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#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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from typing import Optional
import jax
import jax.numpy as jnp
import numpy as np
from functools import partial
from flax import struct
from .base import MetropolisRule
import netket.jax as nkjax
[docs]
class LangevinRule(MetropolisRule):
r"""
A transition rule that uses Langevin dynamics [1] to update samples.
.. math::
x_{t+dt} = x_t + dt \nabla_x \log p(x) \vert_{x=x_t} + \sqrt{2 dt}\eta,
where :math:`\eta` is normal distributed noise :math:`\eta \sim \mathcal{N}(0,1)`.
This rule only works for continuous Hilbert spaces.
[1]: https://en.wikipedia.org/wiki/Metropolis-adjusted_Langevin_algorithm
"""
dt: float
"""Time step in the Langevin dynamics."""
chunk_size: Optional[int] = struct.field(pytree_node=False)
"""Chunk size for computing gradients of the ansatz."""
[docs]
def __init__(self, dt: float = 0.001, chunk_size: Optional[int] = None):
"""
Constructs the Langevin Hastings proposal rule.
Args:
dt: the timestep for the langevin dynamics (default=0.001)
chunk_size: optional chunk size to reduce memory usage
"""
self.dt = dt
self.chunk_size = chunk_size
[docs]
def transition(rule, sampler, machine, parameters, state, key, r):
if jnp.issubdtype(r.dtype, jnp.complexfloating):
raise TypeError("LangevinRule does not work with complex basis elements.")
n_chains = r.shape[0]
hilb = sampler.hilbert
pbc = np.array(hilb.n_particles * hilb.pbc, dtype=r.dtype)
boundary = np.tile(pbc, (n_chains, 1))
Ls = np.array(hilb.n_particles * hilb.extent, dtype=r.dtype)
modulus = np.where(np.equal(pbc, False), jnp.inf, Ls)
# one langevin step
rp, log_corr = _langevin_step(
key,
r,
machine.apply,
parameters,
sampler.machine_pow,
rule.dt,
chunk_size=rule.chunk_size,
return_log_corr=True,
)
rp = jnp.where(np.equal(boundary, False), rp, rp % modulus)
return rp, log_corr
def __repr__(self):
return f"LangevinRule(dt={self.dt})"
@partial(jax.jit, static_argnames=("apply_fun", "chunk_size", "return_log_corr"))
def _langevin_step(
key,
r,
apply_fun,
parameters,
machine_pow,
dt,
chunk_size=None,
return_log_corr=True,
):
"""Single step of samples with Langevin dynamics"""
n_chains, hilb_size = r.shape
# steps with Langevin dynamics
noise_vec = jax.random.normal(key, shape=(n_chains, hilb_size), dtype=r.dtype)
def _log_prob(x):
"""Conversion to a log probability"""
return machine_pow * apply_fun(parameters, x).real
def _single_grad(x):
"""Derivative of log_prob with respect to a single sample x"""
x = x.reshape(x.shape[-1])
g = nkjax.grad(lambda xi: _log_prob(xi).ravel()[0])(x)
return g if jnp.iscomplexobj(r) else g.real
grad_logp_r = nkjax.vmap_chunked(_single_grad, chunk_size=chunk_size)(r)
rp = r + dt * grad_logp_r + jnp.sqrt(2 * dt) * noise_vec
if not return_log_corr:
return rp
else:
log_q_xp = -0.5 * jnp.sum(noise_vec**2, axis=-1)
grad_logp_rp = nkjax.vmap_chunked(_single_grad, chunk_size=chunk_size)(rp)
log_q_x = -jnp.sum((r - rp - dt * grad_logp_rp) ** 2, axis=-1) / (4 * dt)
return rp, log_q_x - log_q_xp
