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Now we need to calculate the loss and actually calculating the loss in neural network is a very big

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deal because what we basically do, we feed data.

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Calculate the loss and change the weights.

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So it's quite important and this is why we need to be very careful about it.

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And it will take a big chunk of our coal.

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So self.

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Dot.

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We start by, of course, identifying the loss.

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We need a criterion.

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Equals torch dot n n.

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And we will use the sample mean squared error loss.

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And we give an iteration value.

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Of one.

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So here we already finished the defining the init method.

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And now what we will do is we need to define the loss function.

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Function.

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And we call self.

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And then we, we well, we, we start by zero zero gradient.

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Of course, this function is not just defining the loss, it's actually the process of calculating the

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loss.

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So we will actually it's it's it's many times this process or this part of the code is is they put it

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in a different place like they put it in the training place.

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But it like we will do different ways of writing a code but let's let's put it just in the loss function.

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So, Grant.

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We zero the Adam grade gradient and we will zero the optimizer gradient.

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And then we will predict.

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Predict equals self.

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Dot model.

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And self dot x.

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Train.

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And.

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Los.

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Data will equals self.

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Of course, we took the extent and we predict all the values and.

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Self.

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Dot.

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The criterion.

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And we will have the predicted one and we will have also our data.

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Of course not.

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Why?

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But not.

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But why?

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So here what we did is we calculate the first type of loss.

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We said there are two types of losses in in pens.

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The first type is the.

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Data loss.

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The second type is the loss.

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So this is going to be the first type, which is the loss related to data.

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And now what we will do is we will calculate the U.

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The actual U value for the whole thing.

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Dot model.

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Self.

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Just the same thing.

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So this is going to be you.

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It's actually predict it's the same.

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But but we we will put it here because we need to use it to actually do the.

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Derivation.

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So d u over d t We said the component of burgers equation we have du over this one and we have of course

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u which now we just calculated it du over.

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We have du over and over x square.

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Now du over and over will be calculated from this one.

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I will show you how, basically.

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And um.

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Or do you not?

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The x the whole data.

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So sorry, because we have you and it will change with x and it will change with time.

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So we take the data which is which is basically a grid of x and time and we will calculate the change

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of you with x.

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With X means with both sides the time and and the actual x.

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So torch dot auto.

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Auto grid.

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And Dot.

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Grad.

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And we need to add you.

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We need to add you.

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Self dot x.

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This is the the the the component we need to compute which is you.

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This is self x, which is the component we need to basically the dominator or the the the basically

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the change of you, the regarding the x in relation to x and.

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The ground output.

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Outputs equals torch dot ones.

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Like you and this is needed in the training regarding the some change of it will measure the change

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of loss when we basically to itself when we change some parameters, how the loss will change.

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So this is why we put it like this.

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But for this is basically it's the same.

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We always put it this the same along with what's coming next.

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But the most important thing for us is the change of U with change of we define it, which is in our

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case, X and then retrain.

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Or actually create.

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Create.

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Create graph.

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Equals.

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True.

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And return retain.

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The graph will also equals true.

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So basically this is just a it's you want the the the computation has to to to be stored and you have

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to keep it.

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So this is creating the graph, creating this like storage of the computation of the over and retain

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it means we keep it as as simple as this.

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Now think this just housekeeping a little bit here.

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I don't like.

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This way, it's better.

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Yeah, this looks better.

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Okay.

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But there's one thing here I didn't say.

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Here we have to put zero.

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And the reason?

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Zero.

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The reason If you.

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If we didn't put zero, I will.

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And basically show this.

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So.

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If we if we didn't put zero this or okay, I will just print it and I will show.

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So they're putting the the actual tensor in, in in containment.

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It's kind of like in a tuple.

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But we don't want that.

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We want the value of the tensor.

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I will show it just like later.

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I will show it.

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So this we will print it, this one.

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And we print.

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Print.

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Just some kind of separator and print later will show this one.

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But basically is just we.

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Just this way.

