perf: use torch.topk to construct nlist (#4751)

This pull request updates the `build_neighbor_list` function in
`deepmd/pt/utils/nlist.py` to improve its performance and correctness
when selecting neighbors. The key change involves replacing `torch.sort`
with `torch.topk` to optimize the selection of the nearest neighbors.

<details><summary>Details</summary>
<p>
Before: 16.4ms
<img width="495" alt="image"
src="https://github.com/user-attachments/assets/e6b0c091-b11b-491a-b2fd-e0aadc6c35ba"
/>

After: 3.4ms
<img width="303" alt="image"
src="https://github.com/user-attachments/assets/81931c76-60eb-46a5-9934-0d837b954df9"
/>

Step time goes from 212.5ms to 200.5ms, ~5% speed-up.

</p>
</details> 

<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

- **Refactor**
- Enhanced efficiency and clarity in neighbor selection, improving
performance in identifying closest neighbors while maintaining the same
user experience.
- **Tests**
- Improved reliability of neighbor list tests by validating neighbor
sets regardless of order.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

---------

Signed-off-by: Chun Cai <amoycaic@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

Author: 3 people

deepmd/pt/utils/nlist.py

@@ -93,33 +93,43 @@ def build_neighbor_list(
 
     """
     batch_size = coord.shape[0]
-    coord = coord.view(batch_size, -1)
     nall = coord.shape[1] // 3
     # fill virtual atoms with large coords so they are not neighbors of any
     # real atom.
     if coord.numel() > 0:
         xmax = torch.max(coord) + 2.0 * rcut
     else:
         xmax = torch.zeros(1, dtype=coord.dtype, device=coord.device) + 2.0 * rcut
+
+    coord_xyz = coord.view(batch_size, nall, 3)
     # nf x nall
     is_vir = atype < 0
-    coord1 = torch.where(
-        is_vir[:, :, None], xmax, coord.view(batch_size, nall, 3)
-    ).view(batch_size, nall * 3)
+    # batch_size x nall x 3
+    vcoord_xyz = torch.where(is_vir[:, :, None], xmax, coord_xyz)
     if isinstance(sel, int):
         sel = [sel]
-    # nloc x 3
-    coord0 = coord1[:, : nloc * 3]
-    # nloc x nall x 3
-    diff = coord1.view([batch_size, -1, 3]).unsqueeze(1) - coord0.view(
-        [batch_size, -1, 3]
-    ).unsqueeze(2)
-    assert list(diff.shape) == [batch_size, nloc, nall, 3]
+
+    # Get the coordinates for the local atoms (first nloc atoms)
+    # batch_size x nloc x 3
+    vcoord_local_xyz = vcoord_xyz[:, :nloc, :]
+
+    # Calculate displacement vectors.
+    diff = vcoord_xyz.unsqueeze(1) - vcoord_local_xyz.unsqueeze(2)
+    assert diff.shape == (batch_size, nloc, nall, 3)
     # nloc x nall
     rr = torch.linalg.norm(diff, dim=-1)
     # if central atom has two zero distances, sorting sometimes can not exclude itself
-    rr -= torch.eye(nloc, nall, dtype=rr.dtype, device=rr.device).unsqueeze(0)
-    rr, nlist = torch.sort(rr, dim=-1)
+    # The following operation makes rr[b, i, i] = -1.0 (assuming original self-distance is 0)
+    # so that self-atom is sorted first.
+    diag_len = min(nloc, nall)
+    idx = torch.arange(diag_len, device=rr.device, dtype=torch.int)
+    rr[:, idx, idx] -= 1.0
+
+    nsel = sum(sel)
+    nnei = rr.shape[-1]
+    top_k = min(nsel + 1, nnei)
+    rr, nlist = torch.topk(rr, top_k, largest=False)
+
     # nloc x (nall-1)
     rr = rr[:, :, 1:]
     nlist = nlist[:, :, 1:]

source/tests/pt/model/test_nlist.py

@@ -152,13 +152,17 @@ def test_build_multiple_nlist(self) -> None:
                 nlists[get_multiple_nlist_key(rcuts[dd], nsels[dd])].shape[-1],
                 nsels[dd],
             )
+
+        # Since the nlist is created using unstable sort,
+        # we check if the set of indices in the nlist matches,
+        # regardless of the order
         torch.testing.assert_close(
-            nlists[get_multiple_nlist_key(rcuts[0], nsels[0])],
-            nlist0,
+            nlists[get_multiple_nlist_key(rcuts[0], nsels[0])].sort(dim=-1).values,
+            nlist0.sort(dim=-1).values,
         )
         torch.testing.assert_close(
-            nlists[get_multiple_nlist_key(rcuts[1], nsels[1])],
-            nlist2,
+            nlists[get_multiple_nlist_key(rcuts[1], nsels[1])].sort(dim=-1).values,
+            nlist2.sort(dim=-1).values,
         )
 
     def test_extend_coord(self) -> None: