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Expand file tree Collapse file tree Original file line number Diff line number Diff line change 3434@BaseFitting .register ("dipole" )
3535@fitting_check_output
3636class DipoleFitting (GeneralFitting ):
37- r"""Fitting rotationally equivariant diploe of the system.
37+ r"""Fitting rotationally equivariant dipole of the system.
38+
39+ The dipole :math:`\boldsymbol{\mu}` is computed from the fitting network output
40+ and the rotation matrix:
41+
42+ .. math::
43+ \boldsymbol{\mu}^i = \mathbf{M}^i \cdot \mathbf{R}^i,
44+
45+ where :math:`\mathbf{M}^i \in \mathbb{R}^{1 \times m_1}` is the output of the fitting
46+ network for atom :math:`i`, and :math:`\mathbf{R}^i \in \mathbb{R}^{m_1 \times 3}` is
47+ the rotation matrix from the descriptor. The fitting network is:
48+
49+ .. math::
50+ \mathbf{M}^i = \mathcal{L}^{(n)} \circ \mathcal{L}^{(n-1)} \circ \cdots \circ \mathcal{L}^{(0)}(\mathcal{D}^i),
51+
52+ where :math:`\mathcal{D}^i` is the descriptor and each layer :math:`\mathcal{L}^{(k)}`
53+ is a fully connected layer with activation function.
3854
3955 Parameters
4056 ----------
Original file line number Diff line number Diff line change 4444class PolarFitting (GeneralFitting ):
4545 r"""Fitting rotationally equivariant polarizability of the system.
4646
47+ The polarizability tensor :math:`\boldsymbol{\alpha} \in \mathbb{R}^{3 \times 3}` is
48+ computed from the fitting network output and the rotation matrix:
49+
50+ **Diagonal fitting** (when `fit_diag=True`):
51+
52+ .. math::
53+ \boldsymbol{\alpha}^i = \mathbf{R}^{i,T} \cdot \mathrm{diag}(\mathbf{p}^i) \cdot \mathbf{R}^i,
54+
55+ where :math:`\mathbf{p}^i \in \mathbb{R}^{m_1}` is the diagonal elements predicted by
56+ the fitting network.
57+
58+ **Full matrix fitting** (when `fit_diag=False`):
59+
60+ .. math::
61+ \boldsymbol{\alpha}^i = \mathbf{R}^{i,T} \cdot \mathbf{P}^i \cdot \mathbf{R}^i,
62+
63+ where :math:`\mathbf{P}^i \in \mathbb{R}^{m_1 \times m_1}` is the full matrix predicted
64+ by the fitting network.
65+
66+ The fitting network is:
67+
68+ .. math::
69+ \mathbf{p}^i \text{ (or } \mathbf{P}^i) = \mathcal{L}^{(n)} \circ \cdots \circ \mathcal{L}^{(0)}(\mathcal{D}^i).
70+
4771 Parameters
4872 ----------
4973 ntypes
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