Causal-prior-constrained deep learning for rapid-intensification warning of western North Pacific tropical cyclones

Xinrui Li; Yijun Jin; Yifan Dong; Shoujuan Shu

cs.LGOct 29, 2026

Causal-prior-constrained deep learning for rapid-intensification warning of western North Pacific tropical cyclones

Authors: Xinrui Li, Yijun Jin, Yifan Dong, Shoujuan Shu

Organizations: Department of Atmospheric Sciences, School of Earth Sciences, Zhejiang University, Hangzhou, 310058, China · School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058, China

Abstract

Rapid intensification (RI) is one of the most dangerous and unpredictable phases of tropical cyclones, and its environmental and structural drivers are difficult to identify and separate in observations. Here we introduce CausalVisionRI, a causal-prior-constrained deep-learning system for 24-h RI warning in the western North Pacific. It integrates infrared remote sensing imagery, atmospheric and oceanic fields, and an observationally discovered causal graph into a unified model. The graph and eight sign-verified effects on 24-h intensity change provide an auditable causal prior for training. Discovered from 522 cyclones in 2000-2017, it identifies causal pathways linking atmospheric and oceanic conditions, the cyclone's dynamical and structural state, and its 24-h intensity change. On a forward holdout covering 2020-2024 and 3,004 records, the five-member ensemble achieves a Brier skill score (BSS) of 0.259 relative to a fixed development climatology, significantly exceeding four reference systems; the three LDA baselines reach at most 0.105. It also attains higher detection rates than a published knowledge-block scheme and a reconstructed contrastive-learning scheme at matched false-detection rates under our USA 30-kt standard and the published RITCF standard. Ablations show that the graph pathway adds 0.032 BSS across the holdout and 0.063 over 2020-2021, with a significant contribution in one ensemble member. A deep-learning model constrained by observationally discovered causal structure thus offers a new route to physically informed RI warning.

Figures & tables

Figure 1: The causal graph is discovered from 522 observed cyclones in 2000–2017. a , b , Prior-constrained PCMCI+ [ 4 ] graph (fit 2000–2017,

n=12{,}647

): a , six contemporaneous (lag 0) links at unadjusted

p\leq 0.05

; b , 81 lagged links at Benjamini–Hochberg false discovery rate (FDR)

q\leq 0.05

(6 h per lag). For legibility panel b retains the 32 strongest lagged partial correlations together with every direct parent of the 24-h intensity change

\Delta V_{24}

(33 of 81 significant lagged links shown); node fill denotes the variable family, edge colour the sign of the partial correlation and edge width/opacity its magnitude. Node outlines are doubled (halo) for the two direct parents of

\Delta V_{24}

: current intensity (VMAX) and outer-area ocean heat content (OHC_OA). c , d , Graph-adjusted effect estimates with bootstrap 95% confidence intervals (CIs;

B=200

) on 24-h intensity change ( c ) and on rapid intensification (RI) as conditional log-odds per SD ( d ), ordered by point estimate; solid black squares mark the eight treatments whose bootstrap-stable

\Delta V_{24}

signs enter the causal training loss, the open diamond marks upper-level divergence D200 (association only on both scales; no directed path to

\Delta V_{24}

in the identification DAG, with an inserted edge for its RI estimate) and open grey circles are not significant (bootstrap

p\geq 0.05

Figure 2: CausalVisionRI fuses satellite, environmental and causal-graph streams under sign-verified constraints. One branch reads storm-centred infrared imagery (TBB, black-body brightness temperature) with a ViT-B/16 vision-transformer backbone initialised from the LingBot-Vision base student [ 4 ] . A second condenses the 21-variable environmental state over five history steps through a multilayer-perceptron (MLP) encoder. These per-record histories also supply the GNN node features, while the discovered graph supplies its fixed topology and edge attributes. The pooled visual token attends to the environmental and causal tokens, with a per-record sigmoid gate

g

scaling the attention output. Adjacency cross-entropy matches incoming-edge attention to the coefficient-normalized prior weights. Sign–gradient and counterfactual losses use the eight estimated effect signs to constrain the

\Delta V_{24}

environmental response. The selected system is the equal-weight ensemble of five members selected on inner-period (2018–2019) skill; configuration details are given in the Methods.

