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Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations
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Proposes GgNet, a nested-graph spatio-temporal GNN that learns both inter-location and intra-location (channel) dependencies to reconstruct missing channels from sparse multivariate sensors.
Problem
Multivariate virtual sensing: inferring missing channels at unmonitored or sparsely monitored locations when spatial proximity offers little interpolation information and no historical data exists for the target.
Approach
A nested graph with a learned inter-location graph (node embeddings define adjacency) and a shared intra-location channel graph, processed by temporal, location and channel graph convolutions, so the model exploits learned location similarity and cross-variable dependencies rather than physical distance.
Key results
- On daily climatic data, GgNet reaches 20.4% average channel MRE versus 22.2% for SAITS and 23.3% for GRIN (13.5% relative improvement over SAITS per the paper's table).
- On hourly climatic data, GgNet achieves the best average MRE of 14.0 in the ablation-level comparison; main table reports 20.4 (daily) and 8.1% improvement over the second best on hourly averages.
- On the photovoltaic dataset, GgNet's relative MAE improvement over SAITS grows from 3.0% at 10 locations to 14.2% at 200 locations (357 vs 416 W*h at N=200).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GgNet's nested inter-location and intra-location graph processing | GgNet · Daily climate test | MRE (%): 15.5_{\pm0.5} -> 13.4_{\pm0.2} | Helped |
| Use GgNet's nested inter-location and intra-location graph processing | GgNet · Hourly climate test | MRE (%): 22.2_{\pm0.5} -> 20.4_{\pm0.6} | Helped |
| Use GgNet instead of the strongest baseline at each location count | Photovoltaic virtual sensing · Photovoltaic test, 10–200 locations | MAE (W*h): 466\pm68 -> 452\pm67; 451\pm46 -> 455\pm39; 446\pm42 -> 439\pm32; 424\pm23 -> 415\pm26; 428\pm21 -> 410\pm26; 420\pm16 - | Mixed |
| Add self-loops to GRIN's Spatial Decoder | GRIN · Daily climate test | MRE (%): 19.8_{\pm0.6} -> 16.5_{\pm0.6} | Helped |
| Add bidirectional processing | RNN · Daily climate test | MRE (%): 22.9_{\pm0.2} -> 20.6_{\pm0.3} | Helped |
| Add learnable node embeddings | Bidirectional RNN · Daily climate test | MRE (%): 20.6_{\pm0.3} -> 19.8_{\pm0.5} | Helped |
| Add inter-location graph convolution | Bidirectional RNN with node embeddings · Daily climate test | MRE (%): 19.8_{\pm0.5} -> 18.4_{\pm0.5} | Helped |
| Add g-convolution to the architecture (ablation) | GgNet · Daily climate test | MRE (%): 23.8_{\pm0.7} -> 14.0_{\pm0.1} | Helped |
| Add temporal convolutions (ablation) | GgNet · Daily climate test | MRE (%): 17.3_{\pm1.1} -> 14.0_{\pm0.1} | Helped |
| Add G-convolution (ablation) | GgNet · Daily climate test | MRE (%): 16.1_{\pm0.4} -> 14.0_{\pm0.1} | Helped |
| Increase the fraction of masked training channels from zero to a small fraction | GgNet · Daily climate test | Accuracy | Helped |
Surprising findings
- Graph-based GRIN underperforms badly at geographically isolated locations, where global non-spatial models like SAITS do better, showing reliance on physical proximity is a failure mode.
- The bidirectional RNN and channel-graph components give large gains, and removing the temporal convolution or the channel graph hurts performance substantially in ablation.
Limitations
- Inter-location graph scales quadratically with number of locations (N^2), limiting scalability.
- Transductive only: node embeddings must be learned per location, so new locations need fine-tuning.
- Graph-based message passing offers little benefit for geographically isolated locations, relying instead on channel covariates.
Experimental setup
Datasets: NASA POWER daily climatic data NASA POWER hourly climatic data Photovoltaic power simulations over continental North America
Benchmarks: NASA POWER daily climatic NASA POWER hourly climatic Photovoltaic power simulation dataset
Metrics: Mean Relative Error (MRE) Mean Absolute Error (MAE)
Baselines: KNN BRITS SAITS GRIN GRIN_m RNN RNN_BiD RNN_Emb
Builds on: GRIN BRITS SAITS Graph WaveNet adaptive adjacency
Closest papers by meaning
- A Scalable Multi-Task Model for Virtual Sensors (NeurIPS 2026 · similarity 0.86)
- DarkFarseer: Robust Spatio-Temporal Kriging Under Graph Sparsity and Noise (AAAI 2026 · similarity 0.85)
- Inductive Graph Neural Networks for Spatiotemporal Kriging (AAAI 2021 · similarity 0.85)
- KITS: Inductive Spatio-Temporal Kriging with Increment Training Strategy (AAAI 2025 · similarity 0.83)
- Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data (AAAI 2024 · similarity 0.83)
- Graph Structure Learning for Spatial-Temporal Imputation: Adapting to Node and Feature Scales (AAAI 2025 · similarity 0.81)
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