Structural Gating and Effect-aligned Lag-resolved Temporal Causal Discovery Framework with Application to Heat-Pollution Extremes

Rui Chen; Jinsong Wu

cs.LGApr 11, 2026

Structural Gating and Effect-aligned Lag-resolved Temporal Causal Discovery Framework with Application to Heat-Pollution Extremes

Authors: Rui Chen, Jinsong Wu

Organizations: School of Artificial Intelligence, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China · Department of Electrical Engineering, University of Chile, Santiago, Santiago Metropolitan Region, 8370451 Chile

Abstract

This study proposes Structural Gating and Effect-aligned Discovery for Temporal Causal Discovery (SGED-TCD), a novel and general framework for lag-resolved causal discovery in complex multivariate time series. SGED-TCD combines explicit structural gating, stability-oriented learning, perturbation-effect alignment, and unified graph extraction to improve the interpretability, robustness, and functional consistency of inferred causal graphs. To evaluate its effectiveness in a representative real-world setting, we apply SGED-TCD to teleconnection-driven compound heatwave--air-pollution extremes in eastern and northern China. Using large-scale climate indices, regional circulation and boundary-layer variables, and compound extreme indicators, the framework reconstructs weighted causal networks with explicit dominant lags and relative causal importance. The inferred networks reveal clear regional and seasonal heterogeneity: warm-season extremes in Eastern China are mainly linked to low-latitude oceanic variability through circulation, radiation, and ventilation pathways, whereas cold-season extremes in Northern China are more strongly governed by high-latitude circulation variability associated with boundary-layer suppression and persistent stagnation. These results show that SGED-TCD can recover physically interpretable, hierarchical, and lag-resolved causal pathways in a challenging climate--environment system. More broadly, the proposed framework is not restricted to the present application and provides a general basis for temporal causal discovery in other complex domains.

Figures & tables

Abbreviation	Variable Description	Spatial Domain (Latitude–Longitude)
Niño3.4	ENSO index representing SST anomalies in the central–eastern tropical Pacific	5 ∘ S–5 ∘ N, 170 ∘ W–120 ∘ W
IO_SST	Indian Ocean sea surface temperature anomaly index	20 ∘ S–20 ∘ N, 40 ∘ E–100 ∘ E
WP_SST	Western Pacific warm pool sea surface temperature anomaly index	0 ∘ –20 ∘ N, 120 ∘ E–160 ∘ E
NA_SST	North Atlantic sea surface temperature anomaly index	0 ∘ –60 ∘ N, 80 ∘ W–0 ∘
AO	Arctic Oscillation index	20 ∘ N–90 ∘ N
NAO	North Atlantic Oscillation index	20 ∘ N–80 ∘ N, 90 ∘ W–40 ∘ E

Table 1: Definitions for Each Considered Variable

Panel of Figure 1 — Figure 1: Monthly time series of heatwave indices and air pollution variables over Eastern China (EC) and Northern China (NC).

Figure 2: Standardized time series of major large-scale teleconnection indices.

Figure 3: Lagged correlations between teleconnection indices and EC near-surface temperature (T2m).

Panel of Figure 4 — Figure 4: Seasonal cycles of key meteorological mediators over EC and NC.

Figure 5: Comparison of meteorological mediators during concurrent and non-concurrent months in EC.

Eastern China (warm season)						Northern China (cold season)
Rank	Source $X_{i}$	Target $X_{j}$	$\tau^{\star}$	$s_{i\to j}$	Sign	Rank	Source $X_{i}$	Target $X_{j}$	$\tau^{\star}$	$s_{i\to j}$	Sign
1	T2m	O 3	0	0.110	+	1	PBLH	PM 2.5	0	0.102	–
2	Z500	T2m	1	0.090	+	2	WS10	PM 2.5	0	0.088	–
3	Niño3.4	Z500	3	0.081	+	3	Z500	PBLH	1	0.079	–
4	PBLH	O 3	0	0.074	+	4	AO	Z500	2	0.073	–
5	WS10	O 3	0	0.069	–	5	NAO	Z500	3	0.067	–

Table 2: Top-K candidate causal links extracted from SGED-TCD composite causal scores for Eastern China (warm season) and Northern China (cold season), ranked by pre-screening edge strength.

