跨建筑的 Brick Schema 知识图谱自动化补全

# Automated Brick Schema Knowledge Graph Completion Across Buildings
Source: [https://arxiv.org/html/2610.27339](https://arxiv.org/html/2610.27339)
Jalil HuseynovAffiliation:National University of SingaporeXinyi PanAffiliation:National University of SingaporeShaked ShalevAffiliation:National University of SingaporeZhang ChiAffiliation:National University of SingaporeAi YamamotoAffiliation:Kajima CorporationSohei ArisakaAffiliation:Kajima Corporation

###### Abstract

The Brick schema represents building equipment, sensors, spaces, and the relationships between them as typed, multi\-relational graphs, providing machine\-readable metadata that supports generalizable control applications\. Current methods for producing complete Brick models require extensive manual examination of building schematics and point lists\. We observe that as Brick models are knowledge graphs, inferring missing relations is naturally posed as a knowledge graph completion problem\. To the best of our knowledge, this is the first application of knowledge graph completion to Brick model generation\. We compare three methods, gradient\-boosted trees, Pairwise Brick Relation Ranking, and CompGCN, on the relationsfeeds,hasPart, andhasPoint, which account for the majority of the schematic\-reading work in building a Brick model by hand\. Models are evaluated on held\-out MORTAR buildings and out\-of\-distribution Kaggle and Building Time Series data\. Although CompGCN is the strongest performer on held\-out buildings under metrics resistant to class imbalance, leading macro\-F1 and AUPRC, no method generalizes uniformly across datasets or relations\.

## 1Introduction

Modern commercial buildings are equipped heavily\. A single site may have thousands of devices and tens of thousands more data points, most exposed by a Building Management System \(BMS\) that controls heating, lighting and electrical equipment\. This data is the foundation of smart building applications, including fault detection, demand response, and occupant comfort optimization\([Pritoni et al\., 2021](https://arxiv.org/html/2610.27339#bib.bib18)\)\. However, data alone is not enough\. A time series named AHU3\_SAT\_SP doesn’t tell software that AHU3 is an air handling unit, or that SAT\_SP is a supply air temperature setpoint or which zones it serves\. Applications need metadata to know what the data means or how it relates to equipment and space\.

Brick Schema is an open ontology that provides this metadata\([Balaji et al\., 2016](https://arxiv.org/html/2610.27339#bib.bib1)\)\. A Brick model represents a building as a graph in which entities such as equipment, points, and spaces are instances of Brick classes, while relationships are typed directed edges such asfeeds,hasPart, andhasPoint\. This standard representation lets applications query entities by type and relationship rather than building\-specific point names, enabling the same application to run across buildings with Brick models\. Figure[1](https://arxiv.org/html/2610.27339#S1.F1)shows a simple example\.

AHUVAVSensorfeedshasPointFigure 1:A two\-hop Brick graph fragment\. Our completion targets are the typed, directed relationsfeeds,hasPart, andhasPoint\.The main obstacle in mass adoption is the difficulty in producing Brick models\. The typical workflow begins with a graph generated from Building Information Modeling \(BIM\)\([Eastman et al\., 2008](https://arxiv.org/html/2610.27339#bib.bib25)\), then augments it with a BMS point list\. From there, the metadata in hand is incomplete, and an engineer must manually consult mechanical drawings to recover what is missing\. Figure[2](https://arxiv.org/html/2610.27339#S1.F2)illustrates this setting, where the BIM and point\-list\-derived metadata form the observed graph, and the topology an engineer recovers from mechanical drawings is what remains missing\.

The edges which remain to be filled after BIM and BMS extraction are not arbitrary\. Entity types and spatial containment are given, as BIM exports carry geometry and hierarchy and point labels follow building naming conventions\. What remains to be added is topology\. The relationsfeeds,hasPart, andhasPointdescribe how equipment connects, what it contains, and which points report on it\. Recovering these relations involves tracing dozens of pages of mechanical drawings, which scales poorly to new buildings\. This process requires domain\-expertise, and must be repeated for every new Brick model\. These three relations account for the vast majority of the schematic\-reading effort in building a Brick model by hand, and they are the relations we target\.

Our key observation is that the partial graph may contain enough structure for edge inference\. Although the BIM and point\-list\-derived graph is incomplete, it carries substantial information about the building, such as entity types, identifiers, spatial structure, and a subset of the observed relationships\. We hypothesize that this partial structure is sufficient to recover the missing relations without examining the mechanical drawings, replacing the schematic\-reading step entirely\. This approach is a well established problem in graph theory and machine learning\. A partially constructed Brick model is a multi\-relational knowledge graph with missing edges, and filling in missing edges is knowledge graph completion \(KGC\), a task with a mature body of methods developed on general\-purpose benchmarks\. These methods have yet to be applied to the buildings domain\. We formulate the final integration step accordingly\. Given a candidate entity pair\(h,t\)\(h,t\), a model must determine whether the pair is linked and, if so, predict which relationrrholds forr∈\{feeds,hasPart,hasPoint\}\.r\\in\\\{\\texttt\{feeds\},\\texttt\{hasPart\},\\texttt\{hasPoint\}\\\}\.

Our contributions are:

1. 1\.We present, to the best of our knowledge, the first systematic study of knowledge\-graph completion for the Brick schema, targeting the relations that dominate manual modeling effort\.
2. 2\.We adapt and evaluate three representative approaches under a shared experimental framework: gradient\-boosted trees over pairwise features \(GBT\), Pairwise Brick Relation Ranking \(PBRR\), and CompGCN\.
3. 3\.We evaluate cross\-dataset generalization across MORTAR, Kaggle, and Building Time Series data\. We find that no method generalizes uniformly: performance depends strongly on the target relation and the dataset, which exposes the limits of aggregate metrics and motivates relation\-specific calibration and evaluation\.

