Presuppositions of Physics Simulations
I haven’t done a simulation project, but these are my presuppositions of simulation. Let’s see how they would change over time (haha pun intended).
§1 Simulation in General
We divide space into several grids, but we also have Adaptive Mesh Refinement, see [2312.05438] Adaptive mesh refinement in binary black holes simulations. Also, there are Adaptive step size.
Butterfly Effect: [2401.13381]Spontaneous stochasticity amplifies even thermal noise to the largest scales of turbulence in a few eddy turnover times
There are 3 kinds of simulation:
- radiative processes, spectrum.
- dark matter halos, n-body/test particle, gravity.
- source population, luminosity distribution, redshift. neutrino in the universe.
§2 Language
n-body - Which programs are fastest? (Benchmarks Game), like that’s even a question.
§3 Memory Usage
In particle n-body simulation, because of the shape of the tensor [num_particles, num_properties] (num_properties refers to $x$, $y$, $z$, $v_x$, $v_y$, $v_z$, spin, etc) does not change, the memory usage is almost const.
Also, if we encode time in this tensor, we should put it in the first dimension such that [time_steps, num_particles, num_properties]. Because now if we want to take a picture from the video, we just do x[time_step]. In terms of semetic, this feels natural. In terms of meaning, this shows that, time is just a set of tensors.
§4 Framework
§4.1 Run
Only use functional programming, instead of object-oriented programming. Because the latter one is not necessary and the previous one, without state and so on, is faster.
def one_step():
...
def save():
...# save as `.parquet`?
for i in range():
one_step()# the next step is determined by the previous step, so GPU is not much useful here
save()
§4.2 Plot
Plot the animation of the simulation, and plot the variation of derived properties such kinetic energy, potential energy and so on:
def plot_animation():
....
def plot_kinetic_energy():
...
def plot_potential_energy():
...