import torch
from torch import nn
from .backflow_kernel_base import BackFlowKernelBase
[docs]class BackFlowKernelInverse(BackFlowKernelBase):
def __init__(self, mol, cuda=False):
"""Compute the back flow kernel, i.e. the function
f(rij) where rij is the distance between electron i and j
This kernel is used in the backflow transformation
.. math:
q_i = r_i + \\sum_{j\\neq i} f(r_{ij}) (r_i-r_j)
with here :
.. math:
f(r_{ij) = \\frac{w}{r_{ij}
"""
super().__init__(mol, cuda)
self.weight = nn.Parameter(
torch.as_tensor([1E-3])) # .to(self.device)
def _backflow_kernel(self, ree):
"""Computes the backflow kernel:
.. math:
\\eta(r_{ij}) = \\frac{w}{r_{ij}}
Args:
r (torch.tensor): e-e distance Nbatch x Nelec x Nelec
Returns:
torch.tensor : f(r) Nbatch x Nelec x Nelec
"""
eye = torch.eye(self.nelec, self.nelec).to(self.device)
mask = torch.ones_like(ree) - eye
return self.weight * mask * (1./(ree+eye) - eye)
def _backflow_kernel_derivative(self, ree):
"""Computes the derivative of the kernel function
w.r.t r_{ij}
.. math::
\\frac{d}{dr_{ij} \\eta(r_{ij}) = -w r_{ij}^{-2}
Args:
ree (torch.tensor): e-e distance Nbatch x Nelec x Nelec
Returns:
torch.tensor : f'(r) Nbatch x Nelec x Nelec
"""
eye = torch.eye(self.nelec, self.nelec).to(self.device)
invree = (1./(ree+eye) - eye)
return - self.weight * invree * invree
def _backflow_kernel_second_derivative(self, ree):
"""Computes the derivative of the kernel function
w.r.t r_{ij}
.. math::
\\frac{d^2}{dr_{ij}^2} \\eta(r_{ij}) = 2 w r_{ij}^{-3}
Args:
ree (torch.tensor): e-e distance Nbatch x Nelec x Nelec
Returns:
torch.tensor : f''(r) Nbatch x Nelec x Nelec
"""
eye = torch.eye(self.nelec, self.nelec).to(self.device)
invree = (1./(ree+eye) - eye)
return 2 * self.weight * invree * invree * invree