5 ms·

I'm sure there's a reason, but it seems like an unusual use of Monte Carlo - it's all deterministic and there is no opposing player making choices. Must have so

I'm sure there's a reason, but it seems like an unusual use of Monte Carlo - it's all deterministic and there is no opposing player making choices. Must have something to do with uncertainties in projected orbits or imperfect simulations maybe?

heikkilevanto 2y ago
Uncertain observations, I'm sure
deleted 2y ago
[deleted]
zacharycohn 2y ago
Right - we only got a short glimpse of it, not enough to get a high confidence of its trajectory.
Projectiboga 2y ago
The guesswork is uncertainity about the object's exact paraneters. Because of this they have to use informed estimates (scientiffic guesswork).
deleted 2y ago
[deleted]
basementcat 2y ago
The observations are not 100% certain. There are a variety of body states and configurations that might result in the same (few) pixels being lit up in the few measurements collected so far. As additional measurements are collected, some possibilities may be eliminated and the uncertainty of the trajectory can be reduced. This usually results in the impact probability converging toward 0%.
- davrosthedalek 2y ago
  ...or 100%. But yeah, the MC comes in this way. You have a current most probable value for the position and some distribution around it, depending on the precision of the measurement device etc. That can be a high-dimensional space. You draw some (many) random points from this space and propagate them all deterministically. Taking into account how likely a certain random point was in the first place, you can then estimate the hit probability. MC is numerically approximating an integral. Here it replaces the high-dim integral over the start parameters.
cozzyd 2y ago
It is very common to use Monte Carlo for deterministic problems. It's just an integral over complicated PDFs
NL807 2y ago
>it's all deterministic and there is no opposing player making choices It's not deterministic, it's chaotic. That is the nature of the N-body problem. We can only approximate trajectories in such a system using numerical methods, within a certain margin of error. In principle, the object is gravitationally interacting with everything else in the solar system. But for the most part, most interactions are negligible and could be ignored (eg, other small objects far away), except of the large bodies. But there are many unknowns (as stated before), where initial conditions will affect the outcome of the trajectory simulation, and errors will certainly amplify over time. I'm guessing Monte Carlo is used to "fuzz" the simulations with randomised initial conditions to account for the range of unknowns, and see what the outcome is under these different scenarios.
- deleted 2y ago
  [deleted]
- jaggederest 2y ago
  At the very least you can use monte carlo to provide examples from the expected distribution. It's hard to visualize a probability cloud.
- coderenegade 2y ago
  Chaotic doesn't mean non-deterministic, it just means that small changes in initial conditions result in a large change in the trajectory. The system itself can be both chaotic and deterministic. It's also a reasonable question to ask, because the simulations are deterministic. It's just that because the system is also chaotic and there's noise in the measurement, that can result in a large spread of deterministic trajectory simulations.
  - NL807 2y ago
    It's only deterministic in the sense of the mathematical constructs that models the system, like differential equations that drive the simulations at each finite time step. But the information or the state which the simulation is applied on is always chaotic. That is because delta at each time step is an approximation with some error. It's impossible to make the state in the system behave deterministically, because that requires time deltas to approach to zero (or infinite amount of infinitely small differential steps).
refulgentis 2y ago
Right: - "Since we saw it so briefly, our knowledge of its orbit is not that great" - "[for example, in 2016 the data shows] a large chunk of sky where it could have been, and [the object is quite small." - "Our knowledge of the diameter of this object is a bit fuzzy, because of surface reflectivity,"
baq 2y ago
Looks like alpha zero stole the original meaning of Monte Carlo… it is not required to have players, or a game, to use the method: https://en.m.wikipedia.org/wiki/Monte_Carlo_method https://en.m.wikipedia.org/wiki/Monte_Carlo_method
- bananaflag 2y ago
  It wasn't stolen, it was a well-established particular case well before alphago https://en.wikipedia.org/wiki/Monte_Carlo_tree_search https://en.wikipedia.org/wiki/Monte_Carlo_tree_search
  - baq 2y ago
    I only meant the total mind share :) looks like folks have never heard of MC in other contexts than game bots.
RossBencina 2y ago
I would assume that it is because we have imperfect knowledge of the state of the asteroid (i.e. mass and current position/velocity/...). This imperfect knowledge is characterised by a probability distribution. Similarly the state of all other objects in the solar system is only known up to some distribution. To propagate the information forward in time to impact requires a complicated function f(state of solar system; state of asteroid). If all of the data was known (and expressible numerically) with perfect accuracy, and f were computable with perfect accuracy then all would be good. But as noted, (state of solar system; state of asteroid) is a probability distribution, and there are very few distributions and very few types of maps f that are amenable to analytic transformation. For example if the state was a normal distribution with mean x and covariance P, and f were a linear transformation, then x,P mapped through f is also normally distributed with mean y and covariance P_y, you can get the mean of the transform as y=fx, and P_y = fPf' (where ' indicates transpose). Needless to say our knowledge of the state of the asteroid and the solar system is probably a rather complicated distribution, and the n-body problem is not a linear transformation. Monte-carlo simulation is often used to propagate probability distributions through non-linear transformations.
andrepd 2y ago
It's "deterministic" the same way the weather is.
- brewtide 2y ago
  Exactly. It will do exactly this, as long as nothing changes.

heikkilevanto 2y ago

Uncertain observations, I'm sure

deleted 2y ago

[deleted]

zacharycohn 2y ago

Right - we only got a short glimpse of it, not enough to get a high confidence of its trajectory.

Projectiboga 2y ago

The guesswork is uncertainity about the object's exact paraneters. Because of this they have to use informed estimates (scientiffic guesswork).

deleted 2y ago

[deleted]

basementcat 2y ago

The observations are not 100% certain. There are a variety of body states and configurations that might result in the same (few) pixels being lit up in the few measurements collected so far. As additional measurements are collected, some possibilities may be eliminated and the uncertainty of the trajectory can be reduced. This usually results in the impact probability converging toward 0%.

davrosthedalek 2y ago
...or 100%. But yeah, the MC comes in this way. You have a current most probable value for the position and some distribution around it, depending on the precision of the measurement device etc. That can be a high-dimensional space. You draw some (many) random points from this space and propagate them all deterministically. Taking into account how likely a certain random point was in the first place, you can then estimate the hit probability. MC is numerically approximating an integral. Here it replaces the high-dim integral over the start parameters.

cozzyd 2y ago

It is very common to use Monte Carlo for deterministic problems. It's just an integral over complicated PDFs

NL807 2y ago

>it's all deterministic and there is no opposing player making choices It's not deterministic, it's chaotic. That is the nature of the N-body problem. We can only approximate trajectories in such a system using numerical methods, within a certain margin of error. In principle, the object is gravitationally interacting with everything else in the solar system. But for the most part, most interactions are negligible and could be ignored (eg, other small objects far away), except of the large bodies. But there are many unknowns (as stated before), where initial conditions will affect the outcome of the trajectory simulation, and errors will certainly amplify over time. I'm guessing Monte Carlo is used to "fuzz" the simulations with randomised initial conditions to account for the range of unknowns, and see what the outcome is under these different scenarios.

deleted 2y ago
[deleted]
jaggederest 2y ago
At the very least you can use monte carlo to provide examples from the expected distribution. It's hard to visualize a probability cloud.
coderenegade 2y ago
Chaotic doesn't mean non-deterministic, it just means that small changes in initial conditions result in a large change in the trajectory. The system itself can be both chaotic and deterministic. It's also a reasonable question to ask, because the simulations are deterministic. It's just that because the system is also chaotic and there's noise in the measurement, that can result in a large spread of deterministic trajectory simulations.
- NL807 2y ago
  It's only deterministic in the sense of the mathematical constructs that models the system, like differential equations that drive the simulations at each finite time step. But the information or the state which the simulation is applied on is always chaotic. That is because delta at each time step is an approximation with some error. It's impossible to make the state in the system behave deterministically, because that requires time deltas to approach to zero (or infinite amount of infinitely small differential steps).

refulgentis 2y ago

Right: - "Since we saw it so briefly, our knowledge of its orbit is not that great" - "[for example, in 2016 the data shows] a large chunk of sky where it could have been, and [the object is quite small." - "Our knowledge of the diameter of this object is a bit fuzzy, because of surface reflectivity,"

baq 2y ago

Looks like alpha zero stole the original meaning of Monte Carlo… it is not required to have players, or a game, to use the method: https://en.m.wikipedia.org/wiki/Monte_Carlo_method https://en.m.wikipedia.org/wiki/Monte_Carlo_method

bananaflag 2y ago
It wasn't stolen, it was a well-established particular case well before alphago https://en.wikipedia.org/wiki/Monte_Carlo_tree_search https://en.wikipedia.org/wiki/Monte_Carlo_tree_search
- baq 2y ago
  I only meant the total mind share :) looks like folks have never heard of MC in other contexts than game bots.

RossBencina 2y ago

I would assume that it is because we have imperfect knowledge of the state of the asteroid (i.e. mass and current position/velocity/...). This imperfect knowledge is characterised by a probability distribution. Similarly the state of all other objects in the solar system is only known up to some distribution. To propagate the information forward in time to impact requires a complicated function f(state of solar system; state of asteroid). If all of the data was known (and expressible numerically) with perfect accuracy, and f were computable with perfect accuracy then all would be good. But as noted, (state of solar system; state of asteroid) is a probability distribution, and there are very few distributions and very few types of maps f that are amenable to analytic transformation. For example if the state was a normal distribution with mean x and covariance P, and f were a linear transformation, then x,P mapped through f is also normally distributed with mean y and covariance P_y, you can get the mean of the transform as y=fx, and P_y = fPf' (where ' indicates transpose). Needless to say our knowledge of the state of the asteroid and the solar system is probably a rather complicated distribution, and the n-body problem is not a linear transformation. Monte-carlo simulation is often used to propagate probability distributions through non-linear transformations.

andrepd 2y ago

It's "deterministic" the same way the weather is.

brewtide 2y ago
Exactly. It will do exactly this, as long as nothing changes.