![Refer to caption](https://arxiv.org/html/2610.27339v1/images/brick.png)\(a\)A Brick graph fragment\.
![Refer to caption](https://arxiv.org/html/2610.27339v1/images/left.png)↦𝑓\\xmapsto\{\\,f\\,\}![Refer to caption](https://arxiv.org/html/2610.27339v1/images/right.png)

\(b\)The completion task\.

Figure 2:Brick represents building entities and their relationships as a typed graph \([2\(a\)](https://arxiv.org/html/2610.27339#S1.F2.sf1)\); our task is to recover missing target edges \([2\(b\)](https://arxiv.org/html/2610.27339#S1.F2.sf2)\)\.
## 2Related Works

### 2\.1Brick Schema

Prior to Brick, building metadata was scattered across formats that each addressed different issues\. Project Haystack\([20](https://arxiv.org/html/2610.27339#bib.bib22)\)gave practitioners a shared tagging vocabulary for points and equipment\. IFC/BIM exports represent relational and spatial structure from design and construction\. Domain ontologies like DogOnt\([Bonino and Corno, 2008](https://arxiv.org/html/2610.27339#bib.bib15)\)modeled smart\-home devices and their interactions more formally, and SAREF\-based extensions for buildings\([Poveda\-Villalón and García\-Castro, 2018](https://arxiv.org/html/2610.27339#bib.bib16)\)pushed toward interoperability with the broader Semantic Web\. Brick\([Balaji et al\., 2016](https://arxiv.org/html/2610.27339#bib.bib1)\)aimed to fold these into one graph\. It keeps Haystack’s tagging instinct for naming entity types, borrows IFC containment structure, and expresses the metadata as an RDF/OWL graph so it can be queried rather than parsed per building\.

Work has since grown Brick outward rather than automating how a model gets built\. Luo et al\.\([Luo et al\., 2022](https://arxiv.org/html/2610.27339#bib.bib17)\)extend the schema to occupant metadata, such as behavior, demographics, adaptive actions, without touching the core equipment/point/space relations, which evidences that the relational structure generalizes reasonably well to new domains\. On the data side, MORTAR\([Fierro et al\., 2019](https://arxiv.org/html/2610.27339#bib.bib2)\)addressed a different bottleneck\. Rather than extending the schema, it packaged real deployed Brick models with time\-series data so researchers could develop and evaluate applications without needing access to an actual building\. We rely on MORTAR for this reason \(Section[4\.1](https://arxiv.org/html/2610.27339#S4.SS1)\)\. To the best of our knowledge, no prior work has addressed recovering and inferring Brick edges, which today is still done manually for every new building\.

### 2\.2Knowledge\-Graph Completion

KGC is a well\-studied problem, and current methods split into three families\. Embedding models learn a fixed\-length vector per entity and relation and score candidate triples against those vectors\. TransE\([Bordes et al\., 2013](https://arxiv.org/html/2610.27339#bib.bib7)\)treats a relation as a translation from head to tail, DistMult\([Yang et al\., 2015](https://arxiv.org/html/2610.27339#bib.bib8)\)and ComplEx\([Trouillon et al\., 2016](https://arxiv.org/html/2610.27339#bib.bib9)\)capture symmetric and antisymmetric relations through bilinear and complex\-valued products, and ConvE\([Dettmers et al\., 2018](https://arxiv.org/html/2610.27339#bib.bib10)\)and RotatE\([Sun et al\., 2019](https://arxiv.org/html/2610.27339#bib.bib11)\)push further with convolutional scoring and relation\-as\-rotation, respectively\. These methods are fast and do well on standard benchmarks, but they share a structural weakness for our setting: an entity’s embedding is tied to its identity, thus the models fail to generalize to out\-of\-distribution entities, which describe every point and piece of equipment in a new building\.

GNN\-based methods look to address this gap\. Rather than memorizing per\-entity vectors, they aggregate information from a node’s local neighborhood, so a representation can be computed for an entity the model has never seen so long as its neighborhood provides sufficient structural information\. R\-GCN\([Schlichtkrull et al\., 2017](https://arxiv.org/html/2610.27339#bib.bib12)\)was the first to extend graph convolution to multi\-relational graphs, assigning each relation a transformation matrix, growing parameter count with the number of relations\. CompGCN\([Vashishth et al\., 2020](https://arxiv.org/html/2610.27339#bib.bib6)\), which we build on in Section 3\.4, addresses this by composing entity and relation embeddings through a single shared transformation instead, which keeps the model small without giving up relation\-awareness\. A separate, older tradition is symbolic rather than learned: the Path Ranking Algorithm\([Lao and Cohen, 2010](https://arxiv.org/html/2610.27339#bib.bib13)\)scores candidates by the relational paths connecting head and tail, and rule\-mining systems like AMIE\+\([Galárraga et al\., 2015](https://arxiv.org/html/2610.27339#bib.bib4)\)and AnyBURL\([Meilicke et al\., 2019](https://arxiv.org/html/2610.27339#bib.bib5)\)extract Horn rules directly from the graph\. These trade raw accuracy for human\-readable rules, which is the design PBRR follows with its hand\-designed, relation\-conditioned features rather than a learned rule set\.