Model	BSS dev	ROC-AUC	PR-AUC	POD	POFD	FARatio	CSI	$\Delta$ BSS [90% CI]
CVRI-Ens	0.259	0.900	0.518	0.680	0.095	0.635	0.311	–
SHIPS-12 LDA (COHC)	0.105	0.820	0.276	0.347	0.060	0.686	0.197	$+0.154$ [ $+0.079$ , $+0.214$ ]
SHIPS-12 LDA (OHCD)	0.095	0.813	0.266	0.473	0.095	0.715	0.216	$+0.164$ [ $+0.095$ , $+0.222$ ]
LDA (21 panel predictors)	0.098	0.813	0.278	0.730	0.250	0.811	0.176	$+0.161$ [ $+0.097$ , $+0.215$ ]
LR (uncalibrated)	$-2.074$	0.826	0.298	0.649	0.173	0.769	0.205	$+2.333$ [ $+1.935$ , $+2.866$ ]

Table 1: CVRI-Ens attains the highest BSS, ROC-AUC, PR-AUC and CSI, and the lowest FARatio, in the 2020–2024 holdout (

n=3{,}004

rows, 131 systems; RI base rate 7.39%). All models share the same rows and metrics; operating metrics use each model’s own inner-period F1 threshold (F1, harmonic mean of precision and recall).

\mathrm{BSS_{dev}}

, Brier skill score against the fixed 2000–2019 development climatology (0.0791).

\Delta

BSS is the storm-cluster paired bootstrap difference relative to CVRI-Ens, Holm adjusted; 90% confidence intervals (CIs) in brackets. POD, probability of detection; POFD, probability of false detection; FARatio, false-alarm ratio (

1-

precision); CSI, critical success index; ROC-AUC and PR-AUC, areas under the receiver-operating-characteristic and precision–recall curves; LR, logistic regression; LDA, linear discriminant analysis; SHIPS-12, 12-predictor Statistical Hurricane Intensity Prediction Scheme; COHC/OHCD, climatological ocean heat content / time-dependent daily OHC. Best value in each metric column in bold.

Figure 3: CVRI-Ens attains a Brier skill score (BSS) of 0.259 in the 2020–2024 holdout, exceeding all four reference systems. a , precision–recall curves (dashed line: rapid intensification (RI) base rate 7.39%); b , receiver-operating-characteristic curves; c , per-year BSS (development climatology) and critical success index (CSI); d , reliability diagram; e , predicted-probability distributions for RI and non-RI records (dashed line: inner-derived threshold 0.225); f , BSS of CVRI-Ens (CausalVisionRI-Ensemble) against the four reference systems (logistic regression, LR, is off scale). References share the same rows and threshold rule throughout.

Figure 4: Disabling the graph pathway costs significant holdout skill in 2020 and 2021. a , Per-year change in Brier skill score of the ensemble when the graph pathway is disabled (C2); positive values favour the graph pathway, and stars mark years where the gain is significant under the locked bootstrap rule. b , The same contrast for the five members individually; all five members gain in 2020 and four of five in 2021. In panel a , blue and orange distinguish positive and negative changes; member colours in panel b identify the ensemble members.

Figure 5: CVRI-Ens attains the highest detection rate at matched false-detection rates under both label standards. a , our standard: USA-agency 30-kt rapid intensification (RI) labels, test 2020–2024,

n=2{,}178

shared rows; b , the published standard of Wang et al. [5] : China Meteorological Administration (CMA) 25.27-kt labels, 2020–2021,

n=949

. Each point is one model at its stated or inner-derived operating rule. The 9.4% FARate values quoted in the text are interpolated from the corresponding score-sweep curves; the open marker in b shows the operating point reported by Wang et al. [5] on its own sample frame (

n=1{,}149

), which is external to the shared sample. POD

=

probability of detection; FARate

=

probability of false detection (POFD); FARatio

=

1-

precision. Panel-specific sample frames are listed in Supplementary Table S7.

Variable	Meaning	Construction	Source
Best-track state
VMAX	Current intensity	USA 1-min sustained wind (kt)	IBTrACS
PER	Recent intensification	VMAX( $t$ ) $-$ VMAX( $t-6$ h)	IBTrACS
SPD	Translation speed	Great-circle displacement rate between best-track positions (kt; nmi h -1 )	IBTrACS
LAT	Latitude	Storm-centre latitude	IBTrACS
LAND_DIST	Distance to land	Great-circle distance (km)	GSHHG coastline

Table 2: Environmental variables and physical definitions. Inner core means 0–2 ∘ and outer area means 2–8 ∘ around the storm centre.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Treatment	Outcome	Effect	CI low	CI high	E-value	E-value CI limit	$\boldsymbol{p}_{\mathrm{boot}}$	Refut.	Adjustment set
SHRD	DV24	$-$ 4.788	$-$ 5.387	$-$ 4.147	1.789	1.705	0.005	3/4	VORT
SHRD	RI	$-$ 0.729	$-$ 0.872	$-$ 0.595	3.386	2.891	0.005	2/4	VORT
RHLO	DV24	2.791	2.045	3.485	1.525	1.423	0.005	2/4	W500
RHLO	RI	0.112	0.003	0.211	1.453	1.059	0.040	1/4	W500
VORT	DV24	$-$ 3.825	$-$ 4.356	$-$ 3.237	1.662	1.585	0.005	3/4	LAT
VORT	RI	$-$ 0.152	$-$ 0.277	$-$ 0.041	1.567	1.240	0.010	2/4	LAT

Appendix

Table S1: Ocean heat content provides the largest positive graph-adjusted effects on 24-h intensity change, and only three of the twenty contrasts have a bootstrap confidence interval that crosses zero. Graph-adjusted effect estimates for the ten environmental treatments on 24-h intensity change (DV24, kt) and rapid intensification (RI, conditional log-odds) in the fit-period (2000–2017) panel (n = 12,647), with a 95% percentile bootstrap interval (200 storm-level resamples), the E-value at the estimate and at the confidence limit nearest the null, the bootstrap p-value, the number of the four refutation tests passed, and the backdoor adjustment set implied by the locked DAG (“none” = empty set).

Rank	Arm	Family	Threshold	BSS 2018	BSS 2019	Worst year	Selected
1	ens_lbB_partial4_sf	lingbot_sf	0.150	0.260	0.314	0.2604	yes
2	ens_lbB_lora16_temp5	lingbot_mf	0.250	0.383	0.247	0.2466	yes
3	ens_lbB_temp2	lingbot_mf	0.225	0.322	0.231	0.2306	yes
4	ens_lbB_lora16_sf	lingbot_sf	0.200	0.268	0.227	0.2275	yes
5	ens_lbB_temp5_slim	lingbot_mf	0.250	0.299	0.227	0.2266	yes
6	ens_lbB_lpft4_sf	lingbot_sf	–	0.256	0.219	0.2195	no

Appendix

Table S2: Ranking the 22 arms by their worse inner year selects five arms from two of the four families, and the resulting uniform-weight ensemble scores a pooled inner BSS of 0.332, above the highest single-arm pooled inner BSS (0.316). Inner-year selection table: per-year inner BSS for 2018 and 2019, the worst of the two years used as the ranking key, the inner-year F1 threshold of each selected member and whether the arm entered the production ensemble.

CVRI-Ens (Top-5)
Year	n	BSS dev	POD	POFD	FARatio	CSI
2020	559	0.276	0.674	0.097	0.633	0.312
2021	757	0.298	0.659	0.073	0.642	0.302
2022	571	0.159	0.639	0.099	0.697	0.258
2023	606	0.287	0.660	0.076	0.545	0.368
2024	511	0.252	0.761	0.142	0.653	0.312

Appendix

Table S3: CVRI-Ens has the highest BSS dev in every one of the five test years and the highest CSI in four of them (SHIPS-12 OHCD leads on CSI in 2020 alone), and both SHIPS-12 variants stay positively skilled throughout while the uncalibrated LR baseline does not. Verification metrics per test year (n = 3,004 rows in total; pooled row at the foot of each block) under the shared evaluation protocol: identical rows, identical RI label, fixed development climatology (2000–2019 RI rate 0.0791), and the operational threshold taken as the inner-year F1 optimum for each model.

