Well NNs like GPs are "basically" non-parametric methods, in the sense that one does not start with a known parameterised statistical distribution that comes from domain expertise. These are worst-case techniques when we dont have the option to start with "the right answer", eg., in the case of large datasets where we have no idea how some pixels distribute over cat/dog images.

In the case of a trajectory we would likey already know the answer, in the form of just doing some physics. The role of computational stats here then is to start with the known form of the solution and find the specific parameters to fit it.

Since we have physics, we can find the "perfect answer" to the trajectory question with very few data points -- and take as many derivatives as we like.

Brute-force ML is often used when we dont have theories, making it all the more dangerous; and alas, all the more useful. We can get a 5% improvement on click-thru rate without having any theory of human behavioural psychology --- god knows then, what we are doing to human behaviour when we implement this system.

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If you’re asking how to solve difficult differential equations in general, we use numerical methods like finite elements or finite differences