After the training is finished, which took the first one.
It took about 445 seconds.
And this is the Adam part.
And the other part, which is the lpg's part, took 767 seconds.
So total about 1200 seconds, which is kind of considerable.
And so let's see the results.
So to do that.
We need to make a sample.
Samples equals GM.
But.
Random.
Points.
And we need a lot of points, of course, because it's neural network.
It's it's quite easy to solve.
It's not like a numerical situation.
We, of course, everything is numerical, but in typical numerical solution, what we have to to always
do or is we have the mesh and we have to calculate all these points, but in neural network, things
are happening much faster.
But of course, this neural network only works with the same initial or not initial.
In this case, we don't have initial with the same boundary condition that we trained it.
It only know this small boundary condition.
If you want a network that can serve for a different, uh, well, values, you have to engineer or
you have to build a different neural network that can that can take into consideration different factors.
So this is why this is only showing you how to apply it.
But in order to build a really good network, you need to consider a network that can take on different
initial conditions, different boundary conditions, different size of domain.
It's not easy to build a network that can solve everything fast.
So.
The good thing is after the model is trained, any future solutions is much faster than using usual
methods.
So this is where things become not so simple.
Predict.
And of course you can use take the advantage of having or solving using neural networks.
So the samples we took and we put the, the samples, which is x Y into the result, we now get the
results and we need to plot.
So color.
Legend.
Equals.
This is just.
Kind of boring just plotting my 4.30.3.
And here.
Zero.
35.
For in in.
Index in.
In range.
Three.
Fealty.
Fig size.
Size.
Fig size.
Size equals.
24.
The idea is to build a scatter plot and every scatter plot, every point will take a be small.
This is why we took very we took half million points every point.
This small points will put it and put different colors so we will have a kind of the effect.
We'll finish.
Samples.
The samples.
Everything.
This is the X.
Samples.
Watch this point and why.
And see and see.
And results or the color result.
Will be everything.
And index.
So we'll do it three times zero one, two, one is for you, one is for V and one is for.
P.
Of course, here is just the color is jet and is equals to is the size of the point which is considered
small.
PLT dot color.
Colour bar.
PLT dot c limit.
And just take the colored legend.
And the index because we have three indexes.
Take it.
Put it here.
PLT dot x limit.
Is from.
Zero minus l l over two.
And.
And to.
Just take this sink.
Replace it with Dee Dee.
And the d plt dot.
Died.
Lay out.
PLT dot show.
Okay.
Finally we finished shift enter.
A fig size.
Fig size.
Since.
Fig.
Figure.
Not Figure.
Figure.
This one.
Sorry.
We finished.
We're done.
It's just plotting is not.
So you can see some here points.
Maybe we put a little bit more points.
If you can see some points, there are some spaces.
This is a little bit strange.
And I checked actually, we plotted from minus 0.4 to 0.4, which is not correct.
What we need is I made a mistake here.
It should be y lim.
And now we plot and hopefully it's a it's no problem because it was like zooming in into a specific
location.
This is why we got a bad wheel.
The result wasn't reasonable.
Here we can see these points, the small points still, it's from this size is not a problem.
And so basically this is you.
You can see that the you start from a value of one and as it goes the flow because of its viscosity,
it will have a boundary layer in here for V because the flow has start making viscosity.
The flow is directing into the center.
So here it will start gaining speed in the V direction.
And here, of course in the lower like in the opposite direction.
And the last thing is we have increase in pressure in this area, in this area, as the flow goes into
the center part of the of the computation domain and of course has to be zero at the output of the flow.
So basically, this is how.
This thing can be computed and and hopefully.
It will be interesting, like if you would like to see if you put something here in the in the flow,
like you defined a boundary, let's say a kind of circle and see how it will it will be considered.
So this is basically or but you have to be careful about, uh, like making this domain in this location
as the domain points should not be allowed to be inside here.
So it's not very also simple computation you have to do so this is basically the way to do or to solve
Navier-Stokes equation.
I hope it was a good course.
And you, you, you, you knew something that you learn something new.
And of course, this is set you into the path of doing work or research or, or actually solving problems
with pins.
And yeah, you will basically you have to train your network and hopefully you can get a good network
that can work on different boundary conditions and initial conditions and then you can get your solution
in a very quick.
Uh, well, a very quick, quickly, basically.