ARROW: An Adaptive Rollout and Routing Method for Global Weather Forecasting
Authors: Jindong Tian
Yifei Ding
Ronghui Xu
Hao Miao
Chenjuan Guo
Bin Yang
Venue: ICLR 2026 Poster (2026)
Keywords: Deep Learning; Spatiotemporal Analysis; Weather Forecasting
Primary area: learning on time series and dynamical systems

Abstract: Weather forecasting is a fundamental task in spatiotemporal data analysis, with broad applications across a wide range of domains. Existing data-driven forecasting methods typically model atmospheric dynamics over a fixed short time interval, e.g., 6 hours, and rely on naive autoregression-based rollout for long-term forecasting, e.g., 5 days. However, this paradigm suffers from two key limitations: (1) it often inadequately models the spatial and multi-scale temporal dependencies inherent in global weather systems, and (2) the rollout strategy struggles to balance error accumulation with the capture of fine-grained atmospheric variations. In this study, we propose ARROW, an Adaptive-Rollout Multi-scale temporal Routing method for Global Weather Forecasting. To contend with the first limitation, we construct a multi-interval forecasting model that forecasts weather across different time intervals. Within the model, the Shared-Private Mixture-of-Experts captures both shared patterns and specific characteristics of atmospheric dynamics across different time scales, while Ring Positional Encoding  accurately encodes the circular latitude structure of the Earth when representing spatial information. For the second limitation, we develop an adaptive rollout scheduler based on reinforcement learning, which selects the most suitable time interval to forecast according to the current weather state. Experimental results demonstrate that ARROW achieves state-of-the-art performance in global weather forecasting, establishing a promising paradigm in this field.

Published as a conference paper at ICLR 2026
ARROW: AN ADAPTIVE ROLLOUT AND ROUTING METHOD FOR GLOBAL WEATHER FORECASTING
Jindong Tian', Yifei Ding', Ronghui Xu', Hao Miao², Chenjuan Guo', Bin Yang East China Normal University, 'he Hong Kong Polytechnic University [jdtian, yfd ng, r ecnu. .du...ddu.a. en, (aaao.mma)@eee.... e yu edu. hk (ciguo, byang @dase ecnu. edu. on
ABSTRACT
Weather forecasting is fundamental task in spatiotemporal data analysis, with broad applications across a wide range of domains. Existing data-driven forecast- ing methods typically model atmospheric dynamics over a fixed short time inter- val (e.g., 6 hours) and rely on naive autoregression-basee forecasting (e.g., 138 hours). However, this paradigm suffers from two key limita- tions: (1) it often inadequately models the spatial and multi-scale temporal depen- dencies inherent in global weather systems, and (2) the rollout strategy struggles to balance error accumulation with the capture of fine-grained atmospheric vari- ations. In this study, we propose ARROW, an Adaltive-Rollout Multi-scale tem- poral Routing method for Global Weather Forecasting. To contend with the first limitation, we construct a multi-interval forecasting model that forecasts weather across different time intervals. Within the model, the -rivadd Mixture-of- Experts captures both shared patterns and specific characteristics of atmospheric dynamics across different time scales, while Ring Positional Encoding accurately encodes the circular latitude structure of the Earth when representing spatial in- formation. For the second limitation, we develop an adaptive rollout scheduler based on reinforcement learning, which selects the most suitable time interval to forecast according to the current weather state. Experimental results demonstrate that ARROW achieves state-of-the-art performance in global weather forecast- ing, establishing a promising paradigm this field. The code available at: https:/gghhbb...oomccccooommlggp
rollout for long-term
1 INTRODUCTION
Global Weather forecasting (GWF) is fundamental task in various domains (Guo et al. 2014]
Hettige et al. 2024; Tian et al. 2025 Lai al., 2026 2025). plays a vital role in supporting decision-making Yuaa et al. 2026) for individual travel p planning as well as for key sectors such as
energy Hu et al. 2024 2026 economics (Mei et al. 2025), and agriculture (Qiu al. 2025).
