forked from Aquila-Consortium/JaxPM_highres
93 lines
No EOL
3 KiB
Python
93 lines
No EOL
3 KiB
Python
import jax
|
|
import jax.numpy as jnp
|
|
|
|
import jax_cosmo as jc
|
|
|
|
from jaxpm.kernels import fftk, gradient_kernel, laplace_kernel, longrange_kernel, PGD_kernel
|
|
from jaxpm.painting import cic_paint, cic_read
|
|
from jaxpm.growth import growth_factor, growth_rate, dGfa
|
|
|
|
def pm_forces(positions, mesh_shape=None, delta=None, r_split=0):
|
|
"""
|
|
Computes gravitational forces on particles using a PM scheme
|
|
"""
|
|
if mesh_shape is None:
|
|
mesh_shape = delta.shape
|
|
kvec = fftk(mesh_shape)
|
|
|
|
if delta is None:
|
|
delta_k = jnp.fft.rfftn(cic_paint(jnp.zeros(mesh_shape), positions))
|
|
else:
|
|
delta_k = jnp.fft.rfftn(delta)
|
|
|
|
# Computes gravitational potential
|
|
pot_k = delta_k * laplace_kernel(kvec) * longrange_kernel(kvec, r_split=r_split)
|
|
# Computes gravitational forces
|
|
return jnp.stack([cic_read(jnp.fft.irfftn(gradient_kernel(kvec, i)*pot_k), positions)
|
|
for i in range(3)],axis=-1)
|
|
|
|
|
|
def lpt(cosmo, initial_conditions, positions, a):
|
|
"""
|
|
Computes first order LPT displacement
|
|
"""
|
|
initial_force = pm_forces(positions, delta=initial_conditions)
|
|
a = jnp.atleast_1d(a)
|
|
dx = growth_factor(cosmo, a) * initial_force
|
|
p = a**2 * growth_rate(cosmo, a) * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dx
|
|
f = a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dGfa(cosmo, a) * initial_force
|
|
return dx, p, f
|
|
|
|
def linear_field(mesh_shape, box_size, pk, seed):
|
|
"""
|
|
Generate initial conditions.
|
|
"""
|
|
kvec = fftk(mesh_shape)
|
|
kmesh = sum((kk / box_size[i] * mesh_shape[i])**2 for i, kk in enumerate(kvec))**0.5
|
|
pkmesh = pk(kmesh) * (mesh_shape[0] * mesh_shape[1] * mesh_shape[2]) / (box_size[0] * box_size[1] * box_size[2])
|
|
|
|
field = jax.random.normal(seed, mesh_shape)
|
|
field = jnp.fft.rfftn(field) * pkmesh**0.5
|
|
field = jnp.fft.irfftn(field)
|
|
return field
|
|
|
|
def make_ode_fn(mesh_shape):
|
|
|
|
def nbody_ode(state, a, cosmo):
|
|
"""
|
|
state is a tuple (position, velocities)
|
|
"""
|
|
pos, vel = state
|
|
|
|
forces = pm_forces(pos, mesh_shape=mesh_shape) * 1.5 * cosmo.Omega_m
|
|
|
|
# Computes the update of position (drift)
|
|
dpos = 1. / (a**3 * jnp.sqrt(jc.background.Esqr(cosmo, a))) * vel
|
|
|
|
# Computes the update of velocity (kick)
|
|
dvel = 1. / (a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a))) * forces
|
|
|
|
return dpos, dvel
|
|
|
|
return nbody_ode
|
|
|
|
|
|
def pgd_correction(pos, params):
|
|
"""
|
|
improve the short-range interactions of PM-Nbody simulations with potential gradient descent method, based on https://arxiv.org/abs/1804.00671
|
|
"""
|
|
kvec = fftk(mesh_shape)
|
|
|
|
delta = cic_paint(jnp.zeros(mesh_shape), pos)
|
|
alpha, kl, ks = params
|
|
delta_k = jnp.fft.rfftn(delta)
|
|
PGD_range=PGD_kernel(kvec, kl, ks)
|
|
|
|
pot_k_pgd=(delta_k * laplace_kernel(kvec))*PGD_range
|
|
|
|
forces_pgd= jnp.stack([cic_read(jnp.fft.irfftn(gradient_kernel(kvec, i)*pot_k_pgd), pos)
|
|
for i in range(3)],axis=-1)
|
|
|
|
dpos_pgd = forces_pgd*alpha
|
|
|
|
return dpos_pgd |