Tianmu-TC: Physics-constraints Generative Artificial Intelligence for Global Tropical Cyclone Forecasting

Shiqi Zhang; Pan Mu; Cheng Huang; Hanting Yan; Yuchao Zhu; Jinglin Zhang; Shengyong Chen; Shoujuan Shu

Figure 1: Physics-constraints for TC forecasting. ( A ) Overall schematic: meteorological factors influencing the development of TCs. ( B ) Proposed physics-constraints govern the generation process and achieve a lower uncertainty score with the smallest prediction area. ( C ) The data composition of atmospheric environment constraint. The large-scale wind field consists of the zonal

u

and meridional wind

v

components from 200 hPa to 850 hPa. High-pressure systems are composed of the South Asian High (SAH,

z200

) and the Western Pacific Subtropical High (WPSH,

z500

), where

z

denotes geopotential height. ( D ) TC tilt metrics: calculated from vorticity data at three pressure levels. See details in Materials and Methods.

Figure 2: Framework of Tianmu-TC. Tianmu-TC consists of three key components: (1) Constraint Encoder for preliminary constraint encoding, (2) Cross-Modal Fusion module to establish correlations between constraints, and (3) Constraint guiding denoising module to perform the final denoising process. The

y_{K}\sim y_{0}

represents the TC prediction results under different diffusion steps

k

. To facilitate clear visualization, only the predicted track is displayed here, whereas wind speed and pressure predictions are simultaneously generated. From

y_{K}

to

y_{0}

, the blue dashed line gradually converges from noise to near ground truth. The single-step denoising process from

y_{k}

to

y_{k-1}

is implemented by the Physics-constraints Denoising Block , which operates under the guidance of physics- constraints.

Figure 3: Results under different constraints. ( A ) Generation results of Typhoon Krosa at 00:00 UTC on August 16, 2019, under five constraint settings with decreasing diffusion steps

k

(from 100 to 0). Shaded regions represent uncertainty. Applying all constraints (

C_{1}

,

C_{2}

, and

C_{3}

; rightmost column) results in the most concentrated predictions with the lowest uncertainty. ( B ) For the Typhoon Krosa at 00:00 UTC on August 16, 2019, corresponding to (A), the mean and variance of the predictions are visualized as spread distributions. Smaller variance leads to a steeper curve, indicating lower prediction uncertainty. ( C ) Average prediction errors across 146 TCs from 2017 to 2023. The rows correspond to ( a ) track, ( b ) pressure, and ( c ) wind speed.

Figure 4: Comparison of average forecast errors with large-scale meteorological models and the authoritative NWP system during the test period from 2017 to 2023. The testing regions cover six ocean basins: ( A ) Eastern North Pacific (EP), ( B ) North Atlantic (NA), ( C ) North Indian (NI), ( D ) South Indian (SI), ( E ) South Pacific (SP), and ( F ) Western North Pacific (WP). ( G ) Comparison of computational efficiency metrics with large-scale meteorological models.

Figure 5: Visualization of track predictions for representative TCs across six ocean basins. Each basin presents forecasts for a specific TC at three consecutive initialization times: ( A ) EP (Jimena), ( B ) NA (Rene), ( C ) NI (Ockhi), ( D ) SI (Enawo), ( E ) SP (Gita), and ( F ) WP (Sonca).

Category	Scenario (Unit)	Methods	Samples	Forecast Horizon
Category	Scenario (Unit)	Methods	Samples	+6h	+12h	+18h	+24h
Track	Anomaly (km)	Pangu	582	44.13	55.90	72.75	104.26
		Fengwu	582	44.19	49.33	65.89	95.62
		ECMWF	582	40.32	50.26	61.82	78.11
		Ours	582	16.90	17.28	34.74	70.38
	Landfall (km)	Pangu	304	47.86	62.09	87.55	125.50

Table 1: Results on special TC scenarios on global area from 2017 to 2021. Samples is the number of cases. Lower values indicate better performance. “Anomaly” consists of circular movement, turning on the ocean, and V-shaped tracks. “ RI ” denotes Rapid Intensification , and “ RW ” denotes Rapid Weakening of TCs.

