Feat: add pair table model to pytorch (#3192)

Migrated from this
[PR](dptech-corp/deepmd-pytorch#174). This is to
reimplement the PairTab Model in Pytorch.

Notes:

1. Different from the tensorflow version, the pytorch version abstracts
away all the post energy conversion operations (force, virial).
2. Added extrapolation when `rcut` > `rmax`. The pytorch version
overwrite energy beyond extrapolation endpoint to `0`. These features
are not available in the tensorflow version. The extrapolation uses a
cubic spline form, the 1st order derivation for the starting point is
estimated using the last two rows in the user defined table. See example
below:


![img_v3_027k_b50c690d-dc2d-4803-bd2c-2e73aa3c73fg](https://github.com/deepmodeling/deepmd-kit/assets/137014849/f3efa4d3-795e-4ff8-acdc-642227f0e19c)


![img_v3_027k_8de38597-ef4e-4e5b-989e-dbd13cc93fag](https://github.com/deepmodeling/deepmd-kit/assets/137014849/493da26d-f01d-4dd0-8520-ea2d84e7b548)


![img_v3_027k_f8268564-3f5d-49e6-91d6-169a61d9347g](https://github.com/deepmodeling/deepmd-kit/assets/137014849/b8ad4d4d-a4a4-40f0-94d1-810006e7175b)


![img_v3_027k_3966ef67-dd5e-4f48-992e-c2763311451g](https://github.com/deepmodeling/deepmd-kit/assets/137014849/27f31e79-13c8-4ce8-9911-b4cc0ac8188c)

---------

Co-authored-by: Anyang Peng <aisi_ap@Anyangs-Laptop.local>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

