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merge hugos LPT2 code
This commit is contained in:
parent
2f509932f5
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2 changed files with 149 additions and 153 deletions
116
jaxpm/kernels.py
116
jaxpm/kernels.py
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@ -1,5 +1,3 @@
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from enum import Enum
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import jax.numpy as jnp
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import jax_cosmo as jc
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import numpy as np
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@ -45,16 +43,18 @@ def interpolate_power_spectrum(input, k, pk, sharding=None):
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def gradient_kernel(kvec, direction, order=1):
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"""
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Computes the gradient kernel in the requested direction
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Parameters:
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Parameters
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-----------
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kvec: array
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Array of k values in Fourier space
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kvec: list
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List of wave-vectors in Fourier space
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direction: int
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Index of the direction in which to take the gradient
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Returns:
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Index of the direction in which to take the gradient
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Returns
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--------
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wts: array
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Complex kernel
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Complex kernel values
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"""
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if order == 0:
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wts = 1j * kvec[direction]
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@ -69,37 +69,43 @@ def gradient_kernel(kvec, direction, order=1):
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return wts
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def laplace_kernel(kvec):
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def invlaplace_kernel(kvec):
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"""
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Compute the Laplace kernel from a given K vector
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Parameters:
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Compute the inverse Laplace kernel
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Parameters
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-----------
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kvec: array
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Array of k values in Fourier space
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Returns:
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kvec: list
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List of wave-vectors
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Returns
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--------
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wts: array
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Complex kernel
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Complex kernel values
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"""
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kk = sum(ki**2 for ki in kvec)
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wts = jnp.where(kk == 0, 1., 1. / kk)
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return wts
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kk_nozeros = jnp.where(kk==0, 1, kk)
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return - jnp.where(kk==0, 0, 1 / kk_nozeros)
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def longrange_kernel(kvec, r_split):
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"""
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Computes a long range kernel
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Parameters:
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-----------
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kvec: array
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Array of k values in Fourier space
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r_split: float
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Computes a long range kernel
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Parameters
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-----------
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kvec: list
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List of wave-vectors
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r_split: float
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Splitting radius
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Returns
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--------
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wts: array
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Complex kernel values
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TODO: @modichirag add documentation
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Returns:
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--------
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wts: array
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kernel
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"""
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"""
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if r_split != 0:
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kk = sum(ki**2 for ki in kvec)
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return np.exp(-kk * r_split**2)
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@ -109,15 +115,21 @@ def longrange_kernel(kvec, r_split):
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def cic_compensation(kvec):
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"""
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Computes cic compensation kernel.
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Adapted from https://github.com/bccp/nbodykit/blob/a387cf429d8cb4a07bb19e3b4325ffdf279a131e/nbodykit/source/mesh/catalog.py#L499
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Itself based on equation 18 (with p=2) of
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`Jing et al 2005 <https://arxiv.org/abs/astro-ph/0409240>`_
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Args:
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kvec: array of k values in Fourier space
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Returns:
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v: array of kernel
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"""
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Computes cic compensation kernel.
