WxFM-XL: Adapting Univariate Foundation Models to Multi-Station Weather Forecasting

Xiao Wang; Changjian Chen; Zhuo Tang; Rongwen Li; Hongwu Liu; Kenli Li

cs.LGOct 7, 2026

WxFM-XL: Adapting Univariate Foundation Models to Multi-Station Weather Forecasting

Authors: Xiao Wang, Changjian Chen, Zhuo Tang, Rongwen Li, Hongwu Liu, Kenli Li

Abstract

With the rise of univariate time series foundation models (e.g., Sundial, Timer), initial efforts have been made to extend them to multivariate settings. However, these models mainly focus on modeling correlations among variables. When they are applied to multi-station weather forecasting, two important factors are often overlooked: (1) the spatial information of stations, and (2) different error priors of different stations relative to the foundation model. In this paper, we propose WxFM-XL, a model for adapting univariate time series foundation models to multi-station weather forecasting. WxFM-XL introduces a cross-station error correlation prior graph to capture stationwise error priors with respect to the foundation model. Building on this, we further propose a dynamic fusion mechanism that adaptively integrates a spatial correlation graph with the error correlation prior graph. Experiments on multiple datasets demonstrate that our model outperforms state of the art baselines.

Figures & tables

Figure 1: Visualization of error correlation dependencies for the v-component of wind speed in the French region. (a) Sundial’s forecast error correlations relative to an anchor station (star). (b) Topologies of spatial and band-specific error correlation graphs (showing top 600 edges with unique connections highlighted).

Figure 2: Overview of the WxFM-XL framework.

Models

WxFM-XL (Timer)

WxFM-XL (Sundial)

Timer

Sundial

AdaPTS (Timer)

AdaPTS (Sundial)

Moirai ft

Moirai

Timer-XL ft

Timer-XL

STELLA

CDPNet

MSGNet

Corrformer

Hunan

temp

5.14 ±0.01

5.06 ±0.09

5.28

5.78

5.33 ±0.05

5.57 ±0.11

5.65 ±0.27

5.24

5.43 ±0.15

5.26

8.56 ±0.84

7.44 ±0.79

5.89 ±0.39

6.01 ±0.47

7.31 ±0.04

7.33 ±0.05

7.52

8.35

7.73 ±0.42

8.51 ±0.51

7.54 ±0.29

7.52

9.29 ±0.27

7.37

16.06 ±1.97

26.94 ±6.19

12.45 ±0.93

8.60 ±0.48

v-wind

2.45 ±0.03

2.43 ±0.01

2.63

3.07

2.52 ±0.03

2.54 ±0.14

2.76 ±0.02

2.81

2.58 ±0.01

2.58

2.50 ±0.03

2.63 ±0.09

2.69 ±0.07

3.46 ±0.12

3.10 ±0.00

3.30 ±0.08

3.12

3.66

3.23 ±0.11

3.27 ±0.16

3.62 ±0.32

3.83

3.37 ±0.37

3.20

3.43 ±0.34

4.54 ±1.41

4.62 ±0.28

3.95 ±0.09

u-wind

2.08 ±0.00

2.02 ±0.00

2.16

2.57

2.14 ±0.13

2.16 ±0.02

2.38 ±0.01

2.37

2.14 ±0.01

2.16

2.03 ±0.01

2.15 ±0.03

2.30 ±0.12

2.14 ±0.05

2.15 ±0.03

2.15 ±0.11

2.35

2.80

2.31 ±0.04

2.29 ±0.13

2.71 ±0.03

2.82

2.27 ±0.03

2.35

2.21 ±0.00

2.51 ±0.09

2.89 ±0.15

2.39 ±0.19

Table 1: MSE results on the Hunan regional, French regional, and global datasets with a 96-hour input window and forecast horizons of 24 and 96 hours. Best and second-best results are shown in bold and underlined , respectively, based on unrounded values. Complete MAE results are reported in the appendix.

