JaxPM_highres/jaxpm/pm.py

import jax
import jax.numpy as jnp
import jax_cosmo as jc

from jaxpm.growth import dGfa, growth_factor, growth_rate
from jaxpm.kernels import (PGD_kernel, fftk, gradient_kernel, laplace_kernel,
                           longrange_kernel)
from jaxpm.painting import cic_paint, cic_read


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, mesh_shape, params):
    """
    improve the short-range interactions of PM-Nbody simulations with potential gradient descent method, based on https://arxiv.org/abs/1804.00671
    args:
      pos: particle positions [npart, 3]
      params: [alpha, kl, ks] pgd parameters
    """
    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


def make_neural_ode_fn(model, mesh_shape):
    def neural_nbody_ode(state, a, cosmo, params):
        """
        state is a tuple (position, velocities)
        """
        pos, vel = state
        kvec = fftk(mesh_shape)

        delta = cic_paint(jnp.zeros(mesh_shape), pos)

        delta_k = jnp.fft.rfftn(delta)

        # Computes gravitational potential
        pot_k = delta_k * laplace_kernel(kvec) * longrange_kernel(kvec, r_split=0)

        # Apply a correction filter
        kk = jnp.sqrt(sum((ki/jnp.pi)**2 for ki in kvec))
        pot_k = pot_k *(1. + model.apply(params, kk, jnp.atleast_1d(a)))

        # Computes gravitational forces
        forces = jnp.stack([cic_read(jnp.fft.irfftn(gradient_kernel(kvec, i)*pot_k), pos) 
                          for i in range(3)],axis=-1)

        forces = forces * 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 neural_nbody_ode