5 ms·

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 mil

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. https://en.wikipedia.org/wiki/Planet_Nine https://en.wikipedia.org/wiki/Planet_Nine

starpilot 7y ago
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.
TuringNYC 7y ago
So...the 8 body problem? https://en.m.wikipedia.org/wiki/Three-body_problem https://en.m.wikipedia.org/wiki/Three-body_problem
- tomrod 7y ago
  Often called the N body problem, but the issue occurs when N>=3, so calling it "the 3 body problem" usually sufficiently identifies it in the literature. Great question, and I am happy to have my 1 in 10k time today! (Nice being on the informing end for once). https://xkcd.com/1053/ https://xkcd.com/1053/
terminalhealth 7y ago
This seems related: https://www.researchgate.net/publication/11955388_Solving_N_-Body_Problems_with_Neural_Networks https://www.researchgate.net/publication/11955388_Solving_N_...
antognini 7y ago
As someone who used to work on the dynamics of few body systems this idea actually isn't too crazy. But there isn't really any need for AI (neural networks wouldn't be necessary). Things like deep learning are really useful when you don't have a good model for the underlying reality (coming up with a principled model of what cats look like is really hard), but in the case of planetary dynamics the physics is well understood and can be modeled explicitly. But the underlying idea of searching for statistical perturbations to known orbits to find new objects is a good one! In fact, Mike Brown and Konsntantin Batygin did just this a few years back. They argued that perturbations to the orbits of objects in the Kuiper belt suggested that there is a planet with about the mass of Neptune somewhere out there: https://ui.adsabs.harvard.edu/abs/2016AJ....151...22B/abstract https://ui.adsabs.harvard.edu/abs/2016AJ....151...22B/abstra... This object hasn't been found yet, but it could still be out there!
- balabaster 7y ago
  Wasn’t this concept the basis of the Netflix show Salvation where they found the asteroid plummeting on a collision course with earth?
- nitwit005 7y ago
  Here's a good talk from around the same date that I watched previously: https://www.youtube.com/watch?v=CMCwezegPNg https://www.youtube.com/watch?v=CMCwezegPNg
c3534l 7y ago
It sounds like you've invented a crappy version of MCTS[0]. [0] https://en.wikipedia.org/wiki/Monte_Carlo_tree_search https://en.wikipedia.org/wiki/Monte_Carlo_tree_search
- deleted 7y ago
  [deleted]
- stanfordkid 7y ago
  MCTS estimates a score for each action by stochastically sampling the future states. It has nothing to do with a problem such as this with continuous inputs and outputs.
ChrisFoster 7y ago
In principle this is actually quite a reasonable idea and is a common pattern of many types of physical measurement. Often we have a detailed and accurate physical model of the forward dynamics of a system, given some system parameters, but we can't measure these parameters directly. Instead, we measure some data in a "sensor domain" and we'd like to map it back to the physical parameters. This setup is known as an "inverse problem" and is often ill conditioned / singular or very complex, therefore requiring some regularization in the form of prior knowledge. Treating the inverse problem as a regression problem (given these observations in sensor domain, predict the state of the system) with a neural network as the regressor is one way of attacking these problems and is becoming very successful in some areas, for example MRI reconstructions, eg https://www.biorxiv.org/content/10.1101/278036v1 https://www.biorxiv.org/content/10.1101/278036v1. In this case you are adding the regularization / priors by constructing the training data with a physical model. I think this kind of approach is interesting because it scales to input and output spaces with high dimensionality. However, it's not exactly clear to me what kind of estimate such a regressor provides (is it kind of like doing maximum likelihood?) From a more standard statistical point of view, you'd like to estimate the full probability distribution over system parameters. In this case, the orbital elements and mass of the unknown bodies. Because this inference problem has relatively low dimensionality (I think?) you might do better to treat it as a problem of Bayesian inference and sample it using MCMC. Then you'd have a rigorous way to understand the uncertainty of the estimates and also to attack the problem of "unknown number of bodies" in a systematic way.
deleted 7y ago
[deleted]
pinouchon 7y ago
Sounds like a good fit for probabilistic programming, much like Stuart Russell did here https://www.youtube.com/watch?v=GYQrNfSmQ0M&feature=youtu.be&t=16m40s https://www.youtube.com/watch?v=GYQrNfSmQ0M&feature=youtu.be.... His method could find locations of nuclear tests better than the existing UN system at the time by a lot. His model uses bayesian inference in a stochastic/symbolic/simplified/statistic model of physics (how shockwaves propagate on the surface of the earth). You could do the same here: assuming the relevant laws (kepler? newton law of gravity?), and a prior distribution on the location/mass of your 9th planet, given what we observe for the other planets, what's the posterior distribution on the mass/location of the 9th planet. The statistical model is likely to be small (the Russell statistical model for Nukes fits on one slide). The issue is how to do inference efficiently. Fortunately, probabilistic systems have come a long way and can do these kind of inferences.

starpilot 7y ago

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.