Traditional weather forecasting primarily relies numerical weather prediction methods that solve Partial Differential Equations in atmospheric dynamics. However, these models are computationally expensive when applied to GWF. Consequently, data-driven models (Liu et al.) 2024a by Zhang jet al., 2026 have emerged as an alternative, leveraging historical data to approximate atmospheric dynamics (Rasp& & Thuerey [22 Rasp al. 2020 Ling al. 2024). A widely adopted strategy in data-driven weather forecasting methods is the iterative prediction paradigm. In this approach, the lead time is divided into shorter intervals, and specific single interval forecasting model (SIFM) is pre-trained for each interval. Predictions are subsequently generated in an autoregressive manner, and cumulative errors mitigated through fine-tuning. For example, as shown in Fig. [a), to predict the weather with lead time 138h, it repeats a SIFM (with interval 6h) 23 times. This strategy reduces training difficulty and better aligns with the incremental evolution of atmospheric processes, thereby alleviating the challenge of directly predicting atmospheric dynamics over long horizons. Despite the significant advancements and promising results achieved by data-driven methods, two fundamental limitations remain:
"Coresponding author

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Published as a conference paper at ICLR 2026
Insufficient modeling of spatiotemporal de- pendencies. The dynamics in weather system across different time intervals are inherently correlated, governed by the same underlying physical principles and exhibiting multi-scale interactions (Frank et al., (2024). However, ex-
138h Prediction
135h Prediction
138K Prediction
Finch? No
(Itterall: 6b)
Maral (ietened
SIFM (intervel 6h)
STFM
+23
5IFM (istenal 24h)
isting methods (Bi et al. 2023 Du et al., 22025) often train an independent SIFM for each time
Curment weather
Iritial weather
Initial weathar
Iratial weather
interval. This isolation not only ignores the in-
trinsic relationships between forecasts at dif- ferent temporal scales, but also increases com- putational overhead and training complexity, as each SIFM must be optimized and main- tained independently. Beyond temporal de- pendencies, spatial dependencies are equally critical for accurate global weather representation. However, existing Transformer-base models often treat the Earth as an "flat image", failing to incorporate its spherical geometry. This simpli- fication introduces distortions in representing global atmospheric phenomena. Effectively unifying the modeling of these spatiotemporal dependencies remains a central challenge.
(a) Naive rollout
(b) Greedy rollout
(c) Adaptive rollout
Figure 1: Different rollout scheme in weather fore- casting. (a) SIFM with naive rollout. (b) Three
SIFMs with greedy rollout. (c) Multi-interval fore- casting model (MIFM) with adaptive rollout.
Inflexible autoregression rollout scheme. Atmospheric evolution is inherently non-uniform, char- acterized by intermittent abrupt transitions and periods of gradual change. An effective autoregres- sive strategy should therefore balance two objectives: leveraging larger time intervals to mitigate er- ror accumulation during stable phases, and employing finer intervals to capture rapid transitions ac- curately. However, current methods predominantly rely on inflexible autoregression rollout schemes. For example, FourcastNet (Pathak et al., (022) employs only a SIFM with 6-hour interval applied iteratively (Fig. [.)) Pangu-weather (Bi et al. 2023) uses multiple SIFMs of different intervals (e.g.. 6-hour, 12-hour, 24-hour) in predefined greedy rollout, selecting the SIFM with largest avail- able interval at each step (Fig. [b)). While capable of generating forecasts autoregressively, these inflexible schemes fail adapt to the non-uniform nature of atmospheric evolution. Thus, there is a need for an adaptive rollout strategy (Fig. [c)) that dynamically selects time intervals based on real-time atmospheric states, enabling improved responsiveness to both short-term changes and long-term trends.