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Adapted from https://github.com/bccp/nbodykit/blob/a387cf429d8cb4a07bb19e3b4325ffdf279a131e/nbodykit/source/mesh/catalog.py#L499
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Itself based on equation 18 (with p=2) of
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[Jing et al 2005](https://arxiv.org/abs/astro-ph/0409240)
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Parameters:
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-----------
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kvec: list
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List of wave-vectors
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Returns:
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--------
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wts: array
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Complex kernel values
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"""
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kwts = [np.sinc(kvec[i] / (2 * np.pi)) for i in range(3)]
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wts = (kwts[0] * kwts[1] * kwts[2])**(-2)
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return wts
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@ -125,20 +137,22 @@ def cic_compensation(kvec):
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def PGD_kernel(kvec, kl, ks):
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"""
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Computes the PGD kernel
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Parameters:
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-----------
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kvec: array
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Array of k values in Fourier space
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kl: float
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initial long range scale parameter
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ks: float
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initial dhort range scale parameter
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Returns:
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--------
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v: array
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kernel
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"""
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Computes the PGD kernel
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Parameters:
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-----------
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kvec: list
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List of wave-vectors
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kl: float
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Initial long range scale parameter
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ks: float
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Initial dhort range scale parameter
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Returns:
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--------
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v: array
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Complex kernel values
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"""
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kk = sum(ki**2 for ki in kvec)
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kl2 = kl**2
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ks4 = ks**4
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186
jaxpm/pm.py
186
jaxpm/pm.py
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@ -9,7 +9,7 @@ from jaxpm.distributed import (autoshmap, fft3d, get_local_shape, ifft3d,
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normal_field)
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from jaxpm.growth import (dGf2a, dGfa, growth_factor, growth_factor_second,
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growth_rate, growth_rate_second)
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from jaxpm.kernels import (PGD_kernel, fftk, gradient_kernel, laplace_kernel,
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from jaxpm.kernels import (PGD_kernel, fftk, gradient_kernel, invlaplace_kernel,
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longrange_kernel)
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from jaxpm.painting import cic_paint, cic_paint_dx, cic_read, cic_read_dx
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@ -29,18 +29,20 @@ def pm_forces(positions,
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mesh_shape = delta.shape
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if delta is None:
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delta_k = fft3d(
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cic_paint_dx(positions, halo_size=halo_size, sharding=sharding))
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else:
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field = cic_paint_dx(positions, halo_size=halo_size, sharding=sharding)
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delta_k = fft3d(field)
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elif jnp.isrealobj(delta):
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delta_k = fft3d(delta)
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else:
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delta_k = delta
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kvec = fftk(delta_k)
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# Computes gravitational potential
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pot_k = delta_k * laplace_kernel(kvec) * longrange_kernel(kvec,
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pot_k = delta_k * invlaplace_kernel(kvec) * longrange_kernel(kvec,
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r_split=r_split)
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# Computes gravitational forces
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forces = jnp.stack([
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cic_read_dx(ifft3d(gradient_kernel(kvec, i) * pot_k),
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cic_read_dx(ifft3d( - gradient_kernel(kvec, i) * pot_k),
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halo_size=halo_size,
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sharding=sharding) for i in range(3)
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],
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@ -49,44 +51,10 @@ def pm_forces(positions,
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return forces
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def lpt2_source(mesh_size, initial_conditions):
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kvec = fftk(mesh_size)
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# TODO : this has already been done for LPT1, we should reuse it
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delta_k = fft3d(initial_conditions)
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source = jnp.zeros_like(delta_k)
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D1 = [1, 2, 0]
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D2 = [2, 0, 1]
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# laplace_kernel should be actually inv laplace_kernel
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# adding a minus sign here that will be negated when computing forces
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# because F = -grad(phi)
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# and phi = -laplace_kernel(delta_k)
