As a data scientist with an interest in space stuff, I am well positioned to give an answer this question. I must confess I don't understand fully what is going on in this system from just the lecture slides, so my answer will be more of an educated guess.
At first glance it doesn't really make sense to use a neural network here. The sort of problems that neural networks are amenable to solve tend to be rather soft and fuzzy (both in the mathematical sense and the is-this-picture-a-cat? sense). Physics simulation problems have well-defined rules, and the best way of solving them is usually through good old fashioned brute-force simulation.
What I think is happening here is that the neural net training is being used to create a statistical object, a sort of probability distribution. One way of thinking about neural networks, is that they're acting as a form of data compression. By training a neural net on something, you are essentially fitting a complicated multidimensional curve made of hundreds of parameters onto data that could contain millions of points. (In a way, humans do this too. We take a kaleidoscopic variety of individual experiences and make sense of them through a relatively small number of rules of thumb, which we then use to guide decisions in future events that are unlikely to be exactly the same as a previous event).
As mentioned in LeWavite's answer to one of your previous questions, for n objects you have 1/2 n(n-1) possible collisions to worry about. There's about ~17000 bits of space debris that are currently tracked, meaning there's ~ 144,500,000 possible collisions to sort through, a rather unwieldy number.
The key slide from her presentation is this one:
(You'll probably need to enlarge it to see better, the original wasn't that good)
From what I can gather from this diagram, there are two neural networks with two different functions. The diagram on the left looks to be some kind of control systems state diagram of the type roboticists use.
The red neural net takes in 5 orbital parameters (the ones needed to define the orbit, but not where the object is in the orbit). It's not clear to me what the three output parameters (Y(1),Y(2),Y(3)) are, they don't seem to appear anywhere else.
The blue neural network appears to act in a similar fashion to an extended Kalman filter, in the sense that the predictions of the red neural network are being continually updated by new data of the tracked objects as their orbits naturally shift from their keplerian ideals. By training the neural network on these updates, it sort of learns a 'sense' of how the object's orbits tend to change over time.
That's about all I can extract from the diagram. Considering this is a proprietary system, I doubt there'll be much more than that.
I do question the usefulness of using convolutional neural nets. They are used for situations where the individual columns of data are related spatially - like points on a grid. You mainly see them with image-processing neural nets, but they can do other stuff, like generating terrain from drawn lines. There are only 5 input parameters in both of the neural networks shown in the talk, and they represent different concepts, so I fail to see how CNNs can help here.
