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

arXiv:2610.10057 · cs.LG · Submitted 2026-10-07 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: Today's paper: "WxFM-XL: Adapting Univariate Foundation Models to Multi-Station Weather Forecasting".

Jane: The gist:

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So, we're looking at this paper called "WxFM-XL: Adapting Univariate Foundation Models to Multi-Station Weather Forecasting." Basically, the thesis is that taking these big univariate time series foundation models and making them work for multiple weather stations isn't just about modeling the correlations between different variables.

Jane: Right, it’s about two things they think we’re often overlooking when we apply these models to multi-station weather forecasting. It’s the spatial information of the stations themselves and how the error priors of different stations relate back to that foundation model.

Tom: Exactly. They propose WxFM-XL, which introduces a cross-station error correlation prior graph to capture those station-specific error priors with respect to the foundation model. Then they build on that by suggesting a dynamic fusion mechanism that adaptively integrates a spatial correlation graph with the error correlation prior graph.

Lu: What's interesting here is how they handle the frequency information. They first apply frequency domain decomposition to separate the foundation model forecasts into distinct "low, mid, and high frequencies" <ref:2610.10057#pg5>. Then they build tailored error correlation prior graphs for each specific band.

Meng: I’m curious about that dynamic fusion part. How do they actually balance using the static spatial graph with these dynamic error correlation priors? Does it get messy when you try to combine things that change based on the frequency?

Jane: It gets structured by what they call the "frequency-aware dynamic fusion prior graphs" <ref:2610.10057#pg5>. They use a learnable gate, alpha f, to combine the spatial correlation graph with the error correlation prior graph, resulting in a fusion prior graph A fusion f which is A spatial + alpha f A error f.

Tom: So they’re balancing the fixed geographic locations with those dynamically calculated error correlations based on frequency. That sounds like a way to make the spatial relationship smarter depending on whether you're looking at short-term or long-term forecasts.

Lalam: I can confirm that the structure of this paper suggests they are trying to capture complex patterns beyond just simple neighborhood relations by looking at those error correlation graphs for low, mid, and high frequencies <ref:2610.10057#pg2>.

Paper summary: Jane: They use a lightweight graph residual adapter guided by this dynamic fusion prior graph to extend the foundation model. This adapter refines the foundation model forecasts using that combined prior while keeping the strong temporal priors it learned during its pretraining phase <ref:2610.10057#pg9>.

Tom: The mechanism for this adapter involves multi-scale time patch embedding, where they divide the forecast into nonoverlapping temporal segments and project them into latent tokens Z(p) <ref:2610.10057#pg5>. They also use a learnable node gate g to adapt the propagation weights based on that fusion prior graph A fusion f.

Meng: From a deployment standpoint, how does this complexity translate? The online complexity is given as O((one + F)N T out T out + FX p in P N T p K D + T p D + D squared + pD) <ref:2610.10057#pg1>. Does that avoid the quadratic station dependence of dense spatial attention, or is that still a problem at scale?

Lu: It says it avoids the quadratic station dependence of joint or dense spatial attention <ref:2610.10057#pg5>, which is important because we’re dealing with large multi-station datasets where that complexity gets really high. The sparse prior graphs themselves require O(FK N) memory, which is manageable.

Jane: The training objective is designed to balance the foundation model's temporal priors with the corrections from the adapter <ref:2610.10057#pg5>. It’s this loss function: L = lambda mse MSE(x: t+T-one x t: t+T-one) + sum f in F lambda f v f uut two where the denominator normalizes each band-specific error by its energy component <ref:2610.10057#pg1>.

Tom: That normalization is key. It prevents low-energy components from overwhelming the optimization process <ref:2610.10057#pg5>. They’re explicitly tuning the contribution of each frequency band during training to ensure everything gets attention.

Lalam: The experimental results show that WxFM-XL outperforms state of the art baselines across multiple datasets <ref:2610.10057#pg5>. They achieve the best MSE in nine settings and second-best in the remaining seven, which is a lot of consistency.

Jane: It’s not just about MSE though. The paper also reports that WxFM-XL generally achieves better performance compared to task-specific models like STELLA, CDPNet, MSGNet, and Corrformer <ref:2610.10057#pg5>. And they find it achieves the lowest MAE across all variables on both regional datasets <ref:2610.10057#pg21>.

