forked from Aquila-Consortium/JaxPM_highres
196 lines
6.4 KiB
Python
196 lines
6.4 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 jax_cosmo import Cosmology
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from jaxpm.growth import growth_factor, growth_rate, dGfa, growth_factor_second, growth_rate_second, dGf2a
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from jaxpm.kernels import PGD_kernel, fftk, gradient_kernel, invlaplace_kernel, longrange_kernel
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from jaxpm.painting import cic_paint, cic_read
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def pm_forces(positions, mesh_shape, 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 delta is None:
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delta_k = jnp.fft.rfftn(cic_paint(jnp.zeros(mesh_shape), positions))
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elif jnp.isrealobj(delta):
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delta_k = jnp.fft.rfftn(delta)
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else:
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delta_k = delta
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# Computes gravitational potential
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kvec = fftk(mesh_shape)
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pot_k = delta_k * invlaplace_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:Cosmology, init_mesh, positions, a, order=1):
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"""
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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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a = jnp.atleast_1d(a)
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E = jnp.sqrt(jc.background.Esqr(cosmo, a))
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delta_k = jnp.fft.rfftn(init_mesh) # TODO: pass the modes directly to save one or two fft?
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mesh_shape = init_mesh.shape
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init_force = pm_forces(positions, mesh_shape, delta=delta_k)
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dx = growth_factor(cosmo, a) * init_force
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p = a**2 * growth_rate(cosmo, a) * E * dx
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f = a**2 * E * dGfa(cosmo, a) * init_force
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if order == 2:
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kvec = fftk(mesh_shape)
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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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# 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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init_force2 = pm_forces(positions, mesh_shape, delta=jnp.fft.rfftn(delta2))
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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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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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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 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 get_ode_fn(cosmo:Cosmology, mesh_shape):
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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) * 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,
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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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"""
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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 * 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:Cosmology, 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 * 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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# 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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