tasks/task_020/instruction.md

Complete the edge-graph scientific capability

The source tree is a real intermediate snapshot from the development of an atomistic-model backend. It contains the first public data contract for a NeighborGraph, but the surrounding scientific capability is incomplete.

A downstream model must be able to start from atom coordinates and, for both ordinary and periodic systems, construct a graph whose edges represent the neighbor displacements used by the potential-energy model. The same graph must remain usable when the number of edges is padded for a compiled/static backend. Per-edge energy derivatives must then be transformed into per-atom forces, per-atom virials, and one virial for each frame. Empty frames, isolated atoms, virtual atoms, periodic-image neighbors, and padded guard edges are all valid scientific situations rather than exceptional test-only cases.

Inspect the source context, run python reproduce.py, and complete the reusable capability under source/. Preserve the public data contract where it is already meaningful, and keep the implementation usable with NumPy and the array-API style used by the source snapshot.

The package-level public API for the completed capability is explicit. Export these names from deepmd.dpmodel.utils (the implementation may live in any module under deepmd/dpmodel/utils/):

• build_neighbor_graph
• from_dense_quartet
• node_validity_mask
• segment_sum and segment_mean
• edge_force_virial

The file layout is your choice; hidden verification checks these public behaviors through the package namespace rather than requiring a particular internal module split.

The derivative contract is also part of the public behavior. For edge_vec = r_src - r_dst and g = dE / d(edge_vec), use

F_k = sum(g for edges with dst=k) - sum(g for edges with src=k)
edge_virial = -outer(g, edge_vec)

Attribute a complete edge virial to its source atom, ignore masked guard edges, and return one (3, 3) virial per frame. Reject non-positive cutoffs and inconsistent coordinate, type, or cell shapes with ValueError rather than silently producing an empty or misaligned graph.

The result must be a coherent workflow, not a fixture-specific patch. It must support more than the public coordinates, more than one frame, and more than one edge count. Do not hard-code atom indices, distances, edge counts, force values, or a particular periodic cell. Keep the sign and tensor-layout conventions explicit in code and documentation so a downstream model can rely on them.

The public reproduction is only a starting point. A successful solution must also preserve ordinary non-periodic behavior while adding the missing general scientific cases.