Paper summary: Meng: So if I'm deploying this to a real-world weather service, what does that mean for the operational cost? The model parameters stay frozen during training, so we only update the adapter and the graph gates, which sounds much more efficient than retraining a foundation model from scratch.

Tom: That’s right. The implementation details show that only the adapter, patch projections, graph gates, fusion factors, temporal modules, and scale scorers are updated during training <ref:2610.10057#pg19>. It keeps the massive foundation model frozen and only trains the necessary correction components.

Lu: The ablation studies back up those results too. Removing either the frequency domain decomposition or the error correlation prior graph consistently degrades forecasting accuracy <ref:2610.10057#pg5>. And without the multi-scale temporal module, they saw the largest overall degradation, especially for temperature and wind forecasting on the French regional dataset.

Jane: So it confirms that frequency-specific correction, error-aware spatial propagation, and multi-scale temporal modeling all contribute to the improvements they see <ref:2610.10057#pg5>. They show these elements are complementary rather than just one single fix for the problem.

Tom: The conclusion is that WxFM-XL successfully adapts those univariate foundation models to multi-station weather forecasting by decomposing forecasts into frequency bands and dynamically integrating band-specific error correlation priors with static spatial relations <ref:2610.10057#pg7>.

Jane: It means they’ve found a way to make these powerful univariate models much more useful for real, messy, multi-station weather data by accounting for the specific errors each station makes.

Tom: And the final implication is that this approach yields consistent improvements over existing baselines when tested on both regional and global datasets <ref:2610.10057#pg22>.

Lu: Future work they mentioned is incorporating dependencies among meteorological variables to move towards joint multivariate and multi-station forecasting <ref:2610.10057#pg7>. That’s the next step in complexity.

Jane: So, for someone just listening, this paper suggests that instead of treating every station as an equal input source, we should be paying attention to how much error each station makes at different time scales and spatial relationships <ref:2610.10057#pg7>.

Conclusion: Tom: So, we’re wrapping up on WxFM-XL, this paper by its authors that tackles adapting univariate time series foundation models to multi-station weather forecasting.

Jane: Right, so what’s the big picture here? It basically takes those huge foundation models that work on one station and makes them work for many stations.

Tom: Exactly. The core idea is using a cross-station error correlation prior graph and a dynamic fusion mechanism to integrate static spatial graphs with those error priors.

Jane: And what does that mean in simple terms? It means the model isn't just looking at the weather at one station; it's looking at how the errors between stations relate to each other, and how that changes depending on the frequency of the forecast.

Tom: That’s right. The paper shows they decompose forecasts into low, mid, and high frequencies and build different error graphs for each band.

Jane: So when you listen to this show after hearing about it, you should think about how these models are trying to correct systematic errors across different locations by understanding the spatial relationships between those stations in a dynamic way.

Tom: It’s important because they didn't just tinker with the model; they built a whole system, from that frequency decomposition all the way down to a lightweight graph residual adapter.

Jane: And what they found is that this approach consistently beats state of the art baselines across nine settings and second-best in seven others.

Tom: The results are pretty strong, especially when you look at those absolute error metrics, like MAE across regional datasets.

Jane: It suggests that this method offers a more consistent improvement than just tweaking one part of the model or using a task-specific approach.

Tom: And they’re leaving room for more work, specifically looking at how dependencies among different weather variables can be incorporated for joint forecasting down the road.

Jane: So, if you’re listening to this, keep in mind that we're moving toward models that understand not just one variable at one place, but how all those things interact across multiple stations dynamically.

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

cs.LG

Submitted: 2026-10-07

Updated: 2026-10-07

Code: https://github.com/meteofrance/meteonet

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 82/100

The gist: The gist: WxFM-XL is a model for adapting univariate time series foundation models to multi-station weather forecasting by introducing a cross-station error correlation prior graph and a dynamic

Key concepts

Frequency Domain Decomposition: This technique breaks down the foundation model's forecast into distinct frequency bands, labeled 'low,' 'mid,' and 'high.' This allows the model to treat different components of the weather prediction separately, tailoring corrections specifically to each frequency band.
Dynamic Fusion Mechanism: This mechanism adaptively combines two types of spatial information: a fixed geographic spatial correlation graph and dynamic error correlation graphs. It uses a learnable gate to balance these static and dynamic priors, creating a frequency-aware fusion prior graph that guides the correction process.
Graph Residual Adapter: This lightweight component extends the frozen foundation model by refining its forecasts. It uses the dynamically fused prior graph to guide how information propagates across time patches, ensuring that cross-station corrections are applied while preserving the model's original temporal patterns.

