3 or n body problem with neural net?

[Kharakov]

Before someone says inconceivable, I'd like to say that I don't think that word means what you think it means.


Anyone try to solve 2d+t or 3d+t n-body problems with neural nets with a single time variable t, and locations of bodies/velocity vectors/ acceleration parameters at t=0?


Just wondered. Maybe there is some other pattern that a neural net would find that we don't see because we are focusing upon discrete mathematical patterns. Discreet? fuck.

 

[steve_bank]

Neural nets are good at pattern recognition. With a neural net how would you arrive at a quantified mathematical answer?

The three body problem solution is non linear. so a solution requires iterative trial and error numerical techniques. Essentially a Turing Machine.

Not a bad question.

 

[Kharakov]

What if there is some underlying pattern that we can't perceive, because we focus on individual relationships between the particles?

Like a non-linear (obviously) solution that cannot be arrived at by looking at the variables the way we currently do. What if we look at the variables (velocity, acceleration, mass) arising from something else?



Say we start out with 3 bodies moving along random paths, can we calculate what mass, at what time, they must have to travel the paths (assuming the paths are not those that would be traced out by entities with static mass, and they are paths with smooth acceleration curves)?

Is there a single equation for only the mass of the objects at various times? I don't think so.

Maybe it's a solution like relative movement of various stalks on the 3d Mandelbrot set (magic angle spun):

Sort of hard to describe with polynomial equations if one introduces y and z pixel components (above is the simplest, most symmetric case), if one isn't aware of the simplest most symmetric case first.

 

[steve_bank]

That something else would probably get you the Nibble Prize in physics.

When gravity is involved there can be no random motion. Given the initial conditions of velocity, acceleration, mass, and relative position I presume there is only one solution. If not the underlying physics and math would be logically inconsistent or ambiguous.

The mathematical problem is that terms of the differential equations are not linearly connected to other variables, they can not be separated as would be in a simple linear algebraic equation. Given F(x,y) = 0 you can not separate x and y on opposite sides of the equal sign. The situation is common in many physical dynamic systems. It requires a sequential trial and error solution, genially called a solver or non linear solver.

If a neural net can mimic a TM then the answers is yes. In cybernetics and AI three is open debate as to whether our brains implement some form of a TM. If not then a TM, aka digital computer, may not be able to mimic the human brain.

 

[J842P]

That something else would probably get you the Nibble Prize in physics.

When gravity is involved there can be no random motion. Given the initial conditions of velocity, acceleration, mass, and relative position I presume there is only one solution. If not the underlying physics and math would be logically inconsistent or ambiguous.

The mathematical problem is that terms of the differential equations are not linearly connected to other variables, they can not be separated as would be in a simple linear algebraic equation. Given F(x,y) = 0 you can not separate x and y on opposite sides of the equal sign. The situation is common in many physical dynamic systems. It requires a sequential trial and error solution, genially called a solver or non linear solver.

If a neural net can mimic a TM then the answers is yes. In cybernetics and AI three is open debate as to whether our brains implement some form of a TM. If not then a TM, aka digital computer, may not be able to mimic the human brain.

Our brains obviously can implement a system that is Turing complete. Obviously, you can instruct a person to do by hand whatever operations are required by a Turing Machine. The question isn't whether your brain is Turing Complete, the question is, *what else can it do and how?*

 

[steve_bank]

That something else would probably get you the Nibble Prize in physics.

When gravity is involved there can be no random motion. Given the initial conditions of velocity, acceleration, mass, and relative position I presume there is only one solution. If not the underlying physics and math would be logically inconsistent or ambiguous.

The mathematical problem is that terms of the differential equations are not linearly connected to other variables, they can not be separated as would be in a simple linear algebraic equation. Given F(x,y) = 0 you can not separate x and y on opposite sides of the equal sign. The situation is common in many physical dynamic systems. It requires a sequential trial and error solution, genially called a solver or non linear solver.

If a neural net can mimic a TM then the answers is yes. In cybernetics and AI three is open debate as to whether our brains implement some form of a TM. If not then a TM, aka digital computer, may not be able to mimic the human brain.

Our brains obviously can implement a system that is Turing complete. Obviously, you can instruct a person to do by hand whatever operations are required by a Turing Machine. The question isn't whether your brain is Turing Complete, the question is, *what else can it do and how?*

Ok.

For now the answer appears unknown at least to me. In a Theory Of Computaion class it was shown that problems can not be solved with logic trees and graphs.

A quarterback throws pass that hits recovers running in various directions, distances, and speeds. Analogues to solving differential equations, a problem in related rates.

I attended a presentation by somebody who was designing equipment to quantitatively evaluate athletes.

To test balanced and recovery a person stands on a balance board kept level by pins. The pins are pulled without warning and position of the board is monitored as the person brings the board back to level, The human response was a classical damped second order response, a damped sine wave. Human dynamics look like traditional physical systems, one could say an analog computer.

Birds do it landing on a branch.