Ensemble	K	n	BSS dev	ROC AUC	PR AUC	POD	POFD	FARatio	CSI
K4 (Top-4)	4	3,004	0.259	0.898	0.513	0.667	0.087	0.621	0.319
Top-5 (main)	5	3,004	0.259	0.900	0.518	0.680	0.095	0.635	0.311
K6 (Top-6)	6	3,004	0.279	0.902	0.527	0.662	0.076	0.589	0.339
all-22	22	3,004	0.244	0.905	0.509	0.743	0.128	0.684	0.285

Appendix

Table S4: K6 attains BSS dev 0.279, compared with 0.259 for K4 and Top-5, while all-22 attains 0.244. Full metric panel for the four ensemble sizes evaluated on the same 3,004 test rows under the locked protocol; members enter with uniform weights and each ensemble carries its own inner-year F1 threshold.

Member	Condition	$\boldsymbol{\Delta}$ BSS	90% CI	$\boldsymbol{p}_{\mathrm{Holm}}$	Significant
Part4	C1	$-$ 0.093	$[$ $-$ 0.160, $-$ 0.038 $]$	0.024	yes
Part4	C2	$-$ 0.014	$[$ $-$ 0.079, 0.053 $]$	0.681	no
Part4	C3s1	$-$ 0.076	$[$ $-$ 0.148, $-$ 0.017 $]$	0.174	no
Part4	C3s2	$-$ 0.071	$[$ $-$ 0.142, $-$ 0.014 $]$	0.174	no
Part4	C3s3	$-$ 0.059	$[$ $-$ 0.142, 0.007 $]$	0.292	no
Part4	C4adj	$-$ 0.072	$[$ $-$ 0.135, $-$ 0.018 $]$	0.174	no

Appendix

Table S5: Ten of the 40 member-by-condition contrasts survive Holm correction and all ten fall in three of the five members, while the protocol-locked C2 contrast (graph branch removed) reaches Holm significance in LoRA-sf. Full ablation panel: delta BSS (M0 minus ablation, positive = the causal prior helps) with 90% storm-cluster bootstrap intervals and Holm-adjusted p-values, for five ensemble members each ablated in eight conditions on the 3,004 test rows.

Member	gate mean	causal share	share $-$ 0.5	gate $\times$ share	gate RI	gate non-RI	$\boldsymbol{\Delta}$ gate
Part4	0.629	0.689	0.189	0.426	0.665	0.626	0.039
T2	0.620	0.299	$-$ 0.201	0.188	0.677	0.615	0.062
T5	0.488	0.260	$-$ 0.240	0.141	0.506	0.487	0.020
LoRA-T5	0.698	0.251	$-$ 0.249	0.175	0.666	0.701	$-$ 0.035
LoRA-sf	0.438	0.230	$-$ 0.270	0.091	0.414	0.440	$-$ 0.026

Appendix

Table S6: Members route different shares of their cross-attention to the causal graph token (causal share 0.230 to 0.689; gate mean 0.438 to 0.698); only one member’s causal share sits above the 0.5 no-preference line. Gate decomposition of the five ensemble members over the 3,004 test rows: mean fusion gate, head-averaged causal-token attention share, its deviation from the two-token no-preference line, the resulting causal influence weight, and the RI-minus-non-RI gate contrast.