None of the methods above, embedding\-based, GNN\-based, or symbolic, have previously been evaluated on Brick, which uses a small, fixed relation vocabulary dominated by three structural relations, and has strong naming regularities in entity IDs that none of these methods are built to exploit\.

## 3Methodology

### 3\.1Problem formulation

Letℰ\\mathcal\{E\}denote the entities in a building graph andℛ=\{feeds,hasPart,hasPoint\}\\mathcal\{R\}=\\\{\\texttt\{feeds\},\\texttt\{hasPart\},\\texttt\{hasPoint\}\\\}the target relations\. Given a candidate entity pair\(h,t\)\(h,t\), each model predicts whether a target relation exists between the two entities and, if so, which relationr∈ℛr\\in\\mathcal\{R\}holds\. The final prediction therefore belongs toℛ∪\{∅\}\\mathcal\{R\}\\cup\\\{\\varnothing\\\}, where∅\\varnothingdenotes that no target relation is predicted\.

We chose three learned models to compare different ways of using information from the Brick graph\. PBRR is the simplest and most interpretable of the three\. It uses a selected set of Brick\-specific features based on ontology information, naming patterns, relation compatibility, and local graph context\. This allows us to test how well a smaller, deliberately chosen feature representation can predict missing relations\. GBT preserves the same pairwise prediction setup, but describes each candidate pair using a much larger set of features\. This gives the model more information and allows it to learn more detailed associations between entity types and naming patterns\. CompGCN takes a different approach by learning directly from the graph structure\. Instead of explicitly describing the neighbourhood around each entity through selected features, it learns structural patterns and entity relationships from the surrounding graph through message passing\. Together, the three models form a natural progression from selected Brick\-specific features, to richer pairwise feature learning, and finally to learning directly from the graph itself\.

### 3\.2Pairwise Brick Relation Ranking

PBRR tests whether a 48\-dimensional set of selected Brick features is sufficient for predicting missing relations\. Brick defines a structured ontology for representing building entities and their relationships, including equipment, points, locations, and their connections\([Balaji et al\., 2016](https://arxiv.org/html/2610.27339#bib.bib1);[Fierro et al\., 2020](https://arxiv.org/html/2610.27339#bib.bib19)\)\. We therefore represent each candidate relation using Brick type information, identifier similarity, nearby observed relationships, and whether the relation is compatible with the entity types\.

Becausefeeds,hasPart, andhasPointrepresent different types of relationships and apply differently across Brick entity types\([Fierro et al\., 2020](https://arxiv.org/html/2610.27339#bib.bib19)\), PBRR trains a separate one\-vs\-rest logistic classifier for each relation\. For candidate pair\(h,t\)\(h,t\)and relationrr, the classifier computes

zr​\(h,t\)=𝐰r⊤​𝐟​\(h,r,t\)\+br,Pr​\(h,t\)=σ⁡\(zr​\(h,t\)\),z\_\{r\}\(h,t\)=\\mathbf\{w\}\_\{r\}^\{\\top\}\\mathbf\{f\}\(h,r,t\)\+b\_\{r\},\\qquad P\_\{r\}\(h,t\)=\\sigma\\\!\\left\(z\_\{r\}\(h,t\)\\right\),\(1\)where𝐟⁡\(h,r,t\)\\mathbf\{f\}\(h,r,t\)is the feature vector for candidate pair\(h,t\)\(h,t\)under relationrr\.

Positive examples are observed target edges, while negatives are sampled from candidate pairs with no known target edge\. Since negative candidates substantially outnumber positive edges, the classification problem is highly imbalanced\. This can reduce the classifier’s ability to identify positive examples reliably with standard logistic regression\([King and Zeng, 2001](https://arxiv.org/html/2610.27339#bib.bib20)\)\. To account for this imbalance, we weight the positive class during training\. We otherwise use the standardL2L\_\{2\}\-regularized logistic classification objective\([Hastie et al\., 2009](https://arxiv.org/html/2610.27339#bib.bib21)\), giving

ℒr=−∑i\[αryi​rlogPr\(hi,ti\)\+\(1−yi​r\)log\(1−Pr\(hi,ti\)\)\]\+λ2∥𝐰r∥22,\\mathcal\{L\}\_\{r\}=\-\\sum\_\{i\}\\left\[\\alpha\_\{r\}y\_\{ir\}\\log P\_\{r\}\(h\_\{i\},t\_\{i\}\)\+\(1\-y\_\{ir\}\)\\log\\left\(1\-P\_\{r\}\(h\_\{i\},t\_\{i\}\)\\right\)\\right\]\+\\frac\{\\lambda\}\{2\}\\lVert\\mathbf\{w\}\_\{r\}\\rVert\_\{2\}^\{2\},\(2\)whereαr=Nr−/Nr\+\\alpha\_\{r\}=N\_\{r\}^\{\-\}/N\_\{r\}^\{\+\}is the positive class weighting term, set according to the negative to positive training ratio, andλ\\lambdacontrols the strength of theL2L\_\{2\}regularization\. A relation\-specific thresholdτr\\tau\_\{r\}is selected on the validation set by maximizing F1\. At inference time, PBRR returns the highest\-scoring compatible relation only if its probability exceeds the corresponding threshold\.