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pot_k = delta_k * laplace_kernel(delta_k)
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nabla_i_nabla_i = [
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ifft3d(gradient_kernel(kvec, i)**2 * pot_k) for i in range(3)
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]
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# for diagonal terms
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source += nabla_i_nabla_i[D1[0]] * nabla_i_nabla_i[D2[0]]
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source += nabla_i_nabla_i[D1[1]] * nabla_i_nabla_i[D2[1]]
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source += nabla_i_nabla_i[D1[2]] * nabla_i_nabla_i[D2[2]]
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# off diag terms
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for i in range(3):
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nabla_i_nabla_j = gradient_kernel(kvec, D1[i]) * gradient_kernel(
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kvec, D2[i])
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phi = ifft3d(nabla_i_nabla_j * pot_k)
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source -= phi**2
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return source
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def lpt(cosmo, initial_conditions, a, halo_size=0, sharding=None):
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def lpt(cosmo, initial_conditions, a, halo_size=0, sharding=None,order=1):
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"""
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Computes first order LPT displacement
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Computes first and second order LPT displacement and momentum,
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e.g. Eq. 2 and 3 [Jenkins2010](https://arxiv.org/pdf/0910.0258)
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"""
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gpu_mesh = sharding.mesh if sharding is not None else None
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spec = sharding.spec if sharding is not None else P()
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@ -99,48 +67,48 @@ def lpt(cosmo, initial_conditions, a, halo_size=0, sharding=None):
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out_specs=spec)() # yapf: disable
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a = jnp.atleast_1d(a)
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E = jnp.sqrt(jc.background.Esqr(cosmo, a))
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delta_k = fft3d(initial_conditions)
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initial_force = pm_forces(displacement,
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delta=initial_conditions,
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delta=delta_k,
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halo_size=halo_size,
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sharding=sharding)
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a = jnp.atleast_1d(a)
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dx = growth_factor(cosmo, a) * initial_force
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p = a**2 * growth_rate(cosmo, a) * jnp.sqrt(jc.background.Esqr(cosmo,
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a)) * dx
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f = a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dGfa(cosmo,
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a) * initial_force
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return dx, p, f
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p = a**2 * growth_rate(cosmo, a) * E * dx
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f = a**2 * E * dGfa(cosmo,a) * initial_force
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if order == 2:
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kvec = fftk(delta_k)
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pot_k = delta_k * invlaplace_kernel(kvec)
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delta2 = 0
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shear_acc = 0
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# for i, ki in enumerate(kvec):
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for i in range(3):
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# Add products of diagonal terms = 0 + s11*s00 + s22*(s11+s00)...
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# shear_ii = jnp.fft.irfftn(- ki**2 * pot_k)
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nabla_i_nabla_i = gradient_kernel(kvec, i)**2
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shear_ii = jnp.fft.irfftn(nabla_i_nabla_i * pot_k)
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delta2 += shear_ii * shear_acc
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shear_acc += shear_ii
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# @Credit Hugo Simon https://github.com/hsimonfroy/montecosmo
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def lpt2(cosmo, initial_conditions, dx, p, f, a, halo_size=0):
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# for kj in kvec[i+1:]:
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for j in range(i+1, 3):
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# Substract squared strict-up-triangle terms
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# delta2 -= jnp.fft.irfftn(- ki * kj * pot_k)**2
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nabla_i_nabla_j = gradient_kernel(kvec, i) * gradient_kernel(kvec, j)
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delta2 -= jnp.fft.irfftn(nabla_i_nabla_j * pot_k)**2
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delta_k2 = fft3d(delta2)
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init_force2 = pm_forces(displacement, delta=delta_k2,halo_size=halo_size,sharding=sharding)
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# NOTE: growth_factor_second is renormalized: - D2 = 3/7 * growth_factor_second
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dx2 = 3/7 * growth_factor_second(cosmo, a) * init_force2
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p2 = a**2 * growth_rate_second(cosmo, a) * E * dx2
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f2 = a**2 * E * dGf2a(cosmo, a) * init_force2
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mesh_size = initial_conditions.shape
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local_mesh_shape = (*get_local_shape(initial_conditions.shape), 3)
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# TODO
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# Displacements have been created in the previous step
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# find a way to reuse them
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displacement = autoshmap(
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partial(jnp.zeros, shape=(local_mesh_shape), dtype='float32'),
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in_specs=(),
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out_specs=P('x', 'y'))() # yapf: disable
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lpt2_delta = lpt2_source(mesh_size, initial_conditions)
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delta2_k = fft3d(lpt2_delta)
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lpt2_forces = pm_forces(displacement,
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mesh_size,
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delta_k=delta2_k,
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halo_size=halo_size)