TuringNYC 7y ago

So...the 8 body problem? https://en.m.wikipedia.org/wiki/Three-body_problem https://en.m.wikipedia.org/wiki/Three-body_problem

tomrod 7y ago
Often called the N body problem, but the issue occurs when N>=3, so calling it "the 3 body problem" usually sufficiently identifies it in the literature. Great question, and I am happy to have my 1 in 10k time today! (Nice being on the informing end for once). https://xkcd.com/1053/ https://xkcd.com/1053/

terminalhealth 7y ago

This seems related: https://www.researchgate.net/publication/11955388_Solving_N_-Body_Problems_with_Neural_Networks https://www.researchgate.net/publication/11955388_Solving_N_...

antognini 7y ago

As someone who used to work on the dynamics of few body systems this idea actually isn't too crazy. But there isn't really any need for AI (neural networks wouldn't be necessary). Things like deep learning are really useful when you don't have a good model for the underlying reality (coming up with a principled model of what cats look like is really hard), but in the case of planetary dynamics the physics is well understood and can be modeled explicitly. But the underlying idea of searching for statistical perturbations to known orbits to find new objects is a good one! In fact, Mike Brown and Konsntantin Batygin did just this a few years back. They argued that perturbations to the orbits of objects in the Kuiper belt suggested that there is a planet with about the mass of Neptune somewhere out there: https://ui.adsabs.harvard.edu/abs/2016AJ....151...22B/abstract https://ui.adsabs.harvard.edu/abs/2016AJ....151...22B/abstra... This object hasn't been found yet, but it could still be out there!

balabaster 7y ago
Wasn’t this concept the basis of the Netflix show Salvation where they found the asteroid plummeting on a collision course with earth?
nitwit005 7y ago
Here's a good talk from around the same date that I watched previously: https://www.youtube.com/watch?v=CMCwezegPNg https://www.youtube.com/watch?v=CMCwezegPNg

c3534l 7y ago

It sounds like you've invented a crappy version of MCTS[0]. [0] https://en.wikipedia.org/wiki/Monte_Carlo_tree_search https://en.wikipedia.org/wiki/Monte_Carlo_tree_search

deleted 7y ago
[deleted]
stanfordkid 7y ago
MCTS estimates a score for each action by stochastically sampling the future states. It has nothing to do with a problem such as this with continuous inputs and outputs.

ChrisFoster 7y ago

In principle this is actually quite a reasonable idea and is a common pattern of many types of physical measurement. Often we have a detailed and accurate physical model of the forward dynamics of a system, given some system parameters, but we can't measure these parameters directly. Instead, we measure some data in a "sensor domain" and we'd like to map it back to the physical parameters. This setup is known as an "inverse problem" and is often ill conditioned / singular or very complex, therefore requiring some regularization in the form of prior knowledge. Treating the inverse problem as a regression problem (given these observations in sensor domain, predict the state of the system) with a neural network as the regressor is one way of attacking these problems and is becoming very successful in some areas, for example MRI reconstructions, eg https://www.biorxiv.org/content/10.1101/278036v1 https://www.biorxiv.org/content/10.1101/278036v1. In this case you are adding the regularization / priors by constructing the training data with a physical model. I think this kind of approach is interesting because it scales to input and output spaces with high dimensionality. However, it's not exactly clear to me what kind of estimate such a regressor provides (is it kind of like doing maximum likelihood?) From a more standard statistical point of view, you'd like to estimate the full probability distribution over system parameters. In this case, the orbital elements and mass of the unknown bodies. Because this inference problem has relatively low dimensionality (I think?) you might do better to treat it as a problem of Bayesian inference and sample it using MCMC. Then you'd have a rigorous way to understand the uncertainty of the estimates and also to attack the problem of "unknown number of bodies" in a systematic way.

deleted 7y ago

[deleted]

pinouchon 7y ago

Sounds like a good fit for probabilistic programming, much like Stuart Russell did here https://www.youtube.com/watch?v=GYQrNfSmQ0M&feature=youtu.be&t=16m40s https://www.youtube.com/watch?v=GYQrNfSmQ0M&feature=youtu.be.... His method could find locations of nuclear tests better than the existing UN system at the time by a lot. His model uses bayesian inference in a stochastic/symbolic/simplified/statistic model of physics (how shockwaves propagate on the surface of the earth). You could do the same here: assuming the relevant laws (kepler? newton law of gravity?), and a prior distribution on the location/mass of your 9th planet, given what we observe for the other planets, what's the posterior distribution on the mass/location of the 9th planet. The statistical model is likely to be small (the Russell statistical model for Nukes fits on one slide). The issue is how to do inference efficiently. Fortunately, probabilistic systems have come a long way and can do these kind of inferences.