### 3\.3Gradient\-boosted trees

We use a singleHistGradientBoostingClassifier\([Friedman, 2001](https://arxiv.org/html/2610.27339#bib.bib3)\)to score each candidate triple\(h,r,t\)\(h,r,t\)\. Let𝐱e∈\{0,1\}C\\mathbf\{x\}\_\{e\}\\in\\\{0,1\\\}^\{C\}be the multi\-hot Brick type encoding of entityee, including all superclasses in the Brick hierarchy so that unseen leaf classes still activate trained ancestors\. The feature map is

ϕ⁡\(h,r,t\)=\[𝐱h;𝐱t;𝐱h⊙𝐱t;\|𝐱h−𝐱t\|;𝐠⁡\(h,t\);𝐞r\],\\phi\(h,r,t\)=\\bigl\[\\,\\mathbf\{x\}\_\{h\}\\;;\\;\\mathbf\{x\}\_\{t\}\\;;\\;\\mathbf\{x\}\_\{h\}\\odot\\mathbf\{x\}\_\{t\}\\;;\\;\\lvert\\mathbf\{x\}\_\{h\}\-\\mathbf\{x\}\_\{t\}\\rvert\\;;\\;\\mathbf\{g\}\(h,t\)\\;;\\;\\mathbf\{e\}\_\{r\}\\,\\bigr\],\(3\)where⊙\\odotis the element\-wise product,𝐠⁡\(h,t\)∈ℝ9\\mathbf\{g\}\(h,t\)\\in\\mathbb\{R\}^\{9\}collects directional string\-similarity statistics between the two identifiers \(shared tokens, prefixes, and numeric suffixes\), and𝐞r∈\{0,1\}3\\mathbf\{e\}\_\{r\}\\in\\\{0,1\\\}^\{3\}one\-hot encodes the candidate relation\. The product and absolute\-difference blocks supply type interactions the trees cannot otherwise form\. WithC=126C=126this gives4​C\+9\+3=5164C\+9\+3=516dimensions\.

One model is trained over all three relations, with𝐞r\\mathbf\{e\}\_\{r\}permitting relation\-specific behaviour while sharing statistical strength—unlike PBRR, which fits one classifier per relation\. At inference it is queried once per relation to obtainsr​\(h,t\)=f⁡\(ϕ⁡\(h,r,t\)\)s\_\{r\}\(h,t\)=f\(\\phi\(h,r,t\)\), and the pair takes the highest\-scoring relation clearing its own validation\-tuned thresholdτr\\tau\_\{r\}:

r^​\(h,t\)=arg​maxr∈𝒜⁡\(h,t\)⁡sr​\(h,t\),𝒜⁡\(h,t\)=\{r∈ℛ:sr​\(h,t\)≥τr\},\\hat\{r\}\(h,t\)=\\operatorname\*\{arg\\,max\}\_\{r\\in\\mathcal\{A\}\(h,t\)\}s\_\{r\}\(h,t\),\\quad\\mathcal\{A\}\(h,t\)=\\\{r\\in\\mathcal\{R\}:s\_\{r\}\(h,t\)\\geq\\tau\_\{r\}\\\},\(4\)predicting∅\\varnothingwhen𝒜⁡\(h,t\)=∅\\mathcal\{A\}\(h,t\)=\\emptyset\. Becausesrs\_\{r\}is a bounded probability estimate rather than a calibrated probability,τr\\tau\_\{r\}is tuned rather than fixed at0\.50\.5\.

### 3\.4CompGCN

A graph neural network \(GNN\) operates directly over the graph structure via message passing, in which each node iteratively aggregates information from its neighbours\. Unlike embedding and feature\-based approaches, a GNN learns structural patterns rather than entity identities, which in principle allows it to generalize to buildings not seen during training: whether a missing edge should exist is often inferable from the shape of a node’s local neighbourhood alone, even without lexical cues from entity names\.

We selected CompGCN\([Vashishth et al\., 2020](https://arxiv.org/html/2610.27339#bib.bib6)\)for two reasons\. First, it treats relations as first\-class learned embeddings rather than fixed identifiers, enabling richer entity\-relation interaction than relation\-agnostic GCN variants\. It also uses a single shared weight matrix with a composition operation rather than one matrix per relation, making it parameter\-efficient at approximately 300,000 parameters, modest relative to comparable relational GNNs\([Schlichtkrull et al\., 2017](https://arxiv.org/html/2610.27339#bib.bib12)\)\.

The core message\-passing update is

𝐡v=f⁡\(∑\(u,r\)∈𝒩⁡\(v\)𝐖λ⁡\(r\)​ϕ​\(𝐱u,𝐳r\)\),𝐡r=𝐖rel​𝐳r,\\mathbf\{h\}\_\{v\}=f\\\!\\left\(\\sum\_\{\(u,r\)\\,\\in\\,\\mathcal\{N\}\(v\)\}\\mathbf\{W\}\_\{\\lambda\(r\)\}\\,\\phi\\\!\\left\(\\mathbf\{x\}\_\{u\},\\,\\mathbf\{z\}\_\{r\}\\right\)\\right\),\\qquad\\mathbf\{h\}\_\{r\}=\\mathbf\{W\}\_\{\\text\{rel\}\}\\,\\mathbf\{z\}\_\{r\},where𝐱u∈ℝd\\mathbf\{x\}\_\{u\}\\in\\mathbb\{R\}^\{d\}are the initial features for entityuu\(here the mean of its Brick class token embeddings\),𝐳r∈ℝd\\mathbf\{z\}\_\{r\}\\in\\mathbb\{R\}^\{d\}are the initial features for relationrr\(randomly initialised and jointly learned\),ϕ:ℝd×ℝd→ℝd\\phi:\\mathbb\{R\}^\{d\}\\times\\mathbb\{R\}^\{d\}\\to\\mathbb\{R\}^\{d\}composes a neighbour embedding with its connecting relation embedding before aggregation,ffis a nonlinearity, and𝐖λ⁡\(r\)∈\{𝐖O,𝐖I,𝐖S\}\\mathbf\{W\}\_\{\\lambda\(r\)\}\\in\\\{\\mathbf\{W\}\_\{O\},\\mathbf\{W\}\_\{I\},\\mathbf\{W\}\_\{S\}\\\}are direction\-specific weight matrices for original, inverse, and self\-loop edges\.