Sample definition	n	Use
Official test set (main table)	3,004	All headline numbers
WRPS1 same-sample subset	2,892	WRPS1 delta-BSS bootstrap
RITCF reconstruction, CMA 30-kt frame	2,385	RITCF CMA 30-kt protocol
Panel A intersection	2,178	Consistent-comparison panel, our label standard
2020–2021 subset	1,316	Two-year supplementary contrast
RITCF as published	1,149	Their reported operating point (external anchor)

Appendix

Table S7: Eight sample frames are used in this study and are not interchangeable. The five in-house frames (3,004, 2,892, 2,178, 1,316 and 949 rows) are subsets of the official test table; 2,178 and 1,316 overlap, and 949 is their common subset. The two reconstructed RITCF frames (2,385 and 1,057 rows) are used for the protocol reconstructions, and the consistent-comparison panels (2,178 and 949 rows) are their intersections with our frozen rows. The 1,149-row frame is the external anchor reported by Wang et al. [5] . Sample-size census, with the use to which each row count belongs.

Panel	n	RI USA	RI CMA	Rate USA	Rate CMA	Jaccard	Agreement
A (our standard)	2,178	209	120	0.096	0.055	0.530	0.954
B (their standard)	949	83	66	0.087	0.070	–	–

Appendix

Table S8: The two wind sources assign the same RI label to 95.4% of the 2,178 panel-A rows; 114 of the 215 rows positive under either source coincide (Jaccard 0.530). Panel A compares USA-30 with CMA-30 (209 and 120 RI rows; base rates 0.096 and 0.055), and panel B compares USA-30 with CMA-25.27 (83 and 66; 0.087 and 0.070). RI counts and base rates are shown for both panels; RI-set Jaccard and row-level label agreement are shown for panel A only.

#	Predictor	Definition (radius)	Source in this study	Fidelity
1	VMAX	Maximum sustained wind (kt)	Panel VMAX (IBTrACS USA_WIND, 1-min)	EXACT
2	INCV	6-h intensity change, t $-$ 6 h to t0 (kt)	Panel PER (6-h IBTrACS track difference)	EXACT
3	POT	Potential intensity minus VMAX (kt), 0–200 km	tcpyPI 1.4.1 [ 2 ] on ERA5 soundings, 0–200 km; Bister–Emanuel algorithm [ 1 ]	APPROX
4	OHCD	Ocean heat content (kJ cm -2 ), 0–100 km	GLORYS12V1 daily field, closed window (source_time $+$ 24 h $\leq$ t0)	BETTER
5	SHRD	850–200 hPa shear magnitude (kt), 200–800 km	ERA5 u/v annular mean difference	EXACT
6	T150	150 hPa temperature ( ∘ C), 200–800 km	Log-p extrapolation from 200/300 hPa (no local 150 hPa level)	SUBSTITUTED

Appendix

Table S9: Six of the twelve SHIPS predictors are reproduced exactly, one near-exactly and one by interpolation; the remaining substitutions are recorded below. The twelve predictors of Horinouchi et al. (2025) as re-derived on our own panel, with the radius of the area average, the source used here and the fidelity label recorded in the baseline documentation.

Assumption	Handling here	If violated
Causal sufficiency (no unobserved confounder)	All candidate drivers drawn from reanalysis and best-track fields; E-values quantify the confounding strength needed to explain each effect away (Table S1)	Estimates may be biased in either direction; E-values give the minimum confounding strength required to explain an effect away (DV24: 1.13–2.08; RI: 1.33–3.39)
Stationarity of links	Discovery on the 2000–2017 fit window only; four sensitivity configurations re-estimated (Note S2)	Within-window sensitivity does not test stationarity; the configurations probe lag selection, climate indices, latitude and OHC dependence (Note S2), and alternative DAG constructions are audited separately (Note S1)
Faithfulness (observed independencies reflect the graph)	Masked tests with mask_type=xyz ; BH control at $q\leq 0.05$ for lagged links and unadjusted $p\leq 0.05$ for contemporaneous links	Weak-signal links may be missed (e.g., MFC), limiting detection power rather than demonstrating unfaithfulness
Temporal ordering	Six-hourly storm-aligned grid; target never interpolated	Lagged-link orientations rely on the six-hourly ordering; lag-0 links are handled separately (flagged or removed in the strict configuration)

Appendix

Table S10: Discovery assumptions, their handling, and the consequences if violated.

