Hello everyone.

So, after we've gone through many different versions of neural networks and the way they are implemented,

I now want to broaden the perspective a little bit and tell you something as sort of overview about how neural networks are applied in science and the natural sciences.

And you can ask yourself in general, so if I have some scientific tasks, can I use neural networks for that task?

And that's maybe not so easy to answer, but I have listed a few considerations you might have.

So, it's very obvious that if you have a task that is some kind of extrapolation, then neural networks might be very good for this task.

Also tasks that have something to do with image processing in one form or another, obviously very suitable for neural networks.

And so, one of the things you have to ask yourself, okay, if my task is of the version that I could reasonably train a neural network on,

so I can give a lot of training examples from one input I have to achieve, I have to go to some output, then how would my input look like?

How would my output look like? This is typically the first question you want to ask.

And so, regarding the input or this mapping from input to output, you have to ask yourself, do I have experimental results available?

Do I have sufficiently many of these experimental results available?

For example, measurement traces that have been measured given certain parameters, and then I change the parameters and the parameters would be the input and the output are these measurement traces.

And the neural network learns to map one to the other.

Maybe there exist already big databases of experimental data or observational data that other people have collected.

So that would be a very good case for using neural networks.

And the cases that I mentioned in the examples that are to follow are often of this sort.

Or then again, maybe it's hard to come by so much experimental data or maybe you are a theoretical scientist who wants to test their more mathematical theory.

So then the question is maybe I have simulations available.

And then, for example, the mapping could go from the parameters or the initial conditions for this particular simulation to the output,

which would be, say, a trajectory or say magnetization pattern or what have you in your particular simulation.

Then one very, very important point is how many training examples do you have?

This is particularly important if it's not about simulations, but if you have to rely on experimental results.

Because we have seen in all the neural network examples that we've discussed.

If you only have 100, 200 examples, maybe that's not quite enough to train a neural network.

And suddenly, if you only have 20 training examples, that's absolutely not enough to train a neural network.

For such cases, there are sometimes ways around it.

Maybe you can have trained on a large artificially generated database and your neural network has become good at that.

And then there are techniques maybe to train it on only a few examples.

It's sometimes called single shot learning.

But these are exceptions and you have to think very carefully about what you are doing in that case.

Then finally, once you've trained, you want to assess the accuracy.

So what do you want to compare against?

Do you want to compare against other machine learning techniques?

Do you want to compare against the performance of humans like one would do in image labeling?

So that's one question.

And especially problematic question if you rely on experimental data.

So the way to do it there is of course to hold back part of the experimental data as validation data.

You train on the rest and then you check it on the data that you have never shown to the neural network.

So testing the accuracy of predictions is always hard.

And you have to be aware that if in the future you want to apply your neural network to cases that are quite a bit different than the usual training examples,

then it may fare worse.

Then the accuracy is not quite the one that you estimated from your validation set.

So that's another problem.

And then of course you want to know whether it has been worth it.

And okay, there can be many reasons why you want to use a neural network.

But one of the reasons might be that you want to have a speed up.

So maybe your usual simulation takes an hour and your neural network only takes a second to provide an approximate answer for the given input.

So that would be a very nice speed up.

But then you have to ask yourself if the speed up is so dramatic, then maybe also doing all the training costs me a lot of time because each simulation takes an hour.