The standard CompGCN formulation targets general\-purpose link prediction and required four changes for the Brick setting\. First, we replace the standard entity\-prediction objective with a joint loss that directly optimises relation prediction\([Chen et al\., 2021](https://arxiv.org/html/2610.27339#bib.bib14)\):

arg⁡max⁡∑⟨h,r,t⟩∈𝒢θ∈Θ⁡\[log⁡Pθ​\(h∣r,t\)\+log⁡Pθ​\(t∣h,r\)\+λ​log​Pθ​\(r∣h,t\)\],\\arg\\max\_\{\\theta\\in\\Theta\}\\sum\_\{\\langle h,r,t\\rangle\\in\\mathcal\{G\}\}\\left\[\\log P\_\{\\theta\}\(h\\mid r,t\)\+\\log P\_\{\\theta\}\(t\\mid h,r\)\+\\lambda\\log P\_\{\\theta\}\(r\\mid h,t\)\\right\],where the first two terms predict the head and tail given the relation, and the third is an auxiliary relation\-prediction term weighted byλ∈ℝ\+\\lambda\\in\\mathbb\{R\}\_\{\+\},

logPθ\(r∣h,t\)=ϕθ\(h,r,t\)−log∑r′∈ℛexp\[ϕθ\(h,r′,t\)\],\\log P\_\{\\theta\}\(r\\mid h,t\)=\\phi\_\{\\theta\}\(h,r,t\)\-\\log\\sum\_\{r^\{\\prime\}\\in\\mathcal\{R\}\}\\exp\\\!\\left\[\\phi\_\{\\theta\}\(h,r^\{\\prime\},t\)\\right\],a softmax over candidate relations given the head–tail pair\. Since relation prediction is our primary task, this term aligns training with inference\.

Second, during training we hide relations only, never entities, in contrast to link\-prediction regimes that mask entities, again to match the downstream task\. Third, we add a dedicated binary head for link existence, conditioned on a name\-similarity feature between head and tail so that lexical signals can inform the existence decision where connectivity is ambiguous; separating the two heads improved end\-to\-end performance by letting the existence head attend to lexical cues while the relation head focuses on structure and type\. Fourth, node features are initialised inductively from Brick class embeddings rather than entity\-specific vectors, so the same Brick class is represented consistently across buildings\.

## 4Experimental Setup

### 4\.1Datasets and preprocessing

We train our models on MORTAR\([Fierro et al\., 2019](https://arxiv.org/html/2610.27339#bib.bib2)\), which contains real commercial\-building Brick graphs and supplies training, validation, and held\-out in\-domain buildings\. After preprocessing, the combined graph has approximately 19,388 entities, seven core relation types, and 69,159 triples\. We additionally evaluate out of distribution on the Kaggle Brick models and Building Time Series \(BTS\) datasets\([Miller, 2021](https://arxiv.org/html/2610.27339#bib.bib24);[Prabowo et al\., 2024](https://arxiv.org/html/2610.27339#bib.bib23)\)\. The benchmark contains 755 MORTAR test edges, 15,507 Kaggle test edges, and 534 BTS test edges\.

We normalize inverse relations \(isPointOf,isPartOf, andisFedBy\) to their canonical forward directions and map equivalent predicates to Brick\. The normalized graphs contain relations beyond our three targets, which we retain as visible context but do not predict\. These are entity class assignments, human\-readable labels, external references linking points to their BMS timeseries streams, and literal\-valued attributes such as floor area\. We exclude them from the prediction task as each is previously supplied\. Class assignments and labels come from the BMS point list, timeseries references from the BMS itself, and dimensional attributes from the BIM export\. Onlyfeeds,hasPart, andhasPointrequire an engineer to consult mechanical drawings\. Splits are made at the building level to prevent entity and edge\-level leakage\. Within an evaluation building, visible context edges remain available to structure\-aware models, while held\-out target edges define the prediction task\.

All experiments were run on a single NVIDIA RTX 4090, with the non\-neural models on CPU\. Each model is trained with three seeds while the building split and masking are held fixed\.

Table 1:Dataset statistics and target\-relation distributions after normalization\. Relation entries report counts with row\-wise percentages in parentheses\.
### 4\.2Metrics

Every model emits a link score and a relation distribution for each candidate pair\. A candidate pair is predicted linked if its score exceeds a frozen threshold, in which we take the argmax over relations; otherwise no edge is predicted\. Positive edges are held\-out target edges and negatives are type\-constrained false edges of the datasets, sampled at ten per positive edge\. Precision\-based metrics therefore depend on that ratio\.

We report Link F1 over the binary task of determining if a link exists between two entities, agnostic of which relation is the final prediction\. Relation classification is scored separately, with counts defined per relationrrover four labels:feeds,hasPart,hasPoint, and∅\\varnothing, where∅\\varnothingdenotes the prediction of no edge\. A true positiveTPr\\mathrm\{TP\}\_\{r\}is a candidate predictedrrwhose true label isrr\. A false positiveFPr\\mathrm\{FP\}\_\{r\}is a candidate predictedrrwhose true label is∅\\varnothingor another relation\. A false negativeFNr\\mathrm\{FN\}\_\{r\}is a candidate whose true label isrrbut which is predicted∅\\varnothingor another relation\. A true negativeTNr\\mathrm\{TN\}\_\{r\}is a candidate predicted∅\\varnothingor another relation whose true label is likewise∅\\varnothingor another relation\. The reported F1 scores follow from these counts in the usual way, with micro\-F1 pooling them across the three target relations and macro\-F1 averaging the per\-relation scores unweighted\. AUPRC is instead computed directly from the link score and is the only threshold\-free metric we report\.