In this paper, we propose ARROW, an Adaptive Rollout and ROuting method for global Weather forecasting. To address the first limitation, we propose a novel multi-interval forecasting model (MIFM) that enables capturing the multi-scale temporal correlations and eircular spatial dependen- cies across different time intervals within a unified model. It has two key components: Shared- Private Mixture-of- Experts (S&P MoE) and Ring Positional Encoding (RPE). Given that the same meteorological phenomena may evolve across different time scales, the S&P MoE leverages shared experts to model variations common to all intervals, while private experts capture interval-specific patterns of atmospheric dynamics. Through its routing mechanism, knowledge of temporal varia- tions at different scales can be effectively exchanged among experts. By introducing two auxiliary losses, the S&P MoE not only promotes specialization of individual experts but also preserves a bal- anced contribution across all experts. Spatially, RPE encodes the Earth's 's circular latitude structure within ARROW's tokenizer, enabling a more faithful representation of global atmospheric phenom- ena.
To overcome the second limitation, we design an Adaptive Rollout Scheduler (AR Scheduler) that selects appropriate rollout strategies based on the initial conditions (e.g., current weather states). This mechanism, similar to adaptive solvers of PDEs in atmospheric dynamics (Hutchinson) 2007). enhances the model's 's ability to adapt to rapidly evolving atmospheric processes. Within the AR Scheduler, we construct a weather forecasting environment with corresponding state, action, and reward spaces. Q-learning is employed to learn the optimal adaptive rollout strategy for the pre- trained MIFM. However, multi-step fine-tuning guided by this strategy alters the MIFM parameters, rendering the original strategy suboptimal. Therefore, we integrate the Q-learning with multi-step fine-tuning in an alternating optimization paradigm. This integration allows ARROW to effectively suppress cumulative errors while learning the corresponding optimal policy. In summary, our con- tributions can be summarized as follows:
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We propose ARROW, an Adaptive-Rollont Routing method for global weather forecasting, AR- ROW formulates the adaptive rollout strategy as a decision makinng problem that balances error accumulation with the accurate capture of fine-graine anneggrined atmospheric dynamics.
We introduce an MIFM that enables forecasts across different time intervals. Within MIFM, the S&P MoE captures evolving weather variations across multiple time scales, while the RPE encodes spatial dependencies arising from the Earth's spherical geometry.
Experimental results demonstrate that ARROW achieves state-of-the-art performance in global weather forecasting, with overall improvements of approximately 10 % in both RMSE and ACC.
2 PRELIMINARIES
2.1 PROBLEM STATEMENT
Global weather forecasting aims to predict the future weather state, given the initial weather state Xy E IR Vx Here, V denotes the number of metcorological variables; H and W represent the spatial resolution of the Earth under the equirectangular projection, determined by the granularity of the global grid. We introduce a MIFM, denoted as f(:: training on a set of short intervals to predict weather changes As = X, Xo rather than the absolute future state X3-- To obtain forecasts at the target lead time, we apply an autoregression rollout along a specified trajectory. For example, given the rollout trajectory I' (6h, 18h, .., 114h, 138h) for the lead time 138h, the forecast obtained as: N138A- 1111 24h) + 8 X114;; .., Xish I [(xoi: 12h) + Ner. Nos. = f(Xo; 6h) + Xo.
2.2 RELATED WORK
Numerical Weather Prediction. Numerical Weather Prediction (NWP), the traditional method for weather forecasting since the 1950s, is based curated partial differential equations (PDEs) derived from atmospheric dynamics (Lycch] 2008: Hurrell et al. 2013). Adaptive time-stepping methods dynamically adjust the temporal resolution according to the Fuurant-Friedrichs-Lee condition, improving computational efficiency while ensuring numerical stability (Hutchinson 2007). Mcsh-
adaptive techniques refine the spatial mesh based on local meteorological conditions, enhancing the model's ability to capture fine-scale atmospheric variations (Skamarock et al. 1989). Although NWP methods are grounded in the first principles of atmospheric physics, they still face significant challenges like systematic errors and computational complexity (Brotzge et al. 2023 Magnusson Källén 2013). Most critically, more observation data cannot be directly leveraged to improve forecast accuracy, NWP fundamentally depends refined PDEs, accurate parameterizations, and numerical solvers.
