Robust soft sensing with causal and injectivity-preserving Graph Neural Network
Bibliographic record
Abstract
Graph Neural Networks (GNNs) excel in soft sensing by effectively modeling complex interdependencies among process variables. This study presents a graph-based framework for improved process quality prediction in nonlinear, dynamic industrial systems. We address two key challenges in chemical process soft sensing: (i) unknown graphs where the structure is not available a priori , and (ii) injectivity issues from scalar features. To resolve non-injective aggregation, where distinct neighborhoods become indistinguishable, we expand the input domain to preserve structural uniqueness in both undirected and directed graphs. We also propose a method for learning directed graphs using Sparse Debiased Dynamic Mode Decomposition, which captures temporal dynamics and produces sparse, interpretable, and noise-resilient representations. An end-to-end framework jointly learns the graph structure and GNN parameters, allowing the graph to adapt during training based on the prediction task. The proposed methods are validated through simulations under varying noise levels and a benchmark case study involving a Sulfur Recovery Unit, demonstrating strong robustness and predictive performance. • Introduces an injectivity-preserving GNN framework for industrial soft sensing. • Proposes sparse, debiased DMD to infer spatiotemporal causal graph structures. • Jointly learns graph topology and GNN weights via an end-to-end loss formulation. • Demonstrates robustness under varying noise through extensive numerical simulations. • Validates superior predictive performance on benchmark Sulfur Recovery Unit process.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".