### 4\.3Baselines

We evaluate two baseline models that bound the learned models\. Both are scored on the same candidate sets as the learned models, and their thresholds are set by the same validation rule and frozen in the same way\.

1. 1\.Random: scores every candidate uniformly at random, giving the value of each metric under chance\. Since this depends on how many candidates are positive, it is a per\-dataset reference rather than a fixed number\.
2. 2\.Type\-pair: uses Brick class alone\. For a candidate pair it returns the relation frequencies observed for that class pair in training; if the pair was never seen, it defers to the frequencies for the corresponding top\-level Brick classes, and then to the overall training frequencies\. Its link score is the largest of the three relation probabilities\.

## 5Results

Table 2:Aggregate link\-existence and relation\-classification performance across MORTAR, Kaggle, and BTS\. Values are mean±\\pmstandard deviation\. Best results per dataset are bold\.Table 3:End\-to\-end F1 for each target relation across datasets\. Values are means across seeds; best results per dataset and relation are bold\.Table[2](https://arxiv.org/html/2610.27339#S5.T2)reports results by dataset and Table[3](https://arxiv.org/html/2610.27339#S5.T3)breaks them down by target relation\. On the in\-distribution MORTAR test set, PBRR and CompGCN both perform well\. PBRR has the highest Link F1 and micro\-F1, CompGCN the highest macro\-F1, and both gaps are smaller than the seed\-to\-seed standard deviation\. The clearer separation is in AUPRC, the only threshold\-free metric we report \(valuable given the ten to one ratio of negative to positive edges\), where CompGCN reaches0\.9160\.916against PBRR’s0\.8150\.815\. MORTAR is also the only dataset on which all models perform well across all three relations rather than relying on one\. This establishes the feasibility of inferring missing relations from information present in a partially constructed graph, with no mechanical drawings supplied to any model\.

Each model degrades out of distribution\. CompGCN leads every metric on Kaggle, but its macro\-F1 of0\.1730\.173barely exceeds the type\-pair baseline’s \(Table[2](https://arxiv.org/html/2610.27339#S5.T2)\)\. CompGCN’s Kaggle performance is almost entirely driven byhasPoint\(0\.3420\.342; Table[3](https://arxiv.org/html/2610.27339#S5.T3)\)\. GBT shows a similar pattern on BTS, where it leads every aggregate metric on the strength of ahasPointF1 of0\.7430\.743, while scoring0\.0000\.000onhasPartand0\.0090\.009onfeeds\(Table[3](https://arxiv.org/html/2610.27339#S5.T3)\)\. In both cases, the aggregate performance is dominated by a single relation rather than balanced completion\. PBRR also fails to generalize to out of distribution datasets, with Link F1 falling from0\.8240\.824on MORTAR to0\.0590\.059on Kaggle and0\.0920\.092on BTS \(Table[2](https://arxiv.org/html/2610.27339#S5.T2)\)\. This sharp decline suggests that the information PBRR relies on is highly relevant to the way relations are represented in MORTAR, but does not transfer consistently when those relationships are encoded differently across Kaggle and BTS\. GBT’s unusually strong BTS result is likewise driven by dataset composition rather than broader generalisation\. Its advantage is confined tohasPoint\(F10\.7430\.743versus0\.0000\.000and0\.0090\.009on the other two relations; Table[3](https://arxiv.org/html/2610.27339#S5.T3)\), which accounts for67%67\\%of BTS target edges \(Table[1](https://arxiv.org/html/2610.27339#S4.T1)\)\. This relation is also lexically easier in BTS than in MORTAR because BTS point URIs are namespaced under their parent equipment identifiers, giving GBT’s string\-overlap features a stronger out\-of\-distribution signal\.

Two more observations complicate declaring a winning model\. First, CompGCN’s AUPRC stays high on both out\-of\-distribution datasets while its Link F1 falls to0\.4070\.407and0\.2280\.228, so its candidate ordering transfers considerably better than its frozen threshold\. Second, the type\-pair baseline performs best in three of the six out\-of\-distribution dataset\-relation combinations, meaning Brick class alone outperforms every learned model onhasPartfor both unseen datasets and onfeedsfor BTS\.

## 6Conclusion

We apply knowledge graph completion methods to the problem of completing Brick schema graphs\. To the best of our knowledge, this is the first application of such methods to this domain\. We compare GBT, PBRR, and CompGCN for predicting relations in incomplete Brick graphs\. On MORTAR, both PBRR and CompGCN recover missing relations at F1 well above baselines across all three target relations, using only the entity types, identifiers, and partial structure present after BIM and BMS extraction\. We conclude that the information needed to complete a Brick model is substantially present in the partial model\.

On Kaggle, CompGCN ranks edges most effectively but its relation performance is driven byhasPoint\. On BTS, GBT’s aggregate lead is also almost solely ahasPointresult, while the type\-pair baseline is best forhasPartandfeeds\. No method generalizes across all three datasets, and the model that wins on aggregate metrics rarely wins on all relations\. We conclude that Brick completion is not well served by a single global architecture\. Recoverability depends not only on the model architecture but also on which signals \(types, identifiers, or graph structure\) are consistently encoded in the target dataset; a practical system should characterize the target graph first and select the model that suits it\. We hope this benchmark encourages further work on automating Brick model construction\.

