Here's my crackpot idea, in case anyone out there is willing and qualified to put in the hard work:
Start with a detailed model of the solar system. Make a million copies of it. In each copy, insert a planet in a random orbit, with random mass. Measure the orbits of everything, perturbed by the new planet.
Feed the measurements of everything, except the new planet, to an A.I., and have it estimate the position of the new planet. Give it feedback on how accurate is was. Repeat a million times. It should learn to pinpoint ninth planets in solar systems like ours, from the perturbations on orbits of known bodies.
Then feed it the real measurement history from the real Solar System. It should output the location of Planet Nine.
Start with a detailed model of the solar system. Make a million copies of it. In each copy, insert a planet in a random orbit, with random mass. Measure the orbits of everything, perturbed by the new planet.
Feed the measurements of everything, except the new planet, to an A.I., and have it estimate the position of the new planet. Give it feedback on how accurate is was. Repeat a million times. It should learn to pinpoint ninth planets in solar systems like ours, from the perturbations on orbits of known bodies.
Then feed it the real measurement history from the real Solar System. It should output the location of Planet Nine.
https://en.wikipedia.org/wiki/Planet_Nine