see map.
The color map will be jet.
Njit.
A.
BLT just to make it complete.
Title to the.
To the.
It.
Bayesian solution.
And.
Dot X label.
X.
PLT dot y.
Label just to know where x and where y and PLT dot show.
Sean.
Shift-enter And it's not a good thing, Fig.
Thick size.
Hm.
There is no the equals.
Okay, now we have it.
Basically like this.
So we have this circle.
This is the sign thing, the sine wave.
0 to 100 is actually the number of points.
The actual value is zero to 4 to 1.
And what we can see is here is, well, basically this high heat and it will like it should be with
time, it should reduce.
So, for example, at zero is like this.
Let's keep let's take this one.
And for example, consider at a 0.1 and shift enter.
Basically we can see here is 0.08 and now is 0.012.
It actually diffused a lot.
It means like the energy is going like this.
And how about if we increase it a bit?
So 0.1, we add five and we shift enter.
Now it's even farther diffused and we put it to.
Shift.
Now it's even more.
It's diffusing and think this way like this will be there is a numerical explanation why it's happening
like this.
But think it it's all about the distance between the center and this.
H So now it's more diffused.
And then if we go zero five shift, enter more diffused.
The reason is not Scimitar is it doesn't have symmetry because in our solution we used a lot of random
things.
So and actually the training, even if we didn't use random, the training, the computation of the
neural networks always has some random variables as we have optimizers.
And actually the optimizer we use is not so let's say strict.
So if you want to have the one, we can see everything got diffused.
But this value like this, of course, it's it's considered high value, but in reality it's not high
0.008 And we start from 0.0.8 or maybe even about here, 0.9.
So basically the value is very low.
But you know, it it has to make this counter plot.
This this legend and this counter plot.
So that's it.
This is how the results we get it and we see the results of solving a 2D heat equation.