Data-driven Weather Forecasting. Recent advances in deep learning (Xu et al. 2023 Ouyang et al. 2024 Zhou et al., 2026 have prompted a shift toward data-driven models for global weather forecasting (Rasp & Thuerey 2021b: Weyn al. 2020). These methods adopt iterative pre- diction paradigm (as described in Section D. which typically consists of two stages: one-step pre-training and multi-step fine-tuning. The core of this paradigm lies the construction of One-
Step Forecasting Model (OSFM). Graph-based methods (Keisler 2022 Lam et al.) 2023 Oskars- son et al. 2024) capture spatiotemporal dependencies in the atmosphere through message passing. Transformer- baasommerr---eddddo approaches (Nguyen et al. 2023 Bi et al., 2023) treat the Earth as 2D or 3D se- quence and model atmospheric variations via attention mechanisms. Subsequent innovations, such as Neural ODE (Verma et al. 2024) and Neural Operators (Pathak et al.) (022), have further ac- celerated progress in this field. To mitigate error accumulation during autoregression (as shown in Fig. most methods apply multi-step fine-tuning to the OSFM. Fengwu (Chen et al., 2023) and Aurora (Bdnarr et al.] 2025) introduce replay buffer to adapt to input errors during the autoregres- sion. However, during inference, existing approaches still rely an inflexible rollout to obtain predictions at the target lead time regardless of different initial weather state. To the best of our knowledge, existing data-driven method consider the adaptive rollout in the weather forecasting.
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mune-tuned by offernate
2 (
)
fre-troined Eq. 18
Fine-ture teneetundd Eq.
Pre-traned Stage
As
MIFM
[d,)r
Head
Head
Autoregnassion Trojectory
Expert
Expert
Expert
Expert
Arch Block
KN
Arch
Acoumulation time
Shored-Private
138h
MoE Layer
Embed
Number fivetions
t
Weather Embedding
Shored
AdoLN
d=?
42h
Svant
Supert
Self-At Attention
Mllti-HHad
oryman
AR Scheduler
Noise Map
Router
Action
Maxomaa
MLP
Embeddinn zirin (5 10-00-111
Embed
...
Weather Enteadding 2
U/66, 12h, 24h]
Multi- Hoad Self Attentioo
flat image"
Ring Positional Encoding
Concat
Tokenizer
F
State Embed
Weather Emboesdinn
Latitude Property
2 11.2 (.)
Weather State Xo
Temporal State
RPE
Takenizer
Stage 1: MIFM Pre-training
Stage AR Scheduler Fine-tuning
Figure 2: The overall framework of ARROW consists of two stages. One-step pre-training of the Intervllterval Forecasting Model captures atmospheric dynamics at different intervals. Then, multi-step fin--tunig of the Adaptive Rollout Scheduler enables adaptive rollout under different lead times.
METHODOLOGY
3.1 MODEL OVERVIEW
We propose ARROW, an adaptive rollout and routing method for global weather forecasting, As shown in Fig. 2 the training process comprises two stages: one-step pre-training for the Multi- Interval Forecasting Model, followed by multi-step fine-tuning for Adaptive Rollout Scheduler.
Multi-Interval Forecasting Model (Pre-training). To capture both spatial and multi-scale tem- poral dependencies, we introduce and pre-train an MIFM (as shown on the left side of Fig. 2 to generate accurate short-term one-step forecasts across different time intervals. Specifically, the weather state X₂ is first processed by weather-specific Tokenizer. Next, we introduce Ring Po- sitional Encoding (RPE), which captures the circular structure of the Earth, to encode the spatial information of weather states and generate the corresponding weather embedding. The resulting weather embedding sequence z(0), together with the embedded time interval ö, is passed into N Arch blocks to produce 7(N), Each Arch block is equipped with a Shared- Private Mixture- of--xperts, enabling the model to capture both shared patterns and scale-specific characteristics across different time intervals. Finally, head module reconstructs the output Z into spatial format, yielding the predicted weather state X3 E R V X for the specified time interval.
