Abstract Effective monitoring of industrial emissions is essential for environmental sustainability. This study presents the Graph Attention Sensor (GAS), a forecasting framework that integrates graph attention networks with Time2Vec to model complex multivariate dependencies among co-located emission sensors. Unlike conventional time-series models, GAS represents pollutant sensors as nodes in a relational graph, enabling selective attention to inter-pollutant interactions while preserving causal temporal dynamics. GAS is benchmarked against random forest, NBeats (neural basis expansion analysis for interpretable time series), temporal convolutional network (TCN), long short-term memory (LSTM), and temporal fusion transformer (TFT) under nested cross-validation on real-world emission data from a high-purity ferrosilicon industrial plant. Results reveal that GAS achieves the highest performance for TSP forecasting under constrained context windows (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$P \le 22$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mo>≤</mo> <mn>22</mn> </mrow> </math></EquationSource> </InlineEquation>) across all forecast horizons, while NBeats dominates for gaseous pollutants (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\text {SO}_x$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>SO</mtext> <mi>x</mi> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\text {NO}_x$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>NO</mtext> <mi>x</mi> </msub> </math></EquationSource> </InlineEquation>) with extended historical context. Across all architectures, GAS exhibits the most stable cross-horizon degradation, maintaining positive R2 for TSP at <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$t_6$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>t</mi> <mn>6</mn> </msub> </math></EquationSource> </InlineEquation>, where random forest collapses to sub-baseline performance. Analysis of aggregated attention maps reveals that GAS identifies that <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\text {NO}_x$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>NO</mtext> <mi>x</mi> </msub> </math></EquationSource> </InlineEquation> is associated with the furnace thermal state, a physically grounded relationship that emerges from the data without explicit encoding. These findings support a pollutant-stratified deployment strategy and provide practical guidance for model selection in industrial emission monitoring. Graphical Abstract

Graph Attention Sensor Transformer for Industrial Emission Forecasting: A Comparative Study Against Classical and Deep Learning Baselines

期刊论文
发表日期：

2026年7月18日

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Roberto Chang-Silva,
Nakhun Song,
Kyungil Lee,
Seonyoung Park

摘要

Abstract

Effective monitoring of industrial emissions is essential for environmental sustainability. This study presents the Graph Attention Sensor (GAS), a forecasting framework that integrates graph attention networks with Time2Vec to model complex multivariate dependencies among co-located emission sensors. Unlike conventional time-series models, GAS represents pollutant sensors as nodes in a relational graph, enabling selective attention to inter-pollutant interactions while preserving causal temporal dynamics. GAS is benchmarked against random forest, NBeats (neural basis expansion analysis for interpretable time series), temporal convolutional network (TCN), long short-term memory (LSTM), and temporal fusion transformer (TFT) under nested cross-validation on real-world emission data from a high-purity ferrosilicon industrial plant. Results reveal that GAS achieves the highest performance for TSP forecasting under constrained context windows ( $P \le 22$ $P \leq 22$ ) across all forecast horizons, while NBeats dominates for gaseous pollutants ( $\text {SO}_x$ ${SO}_{x}$ , $\text {NO}_x$ ${NO}_{x}$ ) with extended historical context. Across all architectures, GAS exhibits the most stable cross-horizon degradation, maintaining positive R² for TSP at $t_6$ $t_{6}$ , where random forest collapses to sub-baseline performance. Analysis of aggregated attention maps reveals that GAS identifies that $\text {NO}_x$ ${NO}_{x}$ is associated with the furnace thermal state, a physically grounded relationship that emerges from the data without explicit encoding. These findings support a pollutant-stratified deployment strategy and provide practical guidance for model selection in industrial emission monitoring.

Graphical Abstract