deepmd/pt/model/model/pair_tab.py

@@ -0,0 +1,312 @@
+# SPDX-License-Identifier: LGPL-3.0-or-later
+from typing import (
+    Dict,
+    List,
+    Optional,
+    Union,
+)
+
+import torch
+from torch import (
+    nn,
+)
+
+from deepmd.model_format import (
+    FittingOutputDef,
+    OutputVariableDef,
+)
+from deepmd.utils.pair_tab import (
+    PairTab,
+)
+
+from .atomic_model import (
+    AtomicModel,
+)
+
+
+class PairTabModel(nn.Module, AtomicModel):
+    """Pairwise tabulation energy model.
+
+    This model can be used to tabulate the pairwise energy between atoms for either
+    short-range or long-range interactions, such as D3, LJ, ZBL, etc. It should not
+    be used alone, but rather as one submodel of a linear (sum) model, such as
+    DP+D3.
+
+    Do not put the model on the first model of a linear model, since the linear
+    model fetches the type map from the first model.
+
+    At this moment, the model does not smooth the energy at the cutoff radius, so
+    one needs to make sure the energy has been smoothed to zero.
+
+    Parameters
+    ----------
+    tab_file : str
+        The path to the tabulation file.
+    rcut : float
+        The cutoff radius.
+    sel : int or list[int]
+        The maxmum number of atoms in the cut-off radius.
+    """
+
+    def __init__(
+        self, tab_file: str, rcut: float, sel: Union[int, List[int]], **kwargs
+    ):
+        super().__init__()
+        self.tab_file = tab_file
+        self.rcut = rcut
+
+        self.tab = PairTab(self.tab_file, rcut=rcut)
+        self.ntypes = self.tab.ntypes
+
+        tab_info, tab_data = self.tab.get()  # this returns -> Tuple[np.array, np.array]
+        self.tab_info = torch.from_numpy(tab_info)
+        self.tab_data = torch.from_numpy(tab_data)
+
+        # self.model_type = "ener"
+        # self.model_version = MODEL_VERSION ## this shoud be in the parent class
+
+        if isinstance(sel, int):
+            self.sel = sel
+        elif isinstance(sel, list):
+            self.sel = sum(sel)
+        else:
+            raise TypeError("sel must be int or list[int]")
+
+    def get_fitting_output_def(self) -> FittingOutputDef:
+        return FittingOutputDef(
+            [
+                OutputVariableDef(
+                    name="energy", shape=[1], reduciable=True, differentiable=True
+                )
+            ]
+        )
+
+    def get_rcut(self) -> float:
+        return self.rcut
+
+    def get_sel(self) -> int:
+        return self.sel
+
+    def distinguish_types(self) -> bool:
+        # to match DPA1 and DPA2.
+        return False
+
+    def forward_atomic(
+        self,
+        extended_coord,
+        extended_atype,
+        nlist,
+        mapping: Optional[torch.Tensor] = None,
+        do_atomic_virial: bool = False,
+    ) -> Dict[str, torch.Tensor]:
+        self.nframes, self.nloc, self.nnei = nlist.shape
+
+        # this will mask all -1 in the nlist
+        masked_nlist = torch.clamp(nlist, 0)
+
+        atype = extended_atype[:, : self.nloc]  # (nframes, nloc)
+        pairwise_dr = self._get_pairwise_dist(
+            extended_coord
+        )  # (nframes, nall, nall, 3)
+        pairwise_rr = pairwise_dr.pow(2).sum(-1).sqrt()  # (nframes, nall, nall)
+
+        self.tab_data = self.tab_data.reshape(
+            self.tab.ntypes, self.tab.ntypes, self.tab.nspline, 4
+        )
+
+        # to calculate the atomic_energy, we need 3 tensors, i_type, j_type, rr
+        # i_type : (nframes, nloc), this is atype.
+        # j_type : (nframes, nloc, nnei)
+        j_type = extended_atype[
+            torch.arange(extended_atype.size(0))[:, None, None], masked_nlist
+        ]
+
+        # slice rr to get (nframes, nloc, nnei)
+        rr = torch.gather(pairwise_rr[:, : self.nloc, :], 2, masked_nlist)
+
+        raw_atomic_energy = self._pair_tabulated_inter(nlist, atype, j_type, rr)
+
+        atomic_energy = 0.5 * torch.sum(
+            torch.where(
+                nlist != -1, raw_atomic_energy, torch.zeros_like(raw_atomic_energy)
+            ),
+            dim=-1,
+        )
+
+        return {"energy": atomic_energy}
+
+    def _pair_tabulated_inter(
+        self,
+        nlist: torch.Tensor,
+        i_type: torch.Tensor,
+        j_type: torch.Tensor,
+        rr: torch.Tensor,
+    ) -> torch.Tensor:
+        """Pairwise tabulated energy.
+
+        Parameters
+        ----------
+        nlist : torch.Tensor
+            The unmasked neighbour list. (nframes, nloc)
+        i_type : torch.Tensor
+            The integer representation of atom type for all local atoms for all frames. (nframes, nloc)
+        j_type : torch.Tensor
+            The integer representation of atom type for all neighbour atoms of all local atoms for all frames. (nframes, nloc, nnei)
+        rr : torch.Tensor
+            The salar distance vector between two atoms. (nframes, nloc, nnei)
+
+        Returns
+        -------
+        torch.Tensor
+            The masked atomic energy for all local atoms for all frames. (nframes, nloc, nnei)
+
+        Raises
+        ------
+        Exception
+            If the distance is beyond the table.