Adaptive Rollout Scheduler (Fine-tuning). To balance eтror accumulation and fine ainengrained at- mospheric evolution, we construct an Adaptive Rollout Scheduler (AR Scheduler, as shown on the right side of Fig. ( The scheduler separately encodes temporal state and current weather state, and then fuses their embeddings. By maximizing the return of AR Scheduler, determines the appropriate time interval to process. This interval is then passed into the MIFM trained in Stage to generate a one-step forecast. By iteratively invoking the scheduler, the lead-time prediction Xy can be obtained along the autoregression trajectory. Through alternating multi-ster step fine-tuning of the MIFM and policy learning for the AR Scheduler, ARROW effectively suppresses cumulative errors under the learned policy.
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3.2
MULTI-INTERVAL FORECASTING MODEL
3.2. 1
RING POSITIONAL ENCODING
After tokenizing the initial weather state Xo using weather-specific tokenization Nguyen et al., 2023 2024), we obtain sequence Z E RIXD, where L = h x denotes the number of tokens (h H/P, w = W/P are the token resolutions under patch size P) and D is the embedding dimension. We propose Ring Positional Encoding (RPE), which enables ARROW to account for the Earth's ' latitude property (as shown on the left side of Fig. 2). For any location : (P))P) on an h x 2D grid sequence, its positional encoding is given by:
RPEx,4: = sin(
Pkc w
2Ti)
W
RPE = cos(
Pk 2Ti)
w
(1)
4i
W
4i
Pk
w
Pk
W
RPE 4:42 sin
2Ti)
RPE = cos(
2mi)
(2)
4i
4i"
where: i = 1, T. The details of the ID RPE and the corresponding property proofs are provided in Appendix B Note that the properties of Eq. do not apply to the 4i and 4i + dimensions, as longitude does not exhibit circularity after equirectangular projection. Then, weather embedding is
obtained as: (0) = + RPE.
3.2.2 SHARRED-RRVVTEED MIXTURE OF EXPERTS
The design of the Adaptive Layer Normalization (AdaLNN) block enables the Transformer incor- porate the time interval 5 as conditional input. To further capture both shared and specific charac- teristics of atmospheric dynamics across different intervals, we propose a -rived-Private Mixture- of-Experts that captures (i) global commonalities across all time intervals, (ii) the unique features specific to each time interval, and (iii) the partial commonalities shared among subsets of time in- tervals.
In the n-th Arch Block's S&P MoE, each token z("-1) at position / the representation sequence (n-1) is routed to M private feed-forward networks (FFNs) based on a gating value g', as defined by the following equation:
M Σ Im.. FP, (z(n-1))= + F² F3(2("
where EP the private FFN, Es the shared FFN. The gate value of for token ž is obtained by perturbing the original gate score 8 with noise 1f. as follows:
Sigmoid (2) W gate),
bf Sigmoid( (2) W Wnoise,a);
(4)
[ sm,l Sm, + b9 Top-k(s: bq) di Softmax(st).
Im.1
0
otherwise
In this formulation, sı and bf represent discrete distributions. By adjusting bf. the routing behavior of 21 can be effectively controlled. It is desirable for the private experts to capture interval-specific features while maintaining load balance. To achieve this, we introduce two auxiliary cross-entropy loss functions, as defined below:
Ps. softmax
Σ
b
H(P.Q) --:;
P: log(g:):
(6)
aux-loss
Σ i<J
(Pozs Pa,), aux-loss2 = H (softmax
Σ E.S).U(B........)
Here, H (..)) denotes the cross-entropy loss, which measures the similarity between two probability distributions. The two auxiliary losses in Eq. 7 serve the following purposes:
Individual characteristics. The aux-loss; in Eq. computes the divergence between the noise distributions of different time intervals. A greater divergence is encouraged to promote interval- specific learning and ensure that each private expert captures unique characteristics.
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Global Balance. The aux-lossg in Eq. computes the distribution formed by aggregating all noise distributions. To maximize the utilization of all private FFNs, we encourage this aggregate distribu- tion to approximate a uniform distribution. This promotes balanced routing, common challenge in MoF.
By jointly optimizing with randomized dynamics forecasting loss La (Eq. 17 Appendix C details), MIFM can be pre-trained to handle all time intervals within a unified model.
