TopoPID: Residual-Guided Equipment Recognition and Graph Completion in P&IDs

Digitizing a piping and instrumentation diagram (P&ID) requires an auditable process graph, not just detected symbols. Project-specific equipment often lacks visual exemplars: closed-vocabulary pipelines preserve structure but miss such devices, whereas whole-page vision–language models (VLMs) face dense visual search and cannot directly authorize graph edits. We formulate recovery as residual-guided constrained semantic completion of a partially observed graph. In TopoPID, unresolved topology localizes equipment-scale candidates, a project roster constrains local VLM verification, and deterministic rules govern evidence-linked graph updates. On 45 held-out industrial P&IDs, with target-equipment images excluded from detector development, prompt demonstrations, and candidate tuning, identity-aware recognition F1 rises from 19.44% for whole-page inference to 93.77%; 489/524 devices are correctly recovered. Without adaptation, the same configuration recovers 54/62 task-compatible devices (86.40% F1) on 12 OPEN100 drawings. These results establish device recovery and useful graph association retrieval while retaining an auditable write-back path.