Technical Summary: DPR-GM for Anomaly Detection in Cyber-Physical Systems

1. Problem Statement

Anomaly detection in multivariate sensor time series is critical for the monitoring of Cyber-Physical Systems (CPS), such as water treatment plants and chemical process control systems. In these environments, even subtle deviations from normal behavior can signal process disruptions, safety incidents, or attacks. However, practical deployment faces two significant challenges:

1. Data Scarcity: Labeled fault examples are rare, necessitating unsupervised approaches that learn normal dynamics from clean operational data.
2. Unreliable Graph Topologies: Recent graph-based approaches using Graph Neural Networks (GNNs) often struggle in small-scale physical systems with limited normal data. Existing methods that construct sensor graphs via end-to-end learning or empirical correlation thresholding tend to capture spurious correlations and produce unstable topologies. These models fail to distinguish between physically meaningful dependencies and transient, non-causal co-movements, leading to noisy graphs and ambiguous anomaly localization.

2. Methodology: DPR-GM

The authors propose DPR-GM (Domain-Prior-Regularized Graph Modeling), a forecasting-based framework that integrates system design knowledge into graph construction. The core principle is that domain knowledge determines which edges may exist, while data statistics determine how strong those edges are. The framework consists of three primary components:

2.1. Domain-Prior-Regularized Graph Construction

Instead of learning the graph structure from data, DPR-GM constructs a fixed structural prior derived from system documentation.

• LLM-Based Extraction: A Large Language Model (specifically Claude Sonnet) is prompted with system design documents, sensor metadata, and subsystem descriptions to extract directed physical couplings between sensor pairs. The output is a structured list of physically sanctioned dependencies ($i \to j$).
• Binary Domain Adjacency Matrix ($D$): These extracted dependencies form a binary matrix $D \in \{0, 1\}^{N \times N}$, where $D_{ij}=1$ if a directed coupling is specified in the documentation. All other entries are set to zero, acting as a structural gate that suppresses any edge not sanctioned by domain knowledge.
• Correlation Modulation: While $D$ dictates topology, edge weights are modulated by empirical evidence. The authors compute the Pearson correlation matrix $\rho$ from normal training data. The final adjacency matrix $A$ is defined as:
  $$A_{ij} = D_{ij} \cdot (0.5 + 0.5 \rho_{ij})$$
  This formulation ensures that:
  • Edges not in $D$ receive a weight of 0.
  • Edges in $D$ with positive correlation receive weights $>0.5$.
  • Edges in $D$ with negative correlation receive weights $<0.5$.
  • Edges in $D$ with zero correlation retain a neutral baseline of 0.5, preventing physically motivated edges from being silenced due to insufficient training statistics.

2.2. CV-Based Node Reliability Weights

Recognizing that sensors exhibit heterogeneous variability during normal operation, the framework assigns reliability weights to nodes based on the Coefficient of Variation (CV).

• Sensors with low temporal variability (low CV) are considered more reliable reference points.
• A reliability score $r_i$ is calculated as the inverse of the CV, and normalized to form node weights $w_i$.
• These weights are used during anomaly scoring to give higher influence to stable sensors, as deviations in their readings are more likely to indicate genuine faults rather than noise.

2.3. Model Architecture and Scoring

• Temporal Encoding: A weight-shared GRU encodes normalized sensor channels independently. To capture temporal dynamics beyond the final state, the model aggregates hidden states via final state, mean pooling, and max pooling, followed by a linear projection.
• Sensor Identity: Learnable sensor embeddings are concatenated with temporal representations to distinguish physical sensors.
• Graph Message Passing: The model propagates information over the fixed domain-prior graph $A$. The authors evaluate various backbones (GCN, GraphSAGE, GAT, Graph Transformer), finding that GraphSAGE (which explicitly consumes edge weights) performs best.
• Forecasting and Scoring: The model predicts future time steps and minimizes Mean Squared Error (MSE). Anomaly scores are computed by aggregating per-sensor forecast errors, normalized via Interquartile Range (IQR), and weighted by the CV-based reliability scores. The final window score combines a mean term (for distributed anomalies) and a max term (for localized high-amplitude deviations).

3. Key Contributions

1. DPR-GM Framework: A novel approach that gates sensor graph topology using domain knowledge and modulates edge weights via Pearson correlation, incorporating CV-based reliability weighting for anomaly scoring.
2. LLM-Driven Prior Extraction: Demonstrating that domain priors can be automatically extracted from system documentation using LLMs, broadening applicability to CPS without requiring manual expert annotation.
3. Performance on Strict Protocols: Showing that DPR-GM outperforms graph-based, statistical, and deep learning baselines on the SKAB benchmark under a strict point-wise evaluation protocol, particularly on threshold-free ranking metrics (AUROC, AUPRC).

4. Experimental Results

The authors evaluated DPR-GM on the SKAB (Skoltech Anomaly Benchmark), a multivariate time-series dataset from a water pump testbed containing 34 fault scenarios across three splits.

• Comparison with Graph-Based Methods: DPR-GM significantly outperformed GDN and GReLeN, which collapsed (near-zero F1) due to instability in learning graphs from limited data. While MTAD-GAT achieved high recall, it suffered from poor threshold-free metrics (AUROC/AUPRC), indicating a lack of score discrimination. DPR-GM achieved superior AUROC (0.7256 vs. 0.5794 for MTAD-GAT) and AUPRC (0.7165 vs. 0.4566).
• Comparison with Non-Graph Baselines: DPR-GM outperformed statistical methods (e.g., T2+Q, MSET) and deep learning models (e.g., Conv-AE, LSTM-VAE, MSCRED) across all metrics except recall. Notably, it improved MCC by +0.050 over Vanilla AE, suggesting better-calibrated decision boundaries rather than exploitation of class imbalance.
• Ablation Studies:
  • Removing Edge-W (signed correlation modulation) degraded performance, confirming that empirical co-movement adds value even with a fixed topology.
  • Removing Node-W (CV-based reliability) also degraded performance, confirming the utility of sensor stability weighting.
  • Backbone Analysis: GraphSAGE (SAGE) yielded the most stable and effective performance, outperforming GCN, GAT, and Graph Transformer, likely due to its explicit consumption of edge weights and separation of self/neighbor transformations.

5. Significance and Claims

The paper claims that domain-structured graph priors are a practical alternative to fully learned topologies in data-scarce CPS environments. By anchoring the graph in known physical coupling rather than treating it as a learnable parameter, DPR-GM avoids the spurious correlations and instability that plague data-driven graph learning when normal-operation data is limited.

The authors emphasize that their approach:

• Requires no learnable parameters for the graph structure or node weights, reducing the risk of overfitting.
• Provides stable and discriminative anomaly scores, evidenced by high AUROC and AUPRC, rather than recall-biased detection.
• Offers a scalable pipeline where LLMs can automate the extraction of structural priors from documentation, making the method applicable to systems lacking manual expert annotation.

The work concludes that explicit domain priors provide a robust foundation for anomaly detection, suggesting a broader direction for incorporating symbolic or causal priors into scientific time-series modeling across various domains.