3.3 ADAPTIVE ROLLOUT SCHEDULER
Although an MIFM can effectively capture the atmospheric dynamics associated with different time intervals, weather forecasting also requires robust autoregressive rollout strategy to balance error accumulation and fine-grained atmospheric evolution.
In this paper, we propose an Adaptive Rollout Scheduler G (AR Scheduler) and a weather fore- casting environment V which includes the pretrained ARROW model and the same weather dataset used in Stage 1. By interacting with the environment, the AR Scheduler learns to generate an autore- gressive trajectory = (TI, T2,-... ...., ....... Trr towards the target lead time (as illustrated in Fig. Autoregression Trajectory). At each step I, the AR Scheduler adaptively selects time interval Og based on the predicted current weather state X its corresponding temporal information. The prediction error for Xr, can then be computed by comparing it to X,, retrieved from the weather dataset. Based this setup, the environment V is formally defined as follows.
State Space (S). For any step i in the autoregression, the state space for adaptive rollout forecasting consists of the weather state X 1. the date&time (e.g.. August 12, 2018, 6:00 AM), and the tempo- ral position T₁ in trajectory, which includes travel time, remaining time, and target lead time. Among these, the weather embedding 7yycatter E RRLDD is ( in the pre-trained ARROW, while the tem- poral embedding Ztime E IIID is generated by the temporal embedding module. (Illustrated the right side of Fig. 2
Action Space (AA). The action space is discrete set consisting of the available time intervals used in the MIFM. As illustrated in Fig. the action space in ARROW {6h, 12h, 24h).
Reward Function (R). The reward r, r(sr, )) is defined the negative latitude-weighted root mean square error of the prediction at each step in the trajectory. To prevent excessive cu- mulative error caused by overly long rollout trajectory, penalty term w is added to the reward at each step, resulting in Tr + w. Accordingly, the return of an arbitrary trajectory I' is defined as: Gr = E w..
To reduce the complexity of trajectory combinations and enhance generalization through neural networks, adopt Deep Q-Network (DQN) estimate the value function the state aateonction space in weather forecasting. As illustrated in Fig. [] the temporal embedding Zuime and the weather embedding Z." w.waathrr are concatenated and passed through a Multi-Head Self-Attention module. The last token is then fed into the head to produce value estimate for each (state, action) pair. The DQN optimized using Eq. 8 and the resulting policy corresponds the environment y equipped with the pre-trained ARROW, denoted as T.RROW.P.
27
Lg = (D..
R
max Itarge -qmain (S, (S) cEA((S))
(8)
where S" denotes the next state, and (S, A, R, S') samples from the distribution related to the en- vironment W. The function g(s, a) is to estimate the to the target network used to compute the temporal difference target, with frozen parameters, while Amain denotes the active main network, which is updated regularly and periodically copied to Quaret- Optimizing the temporal difference eтror (Eq. g is very common in reinforcement learning (Mnih) et al. 2015 Van Hasselt et al. 2016 Liu et al. 2025b). Obviously, the pre-trained ARROW is not adapted to the error accumulation induced by the adaptive rollout policy AARrow.. Although AR- ROW can be fine-tuned under TARROW. using Eq. 9 the resulting optimal policy will longer be
value. Specifically, Qurget refers

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AARROW-,, the environment V/ changes due the fine-tuning process.
H W TIVHW ΣΣΣΣ TEL
E T~ ['arrr V)
u(v)La((i(( - 2
where the rollout trajectory I' is generated by the AR Scheduler S through interaction with the environment, and A, the weather changes described in Section 2.1 The correct approach is to jointly optimize both the environment v/ and the value estimator 9main as shown below:
arg min Lyp- (Gmain: Starget)
r r== =='""""v""
(10)
s.d., V arg min Liusee (V))
Here, I* denotes the trajectory generated by the optimal policy with learned state-action values I" and the environment V/ with adaptive trajectory fine-tuned ARROW. However, and ((s, influence each other, forming a bi-level optimization problem that makes Eq. TT difficult to opti- mize jointly. To address this, we design an adaptive rollout fine-tuning algorithm that alternately optimizes these two objectives, allowing v and q(s, a) to gradually converge toward optimality (see Appendix for algorithmic details).