## Acknowledgments

We thank the Institute for Pure and Applied Mathematics \(IPAM\) Research in Industrial Projects for Students \(RIPS\) program and the Institute for Mathematical Sciences at the National University of Singapore for hosting this research, and Kajima Corporation for sponsoring this project\.

## References

- Balajiet al\.\(2016\)B\. Balaji, A\. Bhattacharya, G\. Fierro, J\. Gao, J\. Gluck, D\. Hong, A\. Johansen, J\. Koh, J\. Ploennigs, Y\. Agarwal, M\. Bergés, D\. Culler, R\. Gupta, M\. B\. Kjærgaard, M\. Srivastava, and K\. WhitehouseBrick: towards a unified metadata schema for buildings\.InProceedings of the 3rd ACM International Conference on Systems for Energy\-Efficient Built Environments,pp\. 41–50\.External Links:[Document](https://dx.doi.org/10.1145/2993422.2993577)Cited by:[§1](https://arxiv.org/html/2610.27339#S1.p2.1),[§2\.1](https://arxiv.org/html/2610.27339#S2.SS1.p1.1),[§3\.2](https://arxiv.org/html/2610.27339#S3.SS2.p1.1)\.
- Bonino and Corno \(2008\)D\. Bonino and F\. CornoDogOnt \- ontology modeling for intelligent domotic environments\.InProceedings of the 7th International Conference on The Semantic Web,pp\. 790–803\.External Links:[Link](https://doi.org/10.1007/978-3-540-88564-1_51),[Document](https://dx.doi.org/10.1007/978-3-540-88564-1%5F51)Cited by:[§2\.1](https://arxiv.org/html/2610.27339#S2.SS1.p1.1)\.
- Bordeset al\.\(2013\)A\. Bordes, N\. Usunier, A\. Garcia\-Duran, J\. Weston, and O\. YakhnenkoTranslating embeddings for modeling multi\-relational data\.InProceedings of the 27th International Conference on Neural Information Processing Systems \- Volume 2,NIPS’13,pp\. 2787–2795\.Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p1.1)\.
- Chenet al\.\(2021\)Y\. Chen, P\. Minervini, S\. Riedel, and P\. StenetorpRelation prediction as an auxiliary training objective for improving multi\-relational graph representations\.External Links:2110\.02834,[Link](https://arxiv.org/abs/2110.02834)Cited by:[§3\.4](https://arxiv.org/html/2610.27339#S3.SS4.p4.1)\.
- Dettmerset al\.\(2018\)T\. Dettmers, P\. Minervini, P\. Stenetorp, and S\. RiedelConvolutional 2d knowledge graph embeddings\.External Links:1707\.01476,[Link](https://arxiv.org/abs/1707.01476)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p1.1)\.
- Eastmanet al\.\(2008\)C\. Eastman, P\. Teicholz, R\. Sacks, and K\. ListonBIM handbook: a guide to building information modeling for owners, managers, designers, engineers and contractors\.John Wiley & Sons, IncWiley Publishing\.External Links:ISBN 0470185287Cited by:[§1](https://arxiv.org/html/2610.27339#S1.p3.1)\.
- Fierroet al\.\(2020\)G\. Fierro, J\. Koh, S\. Nagare, X\. Zang, Y\. Agarwal, R\. K\. Gupta, and D\. E\. CullerFormalizing tag\-based metadata with the brick ontology\.Frontiers in Built EnvironmentVolume 6 \- 2020\.External Links:[Document](https://dx.doi.org/10.3389/fbuil.2020.558034),[Link](https://www.frontiersin.org/journals/built-environment/articles/10.3389/fbuil.2020.558034),ISSN 2297\-3362Cited by:[§3\.2](https://arxiv.org/html/2610.27339#S3.SS2.p1.1),[§3\.2](https://arxiv.org/html/2610.27339#S3.SS2.p2.1)\.
- Fierroet al\.\(2019\)G\. Fierro, M\. Pritoni, M\. Abdelbaky, D\. Lengyel, J\. Leyden, A\. Prakash, P\. Gupta, P\. Raftery, T\. Peffer, G\. Thomson, and D\. E\. CullerMortar: an open testbed for portable building analytics\.ACM Trans\. Sen\. Netw\.16\(1\)\.External Links:ISSN 1550\-4859,[Link](https://doi.org/10.1145/3366375),[Document](https://dx.doi.org/10.1145/3366375)Cited by:[§2\.1](https://arxiv.org/html/2610.27339#S2.SS1.p2.1),[§4\.1](https://arxiv.org/html/2610.27339#S4.SS1.p1.1)\.
- Friedman \(2001\)J\. H\. FriedmanGreedy function approximation: a gradient boosting machine\.The Annals of Statistics29\(5\),pp\. 1189–1232\.External Links:[Document](https://dx.doi.org/10.1214/aos/1013203451)Cited by:[§3\.3](https://arxiv.org/html/2610.27339#S3.SS3.p1.1)\.
- Galárragaet al\.\(2015\)L\. Galárraga, C\. Teflioudi, K\. Hose, and F\. M\. SuchanekFast rule mining in ontological knowledge bases with AMIE\+\.The VLDB Journal24\(6\)\.External Links:[Document](https://dx.doi.org/10.1007/s00778-015-0394-1)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p2.1)\.
- Hastieet al\.\(2009\)T\. Hastie, R\. Tibshirani, and J\. FriedmanThe elements of statistical learning: data mining, inference, and prediction\.2 edition,Springer Series in Statistics,Springer,New York, NY\.External Links:[Document](https://dx.doi.org/10.1007/978-0-387-84858-7),ISBN 978\-0\-387\-84858\-7Cited by:[§3\.2](https://arxiv.org/html/2610.27339#S3.SS2.p3.1)\.
