5 ms·

If it isn't based on the Navier Stokes equations, can I actually use this to reliably simulate fluid behavior? Or is this more useful for creating pseudo-realis

by krapht 11y ago

If it isn't based on the Navier Stokes equations, can I actually use this to reliably simulate fluid behavior? Or is this more useful for creating pseudo-realistic water scenes?

modeless 11y ago
"Our approach showed the potential to be a good replacement of standard solvers in settings, where running times is more important than the exactness of a simulation, such as in computer games or interactive design." "In our future work we want to [...] combine learning methods with standard solvers to obtain both fast and highly accurate simulations." From the paper's conclusion.
jimfleming 11y ago
It appears to be based on Navier-Stokes, from the abstract: > We designed a feature vector, directly modelling individual forces and constraints from the Navier-Stokes equations, giving the method strong generalization properties to reliably predict positions and velocities of particles in a large time step setting on yet unseen test videos.
Crazywater 11y ago
This is the latter. There are a lot of reasons you would not want this for accurate simulation, one being that you basically prime your simulation on your training data. The other one being that SPH is already quite an approximation of Navier Stokes. But for real-time animation, this is very nice. The problem with particle fluid simulations is that everything scales linearly, but only in the number of operations per particle per simulation timestep. But the more particles you have, the smaller the timestep needs to be in order to not let the simulation explode. And this is a real problem, because you want multi-million particle simulations for realistic water, but then the number of steps you need to compute per frame increases. They managed to do a single simulation step per frame.
daniel-levin 11y ago
The main goal of mechanics is finding solutions for important variables of interest, from which every other dynamical variable can be easily computed. In fluid mechanics, the main objective for a given problem is finding a velocity field (once you have this, you're done). Since the NS equations are non-linear partial differential equations, finding exact solutions is impossible in most cases. Some notable non-trivial exceptions exist [1]. Navier-Stokes is extremely successful in describing flows in many real physical situations. It is believed, but has not been experimentally confirmed, that Navier-Stokes successfully describes turbulent flow. Most physical theories have a fairly well known domain in which they are applicable and not applicable (Newtonian physics breaks down at velocities near the speed of light). Currently, we don't even know if solutions to NS always exist, never mind make physical sense [2]. With this in mind, we have to acknowledge the uncertainty of the correctness of NS in describing an arbitrary flow. It is backed by well-grounded theory (parts of the equations can be derived from conservation laws) and works under many different conditions. This comment landed up longer than I expected, but my main point is that the question can we "reliably simulate fluid behavior" for an arbitrary fluid - is largely up in the air [3]. However, we should restrict our attention to flows that we very strongly believe are correctly described by NS. From the original paper: >> The main problem of our method is the same as the weakness of all machine learning approaches; the learning methods are not capable to extrapolate the model far outside the data observed during training. The training data are existing numerical simulations of specific fluid flows. The learning algorithm learned fluid flow dynamics from simulations. This is extremely impressive. It also achieves a significant speed up in simulation time - which is also very impressive. However, as the authors say, it does not generalise well. So, in short the answer to your first question is probably "sometimes yes, but in general not really". edit: I should add that the simulations in the paper are decidedly based on Navier-Stokes. [1] https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_flow_from_the_Navier%E2%80%93Stokes_equations https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_flow_... [2] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc... [3] https://en.wikipedia.org/wiki/Turbulence https://en.wikipedia.org/wiki/Turbulence
- irascible 11y ago
  I think they are using navies stokes to generate the dataset to learn from.. and the regression forest learns how to reproduce what navier stokes did with a bunch of smaller timesteps, but learns to do it in a single timestep.. which sounds amazing so I'm probably wrong

by krapht 11y ago

If it isn't based on the Navier Stokes equations, can I actually use this to reliably simulate fluid behavior? Or is this more useful for creating pseudo-realistic water scenes?

modeless 11y ago

"Our approach showed the potential to be a good replacement of standard solvers in settings, where running times is more important than the exactness of a simulation, such as in computer games or interactive design." "In our future work we want to [...] combine learning methods with standard solvers to obtain both fast and highly accurate simulations." From the paper's conclusion.

jimfleming 11y ago

It appears to be based on Navier-Stokes, from the abstract: > We designed a feature vector, directly modelling individual forces and constraints from the Navier-Stokes equations, giving the method strong generalization properties to reliably predict positions and velocities of particles in a large time step setting on yet unseen test videos.

Crazywater 11y ago

This is the latter. There are a lot of reasons you would not want this for accurate simulation, one being that you basically prime your simulation on your training data. The other one being that SPH is already quite an approximation of Navier Stokes. But for real-time animation, this is very nice. The problem with particle fluid simulations is that everything scales linearly, but only in the number of operations per particle per simulation timestep. But the more particles you have, the smaller the timestep needs to be in order to not let the simulation explode. And this is a real problem, because you want multi-million particle simulations for realistic water, but then the number of steps you need to compute per frame increases. They managed to do a single simulation step per frame.

daniel-levin 11y ago

The main goal of mechanics is finding solutions for important variables of interest, from which every other dynamical variable can be easily computed. In fluid mechanics, the main objective for a given problem is finding a velocity field (once you have this, you're done). Since the NS equations are non-linear partial differential equations, finding exact solutions is impossible in most cases. Some notable non-trivial exceptions exist [1]. Navier-Stokes is extremely successful in describing flows in many real physical situations. It is believed, but has not been experimentally confirmed, that Navier-Stokes successfully describes turbulent flow. Most physical theories have a fairly well known domain in which they are applicable and not applicable (Newtonian physics breaks down at velocities near the speed of light). Currently, we don't even know if solutions to NS always exist, never mind make physical sense [2]. With this in mind, we have to acknowledge the uncertainty of the correctness of NS in describing an arbitrary flow. It is backed by well-grounded theory (parts of the equations can be derived from conservation laws) and works under many different conditions. This comment landed up longer than I expected, but my main point is that the question can we "reliably simulate fluid behavior" for an arbitrary fluid - is largely up in the air [3]. However, we should restrict our attention to flows that we very strongly believe are correctly described by NS. From the original paper: >> The main problem of our method is the same as the weakness of all machine learning approaches; the learning methods are not capable to extrapolate the model far outside the data observed during training. The training data are existing numerical simulations of specific fluid flows. The learning algorithm learned fluid flow dynamics from simulations. This is extremely impressive. It also achieves a significant speed up in simulation time - which is also very impressive. However, as the authors say, it does not generalise well. So, in short the answer to your first question is probably "sometimes yes, but in general not really". edit: I should add that the simulations in the paper are decidedly based on Navier-Stokes. [1] https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_flow_from_the_Navier%E2%80%93Stokes_equations https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_flow_... [2] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc... [3] https://en.wikipedia.org/wiki/Turbulence https://en.wikipedia.org/wiki/Turbulence

irascible 11y ago
I think they are using navies stokes to generate the dataset to learn from.. and the regression forest learns how to reproduce what navier stokes did with a bunch of smaller timesteps, but learns to do it in a single timestep.. which sounds amazing so I'm probably wrong