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Later I will, of course, when we run the whole code, because it's not ready now.

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Basically, this will be they will put it in in tuple and just want to get it from tuple.

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It's as simple as simple as this, but I will show it anyway, like just for you to have a very clear

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understanding of what's happening.

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Okay, now we found the change of view to X.

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Now we don't want that.

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What we want is the change of U with change of T and we change of u with change of x, not x the data

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this x capital x we call the data, but we're changing the whole thing.

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So d u.

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We take basically this one, maybe it's better than X, We just put data as I feel is better and we

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need basically everything with zero.

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This will be basically.

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Well, a tensor everything is tensor.

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But what we will get is basically we will have two values, which is the change of U in relation to

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X and the change of U in relation to T.

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So this we take the first one, the not this one actually the first, the second one, it will be the

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time and the first one will be basically the.

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The X.

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Okay.

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That's that's good.

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That's.

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That's quite useful.

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Now, we need to repeat this one.

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Why?

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We need to repeat it?

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Because we need to compute the two dimensions.

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So.

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We need to calculate x.

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X.

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So in order to do so, we do the same.

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But now we change the input.

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We take this input.

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Which is this one should not have this.

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This just looks it will have.

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We want to derive the thing again so we derive it again in response to again the X and it will give

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us this one.

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But again, we don't want that or even that second derivative of time.

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What we want is do the x x the second derivative of regarding the space and this will will be.

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Everything and zero.

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So this is will derive already.

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The first derivative will derive it again, this means the second derivative.

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And then we assign the zero.

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Are we done?

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Just a little bit.

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We need to put the loss now.

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PD.

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PD equals.

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And.

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Again.

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The list.

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The Self Criterion.

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Of predicted and the actual thing.

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But first, let's see what is the predicted one and it will be we need to well, basically we need to

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write the equation we have over dt plus u d u over d x equals a viscosity d the second derivative of

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d of u and x.

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This has to be all well, basically it has to be zero.

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So.

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So actually, we don't need this one or actually we can put here zero, but just having this way, it

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will consider it zero.

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So.

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We need to move this guy here.

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And this will be zero.

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You can put it zero, but of course.

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Or just by having the value itself, because at the end, what we're trying always to do is to minimize

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the loss.

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So by computing it as a loss is already.

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Oh, well, it's already computed as a loss, so we don't really need to compare it with an actual Y

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train because the value itself is the loss.

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So do over.

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Plus you dot.

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This time we need to squeeze.

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This value.

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Squeeze.

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And this is just again, like it's the reverse with Unsqueezed what we did, we have these values will

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be separated because it's an output of the prediction.

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We need to make it into a list which these losses are already formatted into this list.

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Um.

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So the equation just we look at it a little bit.

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It's over.

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This is the u over d t u d u over d.

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We need to u.

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And squeeze or squeeze.

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Sorry.

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And d u over d x.

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Okay.

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And.

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Well, actually, we can just put it.

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Minus.

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Minus.

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0.01 divided by.

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Math dot pi.

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This is just a.

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A basically diffusion term.

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U over the x x.

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Yeah.

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So this is the diffusion part of the equation.

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And it all has to.

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B equals.

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And actually we can compare it to zero.

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So d u over t u d u d minus all this part.

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The EU over the.

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As he.

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Okay.

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This way.

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Or the final thing.

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What we need to do is we need to.

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Los.

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Well equals loss.

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P.

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D e.

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Plus loss.

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Date.

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But actually maybe this one a little bit.

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She seems dangerous.

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The thing this way is better.

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The U.S..

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And then loss dot.

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Backward.

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Backpropagation.

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And if self dot letter.

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Divide by 100.

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So every 100 steps we need to print the loss.

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Print.

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Self.

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Dot editor.

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And the loss.

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And of course, we need to increase the iteration number by one.

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Return.

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Los.

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Okay, this way.

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We finished computing the loss and of course, later we will see this one.

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Why I put it like this is just simply it's just the way it went out from this.

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We need to a little bit modified.