Model variant	Hunan regional			French regional
Model variant	temp	v-wind	u-wind	temp	v-wind	u-wind
WxFM-XL (Timer)	5.143 ±0.013	2.450 ±0.034	2.084 ±0.003	6.571 ±0.065	4.501 ±0.032	4.602 ±0.028
w/o frequency domain decomposition	5.393 ±0.022	2.559 ±0.067	2.140 ±0.011	6.773 ±0.065	4.696 ±0.032	4.900 ±0.024
w/o error correlation prior graph	5.430 ±0.033	2.534 ±0.019	2.110 ±0.002	6.808 ±0.124	4.672 ±0.073	4.882 ±0.025
w/o multi-scale temporal module	5.671 ±0.036	2.616 ±0.035	2.149 ±0.021	6.986 ±0.108	5.251 ±0.056	5.551 ±0.035

Table 2: Ablation results (MSE) on the Hunan regional and French regional datasets with a 96-hour input window and a 24-hour forecast horizon. Results are reported as the mean and sample standard deviation over three random seeds. Best results are shown in bold . Complete MAE results are provided in the appendix.

Figure 3: Performance comparison of WxFM-XL (Timer) under different time patch size configurations. The look-back window is set to 96, and the prediction horizon is 24.

Figure 4: Structural properties of prior graphs (taking the v-component of wind speed in the French region as an example).

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

Models

WxFM-XL (Timer)

WxFM-XL (Sundial)

Timer

Sundial

AdaPTS (Timer)

AdaPTS (Sundial)

Moirai ft

Moirai

Timer-XL ft

Timer-XL

STELLA

CDPNet

MSGNet

Corrformer

Hunan

temp

1.552 ±0.031

1.586 ±0.005

1.627

1.679

1.661 ±0.055

1.735 ±0.056

1.715 ±0.103

1.590

1.697 ±0.015

1.662

2.236 ±0.131

2.023 ±0.111

1.760 ±0.110

1.841 ±0.100

1.952 ±0.016

1.947 ±0.005

1.987

2.119

2.094 ±0.078

2.861 ±0.127

1.981 ±0.019

1.991

2.269 ±0.041

1.966

3.100 ±0.181

4.027 ±0.564

2.680 ±0.095

2.256 ±0.068

v-wind

0.737 ±0.003

0.761 ±0.002

0.745

0.817

0.751 ±0.032

0.763 ±0.020

0.766 ±0.012

0.771

0.794 ±0.002

0.766

0.759 ±0.011

0.797 ±0.013

0.775 ±0.054

0.882 ±0.064

0.842 ±0.004

0.931 ±0.028

0.850

0.899

0.875 ±0.040

0.882 ±0.044

0.891 ±0.039

0.898

0.847 ±0.040

0.846

0.888 ±0.045

1.114 ±0.335

1.001 ±0.039

0.949 ±0.073

u-wind

0.689 ±0.002

0.661 ±0.018

0.676

0.751

0.698 ±0.023

0.712 ±0.016

0.711 ±0.003

0.710

0.698 ±0.003

0.686

0.674 ±0.010

0.711 ±0.017

0.719 ±0.038

0.676 ±0.045

0.696 ±0.004

0.693 ±0.018

0.709

0.795

0.717 ±0.022

0.740 ±0.011

0.767 ±0.005

0.778

0.699 ±0.003

0.720

0.707 ±0.006

0.769 ±0.038

0.792 ±0.042

0.724 ±0.050

Appendix

Table 3: Complete MAE results on the Hunan regional, French regional, and global datasets with a 96-hour input window and forecast horizons of 24 and 96 hours. Results are reported as the mean and sample standard deviation over three random seeds where applicable. Best and second-best results are shown in bold and underlined , respectively.

Model variant	Hunan regional			French regional
Model variant	temp	v-wind	u-wind	temp	v-wind	u-wind
WxFM-XL (Timer)	1.552 ±0.031	0.737 ±0.003	0.689 ±0.002	1.943 ±0.011	1.487 ±0.006	1.556 ±0.007
w/o frequency domain decomposition	1.682 ±0.041	0.791 ±0.008	0.712 ±0.016	1.985 ±0.020	1.586 ±0.016	1.641 ±0.004
w/o error correlation prior graph	1.684 ±0.038	0.793 ±0.003	0.713 ±0.004	1.977 ±0.022	1.619 ±0.004	1.636 ±0.018
w/o multi-scale temporal module	1.753 ±0.062	0.797 ±0.008	0.714 ±0.010	2.002 ±0.014	1.652 ±0.010	1.737 ±0.015

Appendix

Table 4: Complete MAE results of the ablation study on the Hunan regional and French regional datasets. The input window is 96 hours, and the forecast horizon is 24 hours. Results are reported as the mean and sample standard deviation over three random seeds. Best results are shown in bold .

Figure 5: Representative forecasting cases on the evaluated datasets. The plots compare the ground truth with predictions from the frozen foundation model and WxFM-XL.

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