EXPERIMENTS
4.1 EXPERIMENT SETTINGS
Datasets. We evaluate performance using the WeatherBench]] [ benchmark, a subset of the ERA5 reanalysis dataset. For meteorological variables, we select five pressure-level variables: geopotential (Z), specific humidity (Q), temperature (T), and the U and V components of wind speed. Each variable provided 13 pressure levels (50, 100, 150, 200, 250, 300, 400, 500, 600, 700, 850, 925, and 1000 hPa). In addition, we include four surface-level variables: 2-meter temperature (T2m), 10-meter and V wind components (U10 and V10), and total cloud cover (TCC). The spatial resolution is set to 1.40625%, corresponding to 128 x 256 grid. The temporal resolution is 6- hourly. The dataset spans 2008-2016 for training, 2017 for validation, and 2018 for testing. During evaluation, focus on four surface variables: U10, V10, T2m, and TCC, and two pressure-level variables: Z500 and T850. Notably, Z500 reflects the mri-trropoppheric dynamical structure, while T850 is closely linked to surface temperature; together, they capture key climatic drivers. U10, V10, and T2m are highly relevant to human activities, whereas TCC plays an important role in renewable energy applications (e.g., photovoltaic power generation).
Baselines. We evaluate ARROW against baselines from four categories: 1) Classical Methods:
Climatology (Jung & Leuthecher 2008) and the Integrated Forecast System (IFS) (Roberts al.
2018). 2) Graph Neural Network- Methods: Keisler (Keisler [2022) and GraphCast (Lam et al,,
2023 3) Neural Operator-based Methods: FourcastNet (Pathak al. [2022). 4) Transformer-basee
Methods: Pangu-weather [Bi et al. 2023) and Stormer (Nguyen et al. 2024). Details of all baselines are provided in Appendix
Evaluation Metrics. We conduct the evaluation based on the average of n-day forecasts, including four target lead times each day: 00:00 UTC, 06:00 UTC, 12:00 UTC, and 18:00 UTC. All forecast- ing methods are assessed using latitude- Root Mean Square Error (RMSE) and Anomaly Correlation Coefficient (ACC) on de-normalized predictions (see Appendix F for more details). Since initial weather states in the IFS results are only available at 00:00 UTC and 12:00 UTC, IFS included the tables for reference only and excluded from overall comparison.
4.2 PERFORMANCE COMPARISON
Overall Performance. Table 4 compares the performance of ARROW against baseline models over a nine-day period (from Day 5 to Day 14) across six key meteorological variables. We use 't" (and 44) to indicate that larger (and smaller) values are better. ARROW consistently outperforms all data-driven baselines both RMSE and ACC on all evaluated days. On average, ARROW achieves improvements of 9.3% in RMSE and 10% in ACC over five days across six atmospheric variables compared to the second- best data-driven models.
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Table I: Overall prediction performance comparison. The best and second-best results are high- lighted in bold and underline, respectively.
Mutloods
C Clonatoloyy RMSE.