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dx2 = 3 / 7 * growth_factor_second(cosmo, a) * lpt2_forces
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p2 = a**2 * growth_rate_second(cosmo, a) * jnp.sqrt(
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jc.background.Esqr(cosmo, a)) * dx2
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f2 = a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dGf2a(cosmo,
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a) * lpt2_forces
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dx += dx2
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p += p2
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f += f2
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dx += dx2
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p += p2
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f += f2
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return dx, p, f
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@ -185,10 +153,33 @@ def make_ode_fn(mesh_shape, halo_size=0, sharding=None):
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return nbody_ode
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def get_ode_fn(cosmo, mesh_shape, halo_size=0, sharding=None):
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def nbody_ode(a, state, args):
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"""
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State is an array [position, velocities]
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Compatible with [Diffrax API](https://docs.kidger.site/diffrax/)
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"""
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pos, vel = state
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forces = pm_forces(pos, mesh_shape, halo_size=halo_size, sharding=sharding) * 1.5 * cosmo.Omega_m
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# Computes the update of position (drift)
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dpos = 1. / (a**3 * jnp.sqrt(jc.background.Esqr(cosmo, a))) * vel
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# Computes the update of velocity (kick)
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dvel = 1. / (a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a))) * forces
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return jnp.stack([dpos, dvel])
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return nbody_ode
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def pgd_correction(pos, mesh_shape, params):
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"""
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improve the short-range interactions of PM-Nbody simulations with potential gradient descent method, based on https://arxiv.org/abs/1804.00671
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improve the short-range interactions of PM-Nbody simulations with potential gradient descent method,
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based on https://arxiv.org/abs/1804.00671
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args:
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pos: particle positions [npart, 3]
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params: [alpha, kl, ks] pgd parameters
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@ -197,24 +188,20 @@ def pgd_correction(pos, mesh_shape, params):
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delta = cic_paint(jnp.zeros(mesh_shape), pos)
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alpha, kl, ks = params
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delta_k = jnp.fft.rfftn(delta)
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PGD_range = PGD_kernel(kvec, kl, ks)
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pot_k_pgd = (delta_k * laplace_kernel(kvec)) * PGD_range
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forces_pgd = jnp.stack([
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cic_read(jnp.fft.irfftn(gradient_kernel(kvec, i) * pot_k_pgd), pos)
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for i in range(3)
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],
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axis=-1)
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dpos_pgd = forces_pgd * alpha
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PGD_range=PGD_kernel(kvec, kl, ks)
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pot_k_pgd=(delta_k * invlaplace_kernel(kvec))*PGD_range
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forces_pgd= jnp.stack([cic_read(jnp.fft.irfftn(- gradient_kernel(kvec, i)*pot_k_pgd), pos)
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for i in range(3)],axis=-1)
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dpos_pgd = forces_pgd*alpha
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return dpos_pgd
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def make_neural_ode_fn(model, mesh_shape):
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def neural_nbody_ode(state, a, cosmo, params):
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def neural_nbody_ode(state, a, cosmo:Cosmology, params):
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"""
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state is a tuple (position, velocities)
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"""
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@ -226,19 +213,15 @@ def make_neural_ode_fn(model, mesh_shape):
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delta_k = jnp.fft.rfftn(delta)
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# Computes gravitational potential
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pot_k = delta_k * laplace_kernel(kvec) * longrange_kernel(kvec,
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r_split=0)
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pot_k = delta_k * invlaplace_kernel(kvec) * longrange_kernel(kvec, r_split=0)
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# Apply a correction filter
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kk = jnp.sqrt(sum((ki / jnp.pi)**2 for ki in kvec))
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pot_k = pot_k * (1. + model.apply(params, kk, jnp.atleast_1d(a)))
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kk = jnp.sqrt(sum((ki/jnp.pi)**2 for ki in kvec))
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pot_k = pot_k *(1. + model.apply(params, kk, jnp.atleast_1d(a)))
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# Computes gravitational forces
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forces = jnp.stack([
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cic_read(jnp.fft.irfftn(gradient_kernel(kvec, i) * pot_k), pos)
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for i in range(3)
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],
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axis=-1)
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forces = jnp.stack([cic_read(jnp.fft.irfftn(- gradient_kernel(kvec, i)*pot_k), pos)
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for i in range(3)],axis=-1)
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forces = forces * 1.5 * cosmo.Omega_m
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@ -249,5 +232,4 @@ def make_neural_ode_fn(model, mesh_shape):
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dvel = 1. / (a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a))) * forces
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return dpos, dvel
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return neural_nbody_ode
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