4 ms·

Orbital equations are straightforward and deterministic, I am wondering why an AI would be needed for this? You could solve explicitly.

crimsonalucard 7y ago
Also one perturbed configuration actually has multiple solutions.
jackpirate 7y ago
Just to clarify, the GP is describing what is essentially the n body problem in physics [1]. There is in general no closed form solution for solving n-body problems, but and so numeric solutions are generally required. [1] https://en.wikipedia.org/wiki/N-body_problem https://en.wikipedia.org/wiki/N-body_problem
opportune 7y ago
Well, an unperturbed orbit is straightforward and deterministic. But three+ body problems (which I believe the original comment is describing) do not have closed form solutions and are general simulated: https://en.wikipedia.org/wiki/Three-body_problem https://en.wikipedia.org/wiki/Three-body_problem. The reason planet nine is suspected to exist is due to the commonalities in the orbits of trans-neptunian objects. That is, there appears to be a large gravitational influence on TNOs that causes the distribution of their orbits to exhibit irregularities that don't make sense with only two factors influencing their orbits.
- analog31 7y ago
  Indeed, and it's worth generalizing that the vast majority of contemporary problems do not yield themselves to closed form solutions. We are constantly finding numerical solutions. If you went to college when I did, first of all, you're eligible to join the AARP, and second, the problems that you studied were overwhelmingly solved in closed form. This was true in math as well, both in college and at the K-12 level. Now, are ML algorithms worth adding to our tool belt of numerical methods? Oh, probably. When the fad is over, some useful applications will remain. We already use regression a lot, and that's a primitive form of ML.
deepnotderp 7y ago
I think he's talking about many body problems.
alexmlamb2 7y ago
It's kind of an inverse problem. Once you put the planets in position you can (reasonably easily?) simulate their oribts with some noise. The idea is that the neural network would try to quickly approximate which planet configurations could produce those stable orbits.

crimsonalucard 7y ago

Also one perturbed configuration actually has multiple solutions.

jackpirate 7y ago

Just to clarify, the GP is describing what is essentially the n body problem in physics [1]. There is in general no closed form solution for solving n-body problems, but and so numeric solutions are generally required. [1] https://en.wikipedia.org/wiki/N-body_problem https://en.wikipedia.org/wiki/N-body_problem

opportune 7y ago

Well, an unperturbed orbit is straightforward and deterministic. But three+ body problems (which I believe the original comment is describing) do not have closed form solutions and are general simulated: https://en.wikipedia.org/wiki/Three-body_problem https://en.wikipedia.org/wiki/Three-body_problem. The reason planet nine is suspected to exist is due to the commonalities in the orbits of trans-neptunian objects. That is, there appears to be a large gravitational influence on TNOs that causes the distribution of their orbits to exhibit irregularities that don't make sense with only two factors influencing their orbits.

analog31 7y ago
Indeed, and it's worth generalizing that the vast majority of contemporary problems do not yield themselves to closed form solutions. We are constantly finding numerical solutions. If you went to college when I did, first of all, you're eligible to join the AARP, and second, the problems that you studied were overwhelmingly solved in closed form. This was true in math as well, both in college and at the K-12 level. Now, are ML algorithms worth adding to our tool belt of numerical methods? Oh, probably. When the fad is over, some useful applications will remain. We already use regression a lot, and that's a primitive form of ML.

deepnotderp 7y ago

I think he's talking about many body problems.

alexmlamb2 7y ago

It's kind of an inverse problem. Once you put the planets in position you can (reasonably easily?) simulate their oribts with some noise. The idea is that the neural network would try to quickly approximate which planet configurations could produce those stable orbits.