Figure S1: All 22 development arms, ranked by two-year-worst inner-period (2018–2019) Brier skill score (BSS); the framed bars form the selected Top-5 equal-weight ensemble. Colour denotes the backbone origin (LingBot-Vision initialised, or masked-autoencoder routes on the global or western North Pacific corpora); hatching denotes multi-frame temporal variants.

Figure S2: The equal-weight Top-5 ensemble exceeds every member on the test period (2020–2024). Bars: test BSS of the five members and of the ensemble (dotted line: best single member).

Panel of Figure 20 — Figure S3: CVRI-Ens lies at or above the reference precision–recall curves for recall $>0.14$ and at or above the reference ROC curves throughout on the shared 2,178-row sample (USA-agency 30-kt labels, 2020–2024). The shared sample intersects the 3,004 frozen holdout records with the RITCF CMA-wind/frame/storm eligibility records, then retains rows with all 12 SHIPS predictors finite. It contains 209 RI events (base rate 9.60%), whereas the full holdout has a base rate of 7.39%. All models are evaluated on the same rows under the same USA-agency 30-kt labels. RITCF curves and public 6/10 points use best-AUC checkpoints; inner-F1 operating markers use the stated validation sweep.

Figure S4: Under CMA 30-kt labels on the same 2,178 rows, CVRI-Ens retains the highest CSI and the highest POD at 9.4% FARate. All models are re-scored from frozen predictions under the CMA labels. Open markers use thresholds re-derived on inner-period data under those labels; filled markers use public or locked rules. The 9.4% FARate POD values are interpolated from the empirical POD–FARate curves; RITCF markers use best-AUC checkpoints.

Figure S5: On the test years nearest the estimation window (2020–2021), all five members benefit from the graph pathway and six of the 40 contrasts are Holm-significant, all favouring the prior. Ablation deltas (

\Delta

BSS

=

full member (M0)

-

ablated member; positive values favour the prior) on the 1,316-row 2020–2021 subset (55 storms), with storm-cluster bootstrap 90% confidence intervals and Holm adjustment within each member’s eight-condition family (

\alpha=0.10

); blue and orange mark contrasts that survive Holm adjustment, grey do not. C1 removes all causal losses, C2 disables the graph neural network (GNN) branch, C3s1–3 replace the prior graph with shuffles that preserve each node’s degree in the environmental subgraph while holding loss weights fixed, and C4 retains a single loss term. The full-period contrasts are listed in Supplementary Table S5.

Figure S6: Members differ in fusion-gate activation and in the share of cross-attention assigned to the prior. a , Mean fusion-gate activation per member on the 3,004 test rows. b , Head-averaged share of cross-attention assigned to the causal token (reference 0.5 for two context tokens).

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Rapid intensification (RI) remains one of the most consequential and difficult aspects of tropical cyclone (TC) forecasting. Although full-physics numerical weather prediction models can represent the processes governing RI, resolving storm-environment interactions remains computationally expensive, while purely data-driven approaches often lack physical interpretability. We present FAST-ML, a hybrid framework that bridges data-driven efficiency with physical constraints. A physically informed dual-stream neural parameterization ingests 3D ERA5 fields to diagnose ventilation controls---environmental wind shear and mid-level entropy deficit. By optimizing these parameters end-to-end through a differentiable FAST intensity model, this architecture establishes a robust new paradigm for observation-driven parameter optimization, ensuring storm evolution remains strictly governed by thermodynamic principles. By better capturing the storm's continuous intensity evolution, FAST-ML improves upon its physical baseline, reducing ensemble CRPS across forecast lead times, with a reduction of approximately 31% at 60 h and nearly halving the RI false alarm ratio without sacrificing detection skill. In a 100-member ensemble configuration, FAST-ML produces intensity forecasts comparable to FNV3 for selected storms under the evaluated input configurations. Furthermore, zero-shot tests on selected Eastern Pacific storms provide encouraging evidence of cross-basin transferability. FAST-ML provides a modular intensity forecasting framework that can be coupled with externally supplied storm tracks and environmental fields. It demonstrates that observation-driven parameter learning within physically constrained dynamics simultaneously enhances accuracy, interpretability, and computational efficiency.

Abstract

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