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Now we are going to solve the burgers equation.

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So when when we talk about the burgers equation, first let's look at the terms of the burgers equation.

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And in this case, we'll have the first one is the temporal difference, which or the temperance, the

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temporal component which is du over DT We can see well, basically it it govern or it.

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Show the difference between the new value with the time itself.

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And plus you itself.

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This is you.

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And then the change of you with respect to the to the which is the change of you with space, which

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is we call it the spatial component of Berger's equations.

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And this will equal to viscosity denoted by V and the second derivative of U with respect to space.

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So we have two spatial components and one temporal component or time well governed or like change of

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U with respect to time.

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So solving this equation means we have to solve U for every time step we have.

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So what we will need to do is we will have an X, which is space, and we will have time.

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And.

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Basically what we need to have is a neural network that will take the space and the time we we assign

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it and it will give us.

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That you value.

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So this is basically what we are doing or what we want to do.

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So let's let's code it and step by step.

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Of course, let's have like discussion of what kind of things we need to consider.

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So the first thing is we need to we start by basically just writing the file.

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Name, which is Burgers, girls.

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It will mean.

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And actually, it's one.

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And we as always, we import the needed libraries.

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So we start with importing math.

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I'm not sure we're going to use math, but but let's import it anyway.

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If we needed some mathematical issues or features or like functions as NP numpy of course import for

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plotting seaborne, we will import we will plot the like heat contour plot so it will be useful, see

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like see Seaborn.

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And then of course import matplotlib.

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Plot lib dot pyplot as plt.

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And.

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But I'm take you.

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The import.

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Dcdm.

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Import.

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Torch and of course import torch dot n.

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N.

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As in n network.

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Tqdm is just to show us the progress bar if we needed to see the progress bar.

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So these are the libraries we need to upload and of course shift enter to take them.

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Now it's set and we can start by first.

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Building our network.

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The network we need to build is going to, as I said, take X and T and provide us with basically the

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value.

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So so let's let's write a neural network for that.

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So we start by class in, in and neural network, we inherit the module.

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And as as as any like TensorFlow.

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In.

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The PyTorch module.

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We.

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We always right this way.

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And super.

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Neural network.

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We take it.

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And self.

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We initiate.

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Well, basically this one.

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In it.

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And now we will start writing the neural network.

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So the neural network has to start with basically two.

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Two inputs.

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So but of course we need a sequential to torch and n dot.

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Sequential.

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And seek.

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One chill seems legit.

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And.

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We start by the neural network.

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Linear.

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Two inputs and it will expand to 20.

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So what's happening here?

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We're starting with two inputs X and T, and then the network will expand to 28 elements.

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And of course, we need to also.

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I'm not sure why it's not.

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Oh, this way.

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Yeah, I wanted to to have on the same line as here.

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So after that we need to put an activation function.

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So we use an activation function very also common activation function.

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And after that, what we will need to do is we said we have 20 a a well after two it will expand to

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20 neurons and then 20 we want to expand to 30.

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So what we have is basically we will start by two neurons.

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And then we will have the first layer.

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It will be 20.

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A well, 20 nodes, and then we will expand to even 30 nodes and we will continue a little bit 30 and

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then we will go back to 20.

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So I think this way.

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So this is what we are trying to build.

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And of course, at the end we need just one, which is the.

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Of course.

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Which is the you here?

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Of course.

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We have to also.

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Consider the activation function.

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And here we take on 30 and let's say we provide another 30 or we keep it the same level.

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Even if you change it differently, it will work.

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Even if all of this is 20 is going to work.

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But the reason I'm doing this is just to try to.

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Have more command over the network.

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So we try to change this network.

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Here, 2020.

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And then basically.

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We take 20 and make it into.

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One value and just remove this one.

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So we'll have to 20, 20, 30, 30, 30, 30, 20, 2020, and then 20 to 1.

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And of course we don't have an activation function after that.

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Okay.

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So this one is going to be the network we have, and then we have to assign the forward pass, which

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is self.

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And X also very usual thing output will equals to self.

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Dot net and it will have.

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And return.

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The output.

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This way we assign the neural network and it is it will have an input size, an input size of two,

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and then you will have the first layer of 20.

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Second layer of 30.

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Third layer of 30.

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Fourth layer of 20.

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And fifth layer is the final layer, which is there's just one, one point.

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It's just the point we need to calculate, which is you.

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So here we, we do this and then we shift enter.

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Now we already took it by now.

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We already assigned the network.

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The next step is going to be considering the data that we need to use.

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And the data means we have the.

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A Well, the state the data means the boundary condition along with the initial condition that this

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network has to bind with to get the right solution for us.