Terminology

Foundation Model — 1× in this paper · explained in 3 episodes
Foundation Models — 1× in this paper · explained in 7 episodes

Summary

The gist: WxFM-XL is a model for adapting univariate time series foundation models to multi-station weather forecasting by introducing a cross-station error correlation prior graph and a dynamic fusion mechanism that adaptively integrates static spatial correlation graphs with dynamic error correlation prior graphs.

How it works

WxFM-XL first applies frequency domain decomposition to disentangle the foundation model forecasts into distinct frequency components, specifically low, mid, and high frequencies <ref:2610.10057#pg5>. Subsequently, tailored error correlation prior graphs are constructed for each specific frequency band <ref:2610.10057#pg5>. The model then introduces a dynamic fusion mechanism that adaptively integrates a spatial correlation graph with the error correlation prior graph <ref:2610.10057#pg5>. This mechanism is guided by the resulting frequency-aware dynamic fusion prior graphs <ref:2610.10057#pg5>.

Dynamic Fusion Mechanism

The Dynamic Fusion Mechanism involves several steps to construct the final graph:

Frequency domain decomposition is applied to decompose the foundation model forecasts into distinct frequency bands, such as low, mid, and high frequencies <ref:2610.10057#pg5>.
Error correlation prior graphs are constructed for each specific frequency band <ref:2610.10057#pg5>. The adjacency weight between stations i and j is defined by their Pearson correlation <ref:2610.10057#pg5>.
The spatial correlation graph is constructed from the fixed geographic locations of stations using a Gaussian kernel to create the Aspatial matrix <ref:2610.10057#pg5>.
A dynamic fusion prior graph is obtained by combining the error correlation prior graph with the spatial correlation graph using a learnable gate αf, resulting in Afusion f = Aspatial + αfAerror f <ref:2610.10057#pg5>. This balances static and dynamic priors <ref:2610.10057#pg5>.

Graph Residual Adapter

Guided by the dynamic fusion prior graph, a lightweight graph residual adapter is implemented to extend the foundation model <ref:2610.10057#pg5>. This adapter refines foundation model forecasts using the resulting dynamic fusion prior graph while preserving strong temporal priors <ref:2610.10057#pg5>. The process involves:

Multi-scale time patch embedding, where the forecast is divided into nonoverlapping temporal segments and projected into latent tokens Z(p) <ref:2610.10057#pg5>.
Graph normalization and propagation, which uses a learnable node gate g to adapt propagation weights based on Afusion f <ref:2610.10057#pg5>.
A multi-scale patch fusion block that combines representations from different temporal scales <ref:2610.10057#pg5>.

Training Objective and Loss Function

The training objective is formulated to balance the foundation model's temporal priors with the structured corrections provided by the adapter <ref:2610.10057#pg5>. The overall training objective is L = λmse MSE (xˆt:t+T−1, xt:t+T−1) + Xf∈F λf vuut∥xˆf t:t+Tout − x f t:t+Tout − 1∥2 F + ε <ref:2610.10057#pg5>. The denominator normalizes each band-specific error by the energy of its target component, preventing low-energy components from overwhelming the optimization <ref:2610.10057#pg5>.

Experimental Results

Experiments across multiple datasets demonstrate that WxFM-XL outperforms state of the art baselines <ref:2610.10057#pg5>. The model achieves the best MSE in nine settings and second-best in the remaining seven settings <ref:2610.10057#pg5>. Furthermore, WxFM-XL generally achieves better performance compared to task-specific models like STELLA, CDPNet, MSGNet, and Corrformer <ref:2610.10057#pg5>. Ablation studies confirm that removing the frequency domain decomposition or the error correlation prior graph consistently degrades forecasting accuracy <ref:2610.10057#pg5>. The complete model achieves the lowest MAE across all variables on both regional datasets, confirming that the improvements observed in MSE are also consistent under the absolute-error metric <ref:2610.10057#pg5>.

