mirror of
https://github.com/DifferentiableUniverseInitiative/JaxPM.git
synced 2025-02-23 18:10:55 +00:00
131 lines
No EOL
4.4 KiB
Python
131 lines
No EOL
4.4 KiB
Python
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 jaxpm.kernels import fftk, gradient_kernel, laplace_kernel, longrange_kernel, PGD_kernel
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from jaxpm.painting import cic_paint, cic_read
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from jaxpm.growth import growth_factor, growth_rate, dGfa
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def pm_forces(positions, mesh_shape=None, delta=None, r_split=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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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 = jnp.fft.rfftn(cic_paint(jnp.zeros(mesh_shape), positions))
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else:
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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=r_split)
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# Computes gravitational forces
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return jnp.stack([cic_read(jnp.fft.irfftn(gradient_kernel(kvec, i)*pot_k), positions)
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for i in range(3)],axis=-1)
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def lpt(cosmo, initial_conditions, positions, a):
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"""
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Computes first order LPT displacement
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"""
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initial_force = pm_forces(positions, delta=initial_conditions)
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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, a)) * dx
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f = a**2 * jnp.sqrt(jc.background.Esqr(cosmo, a)) * dGfa(cosmo, a) * initial_force
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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 for i, kk in enumerate(kvec))**0.5
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pkmesh = pk(kmesh) * (mesh_shape[0] * mesh_shape[1] * mesh_shape[2]) / (box_size[0] * box_size[1] * box_size[2])
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field = jax.random.normal(seed, mesh_shape)
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field = jnp.fft.rfftn(field) * pkmesh**0.5
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field = jnp.fft.irfftn(field)
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return field
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def box_muller_field(amplitude, phase, pkmesh):
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"""
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Obtain Gaussian random field given uniform random numbers and Pk amplitude.
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"""
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field = pkmesh**0.5 * jnp.sqrt(-jnp.log(amplitude)) * (jnp.cos(phase) + 1j * jnp.sin(phase))
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return jnp.fft.irfftn(field, (amplitude.shape[0],)*3, norm='ortho')
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def linear_field_box_muller(mesh_shape, box_size, pk, seed, fixamp = False, inv_phase = False):
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"""
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Generate initial conditions with fixed amplitude and/or inverted phase.
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"""
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key, subkey1, subkey2 = jax.random.split(seed, 3)
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kvec = fftk(mesh_shape)
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kmesh = sum((kk / box_size[i] * mesh_shape[i])**2 for i, kk in enumerate(kvec))**0.5
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pkmesh = pk(kmesh) * (mesh_shape[0] * mesh_shape[1] * mesh_shape[2]) / (box_size[0] * box_size[1] * box_size[2])
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if fixamp:
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amplitude = jnp.ones_like(kmesh)
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else:
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amplitude = jax.random.uniform(subkey1, kmesh.shape, minval=1e-8)
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if inv_phase:
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phase = jax.random.uniform(subkey2, kmesh.shape, minval=1e-8) * 2 * jnp.pi
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ret = []
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ret.append(box_muller_field(amplitude, phase, pkmesh))
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phase = (phase + jnp.pi)
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ret.append(box_muller_field(amplitude, phase, pkmesh))
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return ret
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return box_muller_field(amplitude, phase, pkmesh)
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def make_ode_fn(mesh_shape):
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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) * 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, 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 |