4 ms·

It says in your readme[1] though that your solar system simulation simulation is off by 70k km (regarding Earth orbit) after only 1 year relative to the JPL eph

by nonbel 10y ago

It says in your readme[1] though that your solar system simulation simulation is off by 70k km (regarding Earth orbit) after only 1 year relative to the JPL ephemerides, for "unknown reasons". I don't see how you can use that to justify not checking for conservation of momentum/energy. I also do not understand your final sentence. [1] https://github.com/strainer/fancy https://github.com/strainer/fancy

strainer 10y ago
Come on it doesnt say "unknown reasons" it says the "It is possible the discrepancy is due to the limitation of javascripts 64bit FP numbers rather than subtle algorithmic or physics error" 70k km / a year (on a billion km long orbit) was a lot closer than I had hoped for, considering its a 64 bit newtonian model. But this is beside the fact that having worked on the project a fair bit, I understand that any model adjustments to conserve energy or momentum are non-physical 'fudges' to correct deficiencies of the model. There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law - a proper account of that eludes me, but it is certainly explained somewhere.
- nonbel 10y ago
  Right, you don't know how much error the floating point error accounts for. You also brought up loss of angular momentum to solar wind, etc. These are all just speculations. That may be fine for the purposes of your simulation, but not for predicting if asteroids will impact the earth or the influence of human activity on Earth's climate. Also, I know you are supposed to use a symplectic integrator to ensure conservation of energy when doing these simulations, so it is not somehow hardcoded into the laws, eg: https://en.wikipedia.org/wiki/Leapfrog_integration https://en.wikipedia.org/wiki/Leapfrog_integration
  - strainer 10y ago
    We could certainly calculate how much error was introduced by rounding, if we had the time and inclination. It is useful to understand that about numerical modelling, it should not be necessary to accept any indeterminable discrepancies. Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration.
    - nonbel 10y ago
      >"Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration." I am not sure about "conservation is encoded" part, but I can believe it. Either way, in practice the simulations will encounter issues along these lines if they are not careful. For example, I left your simulation running for what amounted to ~120 yrs and saturn lost all her moons. This is the best pic I could get, sorry (hopefully it is reproducible): https://i.imgur.com/C7emd28.png https://i.imgur.com/C7emd28.png Since you do not report anything about conservation of energy/momentum, how do we know that isn't the problem?
      - strainer 10y ago
        >For example, I left your simulation running for what amounted to ~120 yrs and saturn lost all her moons. Thanks! heh, it is rather complex there are all sorts of things... most likely the new gravity function set for that model messed up, which can apply attraction between groups of objects if they are distant and weak enough. But honestly I am certain that it is something in particular and not something mysterious about conservation of energy/momentum which i have not come across yet, because there is no formula in that gravity simulation which should be able to destroy momentum. In the other models, there are quasi-physical friction and pressure functions which do destroy momentum and do have some rough adjustments to compensate for that somewhat, but accuracy is lost whether things are compensated for or not. Tracking energy and momentum can be a good way for tracking accuracy of a model, but if you do any adjustments to correct it, that is a kind of fudge not based in true physics. It is poignant that you expressed scepticism of climate models because of a perceived lack of such adjustments, while the opposite is actually true. Climate models have to include a lot of calibrated adjustment and quasi-physics, because the whole system is too complex to represent at all relevant scales. This should not condemn the work of computer scientists specialised in climate modelling to undue scepticism.
- petters 10y ago
  > There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law The physical laws guarantee conservation, yes. But not all numerical methods for solving differential equations do.

by nonbel 10y ago

strainer 10y ago

Come on it doesnt say "unknown reasons" it says the "It is possible the discrepancy is due to the limitation of javascripts 64bit FP numbers rather than subtle algorithmic or physics error" 70k km / a year (on a billion km long orbit) was a lot closer than I had hoped for, considering its a 64 bit newtonian model. But this is beside the fact that having worked on the project a fair bit, I understand that any model adjustments to conserve energy or momentum are non-physical 'fudges' to correct deficiencies of the model. There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law - a proper account of that eludes me, but it is certainly explained somewhere.

nonbel 10y ago
Right, you don't know how much error the floating point error accounts for. You also brought up loss of angular momentum to solar wind, etc. These are all just speculations. That may be fine for the purposes of your simulation, but not for predicting if asteroids will impact the earth or the influence of human activity on Earth's climate. Also, I know you are supposed to use a symplectic integrator to ensure conservation of energy when doing these simulations, so it is not somehow hardcoded into the laws, eg: https://en.wikipedia.org/wiki/Leapfrog_integration https://en.wikipedia.org/wiki/Leapfrog_integration
- strainer 10y ago
  We could certainly calculate how much error was introduced by rounding, if we had the time and inclination. It is useful to understand that about numerical modelling, it should not be necessary to accept any indeterminable discrepancies. Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration.
  - nonbel 10y ago
    >"Conservation of energy, momentum, information is hardcoded into all known laws of Physics. It is our integration algorithms which do not all ensure conservation of information - but that is carefully achievable with basic first order schemes, such as Verlet and leapfrog integration." I am not sure about "conservation is encoded" part, but I can believe it. Either way, in practice the simulations will encounter issues along these lines if they are not careful. For example, I left your simulation running for what amounted to ~120 yrs and saturn lost all her moons. This is the best pic I could get, sorry (hopefully it is reproducible): https://i.imgur.com/C7emd28.png https://i.imgur.com/C7emd28.png Since you do not report anything about conservation of energy/momentum, how do we know that isn't the problem?
    - strainer 10y ago
      >For example, I left your simulation running for what amounted to ~120 yrs and saturn lost all her moons. Thanks! heh, it is rather complex there are all sorts of things... most likely the new gravity function set for that model messed up, which can apply attraction between groups of objects if they are distant and weak enough. But honestly I am certain that it is something in particular and not something mysterious about conservation of energy/momentum which i have not come across yet, because there is no formula in that gravity simulation which should be able to destroy momentum. In the other models, there are quasi-physical friction and pressure functions which do destroy momentum and do have some rough adjustments to compensate for that somewhat, but accuracy is lost whether things are compensated for or not. Tracking energy and momentum can be a good way for tracking accuracy of a model, but if you do any adjustments to correct it, that is a kind of fudge not based in true physics. It is poignant that you expressed scepticism of climate models because of a perceived lack of such adjustments, while the opposite is actually true. Climate models have to include a lot of calibrated adjustment and quasi-physics, because the whole system is too complex to represent at all relevant scales. This should not condemn the work of computer scientists specialised in climate modelling to undue scepticism.
petters 10y ago
> There are no laws of physics dedicated to adjusting energy, momentum, information in order to conserve them. They are conserved by a mathematical correctness of every physical law The physical laws guarantee conservation, yes. But not all numerical methods for solving differential equations do.