+
+        Notes
+        -----
+        This function is used to calculate the pairwise energy between two atoms.
+        It uses a table containing cubic spline coefficients calculated in PairTab.
+        """
+        rmin = self.tab_info[0]
+        hh = self.tab_info[1]
+        hi = 1.0 / hh
+
+        self.nspline = int(self.tab_info[2] + 0.1)
+
+        uu = (rr - rmin) * hi  # this is broadcasted to (nframes,nloc,nnei)
+
+        # if nnei of atom 0 has -1 in the nlist, uu would be 0.
+        # this is to handle the nlist where the mask is set to 0, so that we don't raise exception for those atoms.
+        uu = torch.where(nlist != -1, uu, self.nspline + 1)
+
+        if torch.any(uu < 0):
+            raise Exception("coord go beyond table lower boundary")
+
+        idx = uu.to(torch.int)
+
+        uu -= idx
+
+        table_coef = self._extract_spline_coefficient(
+            i_type, j_type, idx, self.tab_data, self.nspline
+        )
+        table_coef = table_coef.reshape(self.nframes, self.nloc, self.nnei, 4)
+        ener = self._calcualte_ener(table_coef, uu)
+
+        # here we need to overwrite energy to zero at rcut and beyond.
+        mask_beyond_rcut = rr >= self.rcut
+        # also overwrite values beyond extrapolation to zero
+        extrapolation_mask = rr >= self.tab.rmin + self.nspline * self.tab.hh
+        ener[mask_beyond_rcut] = 0
+        ener[extrapolation_mask] = 0
+
+        return ener
+
+    @staticmethod
+    def _get_pairwise_dist(coords: torch.Tensor) -> torch.Tensor:
+        """Get pairwise distance `dr`.
+
+        Parameters
+        ----------
+        coords : torch.Tensor
+            The coordinate of the atoms shape of (nframes * nall * 3).
+
+        Returns
+        -------
+        torch.Tensor
+            The pairwise distance between the atoms (nframes * nall * nall * 3).
+
+        Examples
+        --------
+        coords = torch.tensor([[
+                [0,0,0],
+                [1,3,5],
+                [2,4,6]
+            ]])
+
+        dist = tensor([[
+            [[ 0,  0,  0],
+            [-1, -3, -5],
+            [-2, -4, -6]],
+
+            [[ 1,  3,  5],
+            [ 0,  0,  0],
+            [-1, -1, -1]],
+
+            [[ 2,  4,  6],
+            [ 1,  1,  1],
+            [ 0,  0,  0]]
+            ]])
+        """
+        return coords.unsqueeze(2) - coords.unsqueeze(1)
+
+    @staticmethod
+    def _extract_spline_coefficient(
+        i_type: torch.Tensor,
+        j_type: torch.Tensor,
+        idx: torch.Tensor,
+        tab_data: torch.Tensor,
+        nspline: int,
+    ) -> torch.Tensor:
+        """Extract the spline coefficient from the table.
+
+        Parameters
+        ----------
+        i_type : torch.Tensor
+            The integer representation of atom type for all local atoms for all frames. (nframes, nloc)
+        j_type : torch.Tensor
+            The integer representation of atom type for all neighbour atoms of all local atoms for all frames. (nframes, nloc, nnei)
+        idx : torch.Tensor
+            The index of the spline coefficient. (nframes, nloc, nnei)
+        tab_data : torch.Tensor
+            The table storing all the spline coefficient. (ntype, ntype, nspline, 4)
+        nspline : int
+            The number of splines in the table.
+
+        Returns
+        -------
+        torch.Tensor
+            The spline coefficient. (nframes, nloc, nnei, 4), shape may be squeezed.
+
+        """
+        # (nframes, nloc, nnei)
+        expanded_i_type = i_type.unsqueeze(-1).expand(-1, -1, j_type.shape[-1])
+
+        # (nframes, nloc, nnei, nspline, 4)
+        expanded_tab_data = tab_data[expanded_i_type, j_type]
+
+        # (nframes, nloc, nnei, 1, 4)
+        expanded_idx = idx.unsqueeze(-1).unsqueeze(-1).expand(-1, -1, -1, -1, 4)
+
+        # handle the case where idx is beyond the number of splines
+        clipped_indices = torch.clamp(expanded_idx, 0, nspline - 1).to(torch.int64)
+
+        # (nframes, nloc, nnei, 4)
+        final_coef = torch.gather(expanded_tab_data, 3, clipped_indices).squeeze()
+
+        # when the spline idx is beyond the table, all spline coefficients are set to `0`, and the resulting ener corresponding to the idx is also `0`.
+        final_coef[expanded_idx.squeeze() > nspline] = 0
+        return final_coef
+
+    @staticmethod
+    def _calcualte_ener(coef: torch.Tensor, uu: torch.Tensor) -> torch.Tensor:
+        """Calculate energy using spline coeeficients.
+
+        Parameters
+        ----------
+        coef : torch.Tensor
+            The spline coefficients. (nframes, nloc, nnei, 4)
+        uu : torch.Tensor
+            The atom displancemnt used in interpolation and extrapolation (nframes, nloc, nnei)
+
+        Returns
+        -------
+        torch.Tensor
+            The atomic energy for all local atoms for all frames. (nframes, nloc, nnei)
+        """
+        a3, a2, a1, a0 = torch.unbind(coef, dim=-1)
+        etmp = (a3 * uu + a2) * uu + a1  # this should be elementwise operations.
+        ener = etmp * uu + a0  # this energy has the extrapolated value when rcut > rmax
+        return ener