Figure 6: Visualization of complex prediction scenarios. ( A ) Track prediction, ( B ) wind speed, and ( C ) pressure. For (A), four challenging track cases are illustrated: ( Aa ) circular track, ( Ab ) post-landfall prediction, ( Ac ) turning on the ocean, and ( Ad ) V-shaped movement. ( Ba )–( Bb ): rapid intensification ; ( Bc )–( Bd ): rapid weakening . Rapid intensification is defined as a tropical cyclone’s wind speed increasing by more than 30 knots (15.43 m/s) within 24 hours, whereas rapid weakening refers to the opposite process. ( C ) displays the corresponding pressure prediction results for (B).

Model	Samples	Track Error (km)			Pressure Error (hPa)			Wind Speed Error (m/s)			Training time	Inference time
Model	Samples	+12h	+24h	Overall	+12h	+24h	Overall	+12h	+24h	Overall	Training time	Inference time
NeuralGCM	684	67.52	83.28	75.40	/	/	/	/	/	/	3 weeks	11.9 s
GenCast	684	43.25	62.00	52.63	10.71	10.75	10.73	10.10	9.93	10.02	5 days	32 s
Tianmu-TC	684	17.52	66.37	41.95	0.39	1.46	0.92	0.72	2.11	1.41	2 days	1.23 s

Table 2: Comparison with deterministic NeuralGCM and GenCast forecasts. Results are reported on test samples for the year 2020 at the overlapping forecast horizons of +12 h and +24 h. Track error, pressure error, and wind speed error are measured in km, hPa, and m/s, respectively. Lower values indicate better performance. In “Inference time”, s denotes seconds.

Task	Model	Samples	Mean Error			Std. Error			Spread			Best-of-50
Task	Model	Samples	+12h	+24h	Overall	+12h	+24h	Overall	+12h	+24h	Overall	+12h	+24h	Overall
Track (km)	NeuralGCM-ENS	521/505	91.75	126.87	109.04	31.88	57.18	44.33	95.02	145.47	119.85	62.36	67.16	64.72
	GenCast-ENS	521/505	92.28	175.74	133.36	51.91	104.05	77.57	96.40	189.52	142.24	24.76	39.86	32.19
	Tianmu-TC-ENS	521/505	28.40	109.86	68.49	8.76	34.16	21.26	22.33	85.29	53.32	10.42	40.94	25.44
Pressure (hPa)	NeuralGCM-ENS	/	/	/	/	/	/	/	/	/	/	/	/	/
	GenCast-ENS	521/505	9.72	10.05	9.88	1.30	1.92	1.60	1.34	2.05	1.69	6.88	6.27	6.58

Table 3: Comparison with ensemble NeuralGCM and GenCast forecasts. Results are reported on test samples for the year 2020 at the overlapping forecast horizons of +12 h and +24 h. The overall value is computed over the combined +12 h and +24 h samples. NeuralGCM-ENS, GenCast-ENS and Tianmu-TC-ENS denote the ensemble versions of NeuralGCM, GenCast and Tianmu-TC, respectively. For a fair comparison, all ensemble-based methods are evaluated using 50 members.

Figure 7: Lifecycle visualization of multi-trend track forecasts for Typhoon ATSANI (WP, 2020). The main panel shows the rolling 12-h forecast path over the TC lifecycle, where each method is represented by the mean track of 50 ensemble members (i.e., multiple possible tracks), and the black curve denotes the best-track positions. The numbered panels show the spatial distributions of the 50 ensemble-predicted TC positions for representative cases selected from the main panel, covering early, middle, and late lifecycle stages as well as unusual looping-track predictions. In each numbered panel, circles indicate the spatial dispersion of the forecast members, and the values

N

,

G

, and

T

denote the corresponding dispersion radii of NeuralGCM-ENS, GenCast-ENS, and Tianmu-TC-ENS, respectively. The black star denotes the best-track position. The selected cases reveal different performance regimes, including accurate and biased situations.

Row	Real-time	Data			Track Error (km)				Pressure Error (hPa)				Wind Speed Error (m/s)
Row	Real-time	$X_{his}$	$X_{ERA5}$	$X_{tilt}$	+6h	+12h	+18h	+24h	+6h	+12h	+18h	+24h	+6h	+12h	+18h	+24h
1	yes	/	/	/	114.88	228.64	331.53	428.40	2.78	4.93	6.04	6.94	1.57	2.84	3.72	4.50
2	yes	6h	/	/	57.30	104.16	146.70	191.52	2.20	3.08	3.62	4.15	1.34	1.93	2.26	2.58
3	yes	12h	/	/	34.71	57.52	83.13	116.12	1.31	1.94	1.91	2.62	0.62	1.25	1.17	1.54
4	yes	18h	/	/	26.43	39.97	61.88	93.99	1.10	2.03	1.97	2.67	0.59	1.13	1.09	1.47
5	yes	24h	/	/	20.97	30.21	46.45	77.19	0.96	1.60	1.61	2.33	0.50	0.86	0.86	1.25

Table 4: Testing results under missing input conditions. The last row corresponds to the complete model (Tianmu-TC).