Conclusion

WxFM-XL successfully adapts univariate time series foundation models to multi-station weather forecasting by decomposing forecasts into frequency bands and dynamically integrating band-specific error correlation priors with static spatial relations <ref:2610.10057#pg7>. A lightweight graph residual adapter then performs structured cross-station correction while preserving the temporal priors of the foundation model <ref:2610.10057#pg9>. Experiments on regional and global datasets demonstrate consistent improvements over existing baselines <ref:2610.10057#pg5>. Future work will further incorporate dependencies among meteorological variables for joint multivariate and multi-station forecasting <ref:2610.10057#pg7>.

Implementation Details

The implementation details specify that the foundation model parameters remain frozen during training, and only the adapter, patch projections, graph gates, fusion factors, temporal modules, and scale scorers are updated <ref:2610.10057#pg19>. The input window is fixed at 96 hours to accommodate the input length required by Timer <ref:2610.10057#pg4>. The number of frequency bands is fixed to three, F = low, mid, high <ref:2610.10057#pg4>. The temporal patch sizes are P = 6, 12, 24 <ref:2610.10057#pg4>. The token dimension is D = 128 <ref:2610.10057#pg4>.

Complexity Analysis

The online complexity of the adapter is O(1 + F)NTout log Tout + FXp∈P NTp KD + TpD + D squared + pD). This avoids the quadratic station dependence of joint or dense spatial attention and remains applicable to large multi-station forecasting datasets. The sparse prior graphs require O(FKN) memory.

Evaluation Metrics

Forecasting accuracy is evaluated using mean squared error (MSE) and mean absolute error (MAE). The standard deviation uses Bessel’s correction, corresponding to ddof=1 in numerical implementations. The complete model achieves the lowest MAE across all variables on both regional datasets. The complete model achieves the lowest MAE across all variables on both regional datasets.

Forecasting Case Studies

Representative forecasting cases are presented to compare ground truth with predictions from the frozen foundation model and WxFM-XL <ref:2610.10057#pg22>. These comparisons allow examination of whether WxFM-XL can correct systematic forecast deviations, preserve the overall temporal trend, and capture local variations across correlated stations <ref:2610.10057#pg22>. The cases cover different datasets, weather variables, and forecasting horizons <ref:2610.10057#pg22>.

Ablation Study

The ablation study confirms that removing either the frequency domain decomposition or the error correlation prior graph consistently degrades the forecasting accuracy. The variant without the multi-scale temporal module exhibits the largest overall degradation, particularly for temperature and wind forecasting on the French regional dataset. These results further demonstrate that frequencyspecific correction, error-aware spatial propagation, and multi-scale temporal modeling contribute complementary improvements.

Additional Results

Table 3 reports the complete MAE results on the Hunan regional, French regional, and global datasets for forecasting horizons of 24 and 96 hours <ref:2610.10057#pg21>. Table 4 provides the complete MAE results corresponding to the MSE ablation study in the main paper <ref:2610.

Improvements for AI systems

Bold header: Adaptive Error Prior Graph Construction

WxFM-XL constructs a cross-station error correlation prior graph to capture stationwise error priors with respect to the foundation model, which allows for modeling nonlocal connections that capture complex patterns beyond simple neighborhood relations. This enables the system to account for different error priors of different stations relative to the foundation model dynamically.

Bold header: Dynamic Fusion Mechanism

The system implements a mechanism that adaptively integrates a spatial correlation graph with the error correlation prior graph, resulting in frequency-aware dynamic fusion prior graphs. This allows the model to balance these static and dynamic priors, preserving geographic constraints while incorporating nonlocal error relations beyond spatial proximity.

Bold header: Frequency-Aware Residual Correction

The WxFM-XL framework applies a lightweight graph residual adapter guided by the fusion graphs to refine forecasts, specifically correcting errors based on frequency components. The training objective is structured to balance this correction with an energy-normalized loss, ensuring that low-frequency components usually contain substantially more signal energy, which prevents them from overwhelming the optimization process.

Bold header: Multi-Scale Temporal Refinement

The system uses a multi-scale temporal module involving different patch sizes (e.g., 6, 12, and 24) to capture residual patterns at varying granularities. This is achieved by combining representations from different scales using a weighted fusion scheme where a lightweight scoring network produces a scalar score to determine the appropriate scale weights.

Bold header: Scalable Online Complexity

The design avoids the quadratic station dependence of joint or dense spatial attention, leading to an online complexity of O((1 + F)NTout log Tout + FX p∈P NTp KD + TpD + D2 + pD). This ensures the model remains applicable to large multi-station forecasting datasets by keeping complexity linear with the number of stations, N.