- King and Zeng \(2001\)G\. King and L\. ZengLogistic regression in rare events data\.Political Analysis9\(2\),pp\. 137–163\.External Links:[Document](https://dx.doi.org/10.1093/oxfordjournals.pan.a004868)Cited by:[§3\.2](https://arxiv.org/html/2610.27339#S3.SS2.p3.1)\.
- Lao and Cohen \(2010\)N\. Lao and W\. W\. CohenRelational retrieval using a combination of path\-constrained random walks\.Machine Learning81\(1\),pp\. 53–67\.Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p2.1)\.
- Luoet al\.\(2022\)N\. Luo, G\. Fierro, Y\. Liu, B\. Dong, and T\. HongExtending the brick schema to represent metadata of occupants\.Automation in Construction139,pp\. 104307\.External Links:[Document](https://dx.doi.org/https%3A//doi.org/10.1016/j.autcon.2022.104307),[Link](https://www.sciencedirect.com/science/article/pii/S0926580522001807)Cited by:[§2\.1](https://arxiv.org/html/2610.27339#S2.SS1.p2.1)\.
- Meilickeet al\.\(2019\)C\. Meilicke, M\. W\. Chekol, D\. Ruffinelli, and H\. StuckenschmidtAnytime bottom\-up rule learning for knowledge graph completion\.InProceedings of the Twenty\-Eighth International Joint Conference on Artificial Intelligence,pp\. 3137–3143\.External Links:[Document](https://dx.doi.org/10.24963/ijcai.2019/435)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p2.1)\.
- Miller \(2021\)C\. MillerReference building bms data brick models\.External Links:[Link](https://www.kaggle.com/datasets/claytonmiller/reference-building-bms-data-brick-models)Cited by:[§4\.1](https://arxiv.org/html/2610.27339#S4.SS1.p1.1)\.
- Poveda\-Villalón and García\-Castro \(2018\)M\. Poveda\-Villalón and R\. García\-CastroExtending the saref ontology for building devices and topology\.InLDAC,External Links:[Link](https://api.semanticscholar.org/CorpusID:53551935)Cited by:[§2\.1](https://arxiv.org/html/2610.27339#S2.SS1.p1.1)\.
- Prabowoet al\.\(2024\)A\. Prabowo, X\. Lin, I\. Razzak, H\. Xue, E\. W\. Yap, M\. Amos, and F\. D\. SalimBTS: building timeseries dataset: empowering large\-scale building analytics\.External Links:2406\.08990,[Link](https://arxiv.org/abs/2406.08990)Cited by:[§4\.1](https://arxiv.org/html/2610.27339#S4.SS1.p1.1)\.
- Pritoniet al\.\(2021\)M\. Pritoni, D\. Paine, G\. Fierro, C\. Mosiman, M\. Poplawski, A\. Saha, and J\. BenderMetadata schemas and ontologies for building energy applications: a critical review and use case analysis\.Energies14\(7\)\.External Links:[Document](https://dx.doi.org/10.3390/en14072024),[Link](https://www.mdpi.com/1996-1073/14/7/2024)Cited by:[§1](https://arxiv.org/html/2610.27339#S1.p1.1)\.
- \[20\]Project haystack\.External Links:[Link](https://project-haystack.org/)Cited by:[§2\.1](https://arxiv.org/html/2610.27339#S2.SS1.p1.1)\.
- Schlichtkrullet al\.\(2017\)M\. Schlichtkrull, T\. N\. Kipf, P\. Bloem, R\. van den Berg, I\. Titov, and M\. WellingModeling relational data with graph convolutional networks\.External Links:1703\.06103,[Link](https://arxiv.org/abs/1703.06103)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p2.1),[§3\.4](https://arxiv.org/html/2610.27339#S3.SS4.p2.1)\.
- Sunet al\.\(2019\)Z\. Sun, Z\. Deng, J\. Nie, and J\. TangRotatE: knowledge graph embedding by relational rotation in complex space\.External Links:1902\.10197,[Link](https://arxiv.org/abs/1902.10197)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p1.1)\.
- Trouillonet al\.\(2016\)T\. Trouillon, J\. Welbl, S\. Riedel, É\. Gaussier, and G\. BouchardComplex embeddings for simple link prediction\.External Links:1606\.06357,[Link](https://arxiv.org/abs/1606.06357)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p1.1)\.
- Vashishthet al\.\(2020\)S\. Vashishth, S\. Sanyal, V\. Nitin, and P\. TalukdarComposition\-based multi\-relational graph convolutional networks\.External Links:1911\.03082,[Link](https://arxiv.org/abs/1911.03082)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p2.1),[§3\.4](https://arxiv.org/html/2610.27339#S3.SS4.p2.1)\.
- Yanget al\.\(2015\)B\. Yang, W\. Yih, X\. He, J\. Gao, and L\. DengEmbedding entities and relations for learning and inference in knowledge bases\.External Links:1412\.6575,[Link](https://arxiv.org/abs/1412.6575)Cited by:[§2\.2](https://arxiv.org/html/2610.27339#S2.SS2.p1.1)\.