X_{his}

,

X_{ERA5}

,

X_{tilt}

refer to TC historical attribute values, ERA5 data, and TC tilt values, respectively.

+6h

to

+24h

indicate prediction horizons in hours. Lower values represent better performance.

Figure 8: Analyzing the correlation between track and intensity prediction. (A) Ablation results when predictions are made individually and jointly. (B) Saliency maps of historical attribute values. The columns correspond to ( a ) track, ( b ) pressure, and ( c ) wind speed.

		Prediction Horizon (hours)
Error Type	Method	$+6h$	$+12h$	$+24h$	$+48h$	$+72h$
Track Error (km)	CMO	32.4	52.9	75.5	132.1	201.1
	ECMWF	42.3	47.0	65.8	116.8	193.6
	Tianmu-TC	17.8	21.9	69.1	238.7	438.9
Pressure Error (hPa)	CMO	2.6	4.37	6.25	9.01	11.25
	ECMWF	10.9	11.2	11.8	12.9	11.7

Table 5: Compare the prediction errors at a 72-hour forecast horizon with authoritative NWP methods in WP basin. The testing years are from 2017 to 2023.

Category	Scenario (Unit)	Methods	Samples	Forecast Horizon
Category	Scenario (Unit)	Methods	Samples	+6h	+12h	+18h	+24h
Track	Anomaly (km)	Pangu	1103	56.25	62.96	77.58	110.94
		Fengwu	1103	44.19	49.33	65.89	95.62
		Ours	1103	18.08	17.72	36.93	73.57
	Landfall (km)	Pangu	582	59.84	76.14	101.26	131.16
		Fengwu	582	52.33	62.04	76.14	93.80

Table S1 : Extended-Sample Comparison on special TC scenarios on global area from 2017 to 2021. Samples is the number of cases. Lower values indicate better performance. “Anomaly” consists of circular movement, turning on the ocean, and V-shaped tracks. “RI” denotes Rapid Intensification , and “RW” denotes Rapid Weakening .

Figure S1 : Central Information Enhancement (CenIE) block. Considering that the center of selected ERA5 data corresponds to the location of the TC center, specifically, the longitude and latitude coordinates in the track task. Besides, pressure represents the lowest pressure near the TC center, and wind speed denotes the two-minute maximum sustained wind speed near the TC center. In other words, the predicted attributes are all the attributes in and around the TC center. Therefore, we define TC center as a highly task-relevant area. To enhance task-relevant information in the selected ERA5 data, CenIE block enhances the center point

E_{a,b}^{t+i^{\prime}}

of original 2D data

E_{t+i}^{\prime}

and

E_{t+i}=concat(E_{t+i}^{\prime},E_{t+i}^{\prime}-E_{a,b}^{t+i^{\prime}})

, where

C

in the figure denotes channel concatenation,

i\in[1,n]

, the

a

and

b

denote the coordinates in the geopotential height map,

H

and

W

denote the width and height of the map, and

n

denotes the length of the historical data. That is, the value of each pixel point in

E_{t+i}^{\prime}

is subtracted from that of the current central point

E_{a,b}^{t+i^{\prime}}

, and concatenated with the original

E_{t+i}^{\prime}

. Finally, CenIE block outputs the enhancement of central information

E_{t+i}

. This data preprocessing method is very simple and does not need GPU resources.

Figure S2 : Comparison with additional operational models in the EP and NA basins. We include authoritative forecasting systems issued by the National Hurricane Center (NHC): the official forecast (OFCL), and the statistical-dynamical model combination OCD5, which merges CLP5 (track) and DSHP (intensity). Other models include EMXI (ECMWF global model from the previous cycle), HCCA (a weighted consensus of multiple dynamical and statistical models), as well as recent large models Pangu and Fengwu. Testing period: from 2017 to 2023.

Figure S3 : More comparison methods on WP.

Figure S4 : Quantitative results of uncertainty for ( a ) track, ( b ) pressure and ( c ) wind speed.

Tianmu-TC: Physics-constraints Generative Artificial Intelligence for Global Tropical Cyclone Forecasting

Abstract

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