mirror of
https://github.com/DifferentiableUniverseInitiative/JaxPM.git
synced 2025-04-07 12:20:54 +00:00
230 lines
7.5 KiB
Python
230 lines
7.5 KiB
Python
from functools import partial
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import jax
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import jax.numpy as jnp
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import jax_cosmo as jc
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from jax.sharding import PartitionSpec as P
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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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longrange_kernel)
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from jaxpm.painting import cic_paint, cic_paint_dx, cic_read, cic_read_dx
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def pm_forces(positions, mesh_shape=None, delta=None, r_split=0, halo_size=0):
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"""
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Computes gravitational forces on particles using a PM scheme
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"""
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if mesh_shape is None:
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assert (delta is not None
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), "If mesh_shape is not provided, delta should be provided"
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mesh_shape = delta.shape
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kvec = fftk(mesh_shape)
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if delta is None:
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delta_k = fft3d(cic_paint_dx(positions, halo_size=halo_size))
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else:
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delta_k = fft3d(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=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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halo_size=halo_size) for i in range(3)
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],
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axis=-1)
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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):
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"""
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Computes first order LPT displacement
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"""
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local_mesh_shape = (*get_local_shape(initial_conditions.shape), 3)
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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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initial_force = pm_forces(displacement,
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delta=initial_conditions,
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halo_size=halo_size)
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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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# @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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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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return dx, p, f
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def linear_field(mesh_shape, box_size, pk, seed):
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"""
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Generate initial conditions.
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"""
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kvec = fftk(mesh_shape)
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kmesh = sum((kk / box_size[i] * mesh_shape[i])**2
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for i, kk in enumerate(kvec))**0.5
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pkmesh = pk(kmesh) * (mesh_shape[0] * mesh_shape[1] * mesh_shape[2]) / (
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box_size[0] * box_size[1] * box_size[2])
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# Initialize a random field with one slice on each gpu
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field = normal_field(mesh_shape, seed=seed)
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field = fft3d(field) * pkmesh**0.5
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field = ifft3d(field)
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return field
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def make_ode_fn(mesh_shape, halo_size=0):
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def nbody_ode(state, a, cosmo):
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"""
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state is a tuple (position, velocities)
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"""
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pos, vel = state
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forces = pm_forces(pos, mesh_shape=mesh_shape,
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halo_size=halo_size) * 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 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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args:
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pos: particle positions [npart, 3]
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params: [alpha, kl, ks] pgd parameters
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"""
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kvec = fftk(mesh_shape)
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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([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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"""
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state is a tuple (position, velocities)
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"""
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pos, vel = state
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kvec = fftk(mesh_shape)
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delta = cic_paint(jnp.zeros(mesh_shape), pos)
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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, 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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# Computes gravitational forces
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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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# 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 dpos, dvel
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return neural_nbody_ode
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