Eastern China (warm season)						Northern China (cold season)
Rank	Edge $i\to j$	$\tau^{\star}$	$f_{\text{boot}}$	$S_{\text{lag}}$	$\Delta$ Loss	Rank	Edge $i\to j$	$\tau^{\star}$	$f_{\text{boot}}$	$S_{\text{lag}}$	$\Delta$ Loss
1	T2m $\to$ O 3	0	0.91	1.00	0.15	1	PBLH $\to$ PM 2.5	0	0.88	1.00	0.14
2	Niño3.4 $\to$ Z500	3	0.82	1.00	0.15	2	WS10 $\to$ PM 2.5	0	0.80	1.00	0.12
3	Z500 $\to$ T2m	1	0.76	1.00	0.11	3	AO $\to$ Z500	2	0.74	1.00	0.10
4	WP_SST $\to$ Z500	3	0.78	0.67	0.12	4	NAO $\to$ Z500	3	0.71	1.00	0.09
5	Z500 $\to$ PBLH	1	0.74	1.00	0.08	5	Z500 $\to$ PBLH	1	0.69	1.00	0.08

Table 3: Top-K robust causal links retained after SGED-TCD robustness diagnostics for Eastern China (warm season) and Northern China (cold season), ranked by robustness.

Figure 6: SGED-TCD-inferred weighted causal networks for (a) Eastern China during the warm season and (b) Northern China during the cold season. Nodes represent large-scale climate indices, regional circulation and boundary-layer variables, and compound extreme indicators. Directed edges indicate robust causal influences retained after structural screening and robustness-guided graph extraction. Edge width is proportional to relative causal importance, edge color denotes the sign of the effect, and numerical labels indicate the dominant lag (months). Only edges that remain stable under lag-window sensitivity, block-bootstrap resampling, and ablation-based validation are retained.

Panel of Figure 7 — Figure 7: Early-warning ROC-AUC versus lead time ( $k=1$ – $4$ months) for compound heat–pollution months. Teleconnection features identified by SGED-TCD provide consistently higher discrimination skill than climatology, persistence, correlation-based selection, and Granger/VAR-selected baselines, with clearer advantages at longer lead times.

Time-Series Causal Discovery

Time-series causal discovery seeks to infer which variables influence others over time and when those effects occur.

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GRACE: Gated Refinement for Accurate Causal Edge Discovery in High-Dimensional Time Series

Mohammad Fesanghary, Abhinav Havaldar

Time-Series Causal Discovery Causal Discovery Constraint-Based Causal Discovery Causal Inference

Open paper AskPDF arXiv

From climate teleconnections to gene regulation, modern time-series datasets encompass tens or hundreds of interacting variables, making causal discovery increasingly challenging. Constraint-based methods offer statistical rigor but their nonlinear CI tests are infeasible at scale, while score-based alternatives avoid CI testing but require arbitrary thresholds to binarize continuous edge scores. We propose GRACE (

\textbf{G}

ated

\textbf{R}

efinement for

\textbf{A}

ccurate

\textbf{C}

ausal

\textbf{E}

dge discovery), which refines constraint-based discovery using Hard Concrete gates with

L_0

regularization: each candidate edge has an independent gate whose values concentrate near 0 or 1, yielding a clean bimodal separation that makes the binary decision robust, unlike the narrow, overlapping score distributions produced by

L_1

and attention-based methods. A fast linear CI skeleton provides high-recall candidates; a single gated model then prunes false positives by learning which edges genuinely improve prediction, with automatic regularization adapted to problem dimensions and skeleton density. Systematic experiments on synthetic benchmarks, spanning diverse graph topologies (scale-free, Erdős-R'enyi, small-world) and dimensionalities up to

d=100

, show that GRACE substantially improves F1 over its base CI method while maintaining high precision, and outperforms attention-based and score-based alternatives. GRACE matches or exceeds expensive nonlinear CI tests at a fraction of the cost (

75\times

faster). On a real-world river flow dataset, where rainfall confounders, variable propagation lags, and distributional shifts violate standard assumptions, a temporal bootstrap variant of GRACE recovers 9 of 11 causal edges along the Elbe River with only 1 false positive (

F_1 = 0.86

, AUROC

{} = 0.99

), reducing the skeleton's 106 false positives by 99%.

Abstract

Time-Series Causal Discovery

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