IFS
Krisker
GraphCast
Pangu-weathe
FiurcantNat
Sturner
ARROW
Variable
Loal
RMSE,
ACC1
RMSEI
RMSEI
ACC1
RMSEI
ACC1
RMSEL
ACC1
RMSEL
day
183
0.76
3.20
0.46
1.54
0.72
1.37
0.59
2.39
0,59
1.76
0.26
1.66
0.50
T3m
9.day
274
231
273
0.1
0.45
4.47
3.57
2.70
0.40
2.65
3.17
0.43
0.31
2.26
2.72
0.47
2.90
0.52
14-day
5.84
0.08
3.24
0.18
3.54
0.16
3.58
0.15
4.15
0.20
2.9
0.29
5-day
2.89
0.72
4.40
0.37
3,02
0.65
3.50
0.54
3.91
0.47
3.63
0.70
2.84
0.73
U10
3,96
3.79
0.52
5.21
0.29
3.86
0.50
3.99
9-bey
4.44
0.34
3.74
0.38
4.85
0.19
4.39
0.33
0.37
14-day
6.90
0.03
4.72
0.09
4,56
0.09
5.24
0.07
5.01
0.10
4.54
0.15
Subay
2.90
0:31
4.52
0.34
3.15
0.64
1.58
0.53
4.00
0.45
3.14
0.68
2.94
0.72
V10
3.05
0.49
0.30
6.11
0.25
5.05
0.15
4.59
0.29
4.25
day
7.38
0.01
4.99
0.07
5,06
0.05
5.42
0.04
5.15
0.07
4.71
0.11
0.45
0.14
0.30
047
0.34
0.26
0.32
0.31
0.30
0.47
0.25
0.51
9ubyy
0.56
033
0.56
0.16
0.34
0.24
0.32
0.28
14day
0.72
0.02
0.42
0.09
0.38
0.09
0.37
0.69
0.39
0.10
0.35
0.15
388.6
0.90
616.49
0.6
461.78
0.83
51011
0.29
617
0.69
994
0.88
170:25
0.90
2500
800.68
565.20
9-day
760.11
0.54
141.20
0.25
251.25
0.40
843.45
01:2
921
0.32
704.03
0.52
715.46
0.56
16-day
1,19.11
0.06
967.44
0.15
A6
0.14
1J65.54
0.11
96
0.19
587.77
0.25
2.04
0.82
3.44
2.99
0.0
2:25
0.23
2.00
T150
9ubby
7:day
3.55
2.80
0.46
0.64
4.35
0.39
4.11
0.76
3.05
3,67
0.42
3.32
0.48
16-day
5.91
0.01
4.25
0.13
4.47
0.12
4.60
0.09
4.31
0.13
3.1
0.21
Note: Climatology is derived from historical averages and therefore yields a constant RMSE across all Larget lead times throughout the By definition, ACC'ss is not applicable to Climatology. The IFS results exclude forecasts beyond 10 days as well as the TCC variable. Missing results both cases are denoted by ".".
From Table 4 we can also observe the following: 1) Deep learning methods exhibit strong perfor- mance in short-term forecasting (e.g.. 5-day), even surpassing IFS in some cases, indicating their potential. 2) Keisler performs poorly overall, especially on 9-day and 14-day forecasts, where its predictions are nearly unusable. In contrast, GraphCast demonstrates superior performance through various technical advancements, such as the multi-scale graphs. It highlights the potential of graph neural networks in weather forecasting. 3) Neural operators have demonstrated the feasibility of operator learning in weather forecasting, but they still lag behind the latest data-driven models. 4) Transformer-based approaches achieve competitive forecasting performance by leveraging com- puter vision techniques, such as the Swin Transformer. Overall, these results highlight ARROW's effectiveness in capturing precise spatiotemporal correlations within atmospheric dynamics while adaptively scheduling rollout trajectories during autoregressive cnddiction-dmmosstaall clear ad- vantages in medium-range weather forecasting.
4.3 ABLATION STUDIES
Effeet of Ring Positional Encoding. To validate the effectiveness of RPE in ARROW, we replace with the 2D Positional Encoding from (Dosovitskiy et al., 2020) and make learnable, as shown in Table 2 (w/o RPE). Since 2D Positional Encoding originally designed for images rather than the Earth, both RMSE and ACC deteriorate in 72h lead time.
Table 2: Effect of RPE, S&P MoE and two auxiliary losses. All methods are evaluated at the 72- hour lead time using the same naive rollout strategy (Nguyen et al. 2024).
72mm72h
U10-72h
V10-72h
Methods
RMSE,
ACC1
RMSE]
ACCT
RMSE
ACC1
w/o RPE
1.12
0.91
1.76
0.90
1.82
0.90
S&P MoE
1.13
0.91
1.77
0.90
1.81
0.90
w/o aux-lossi
1.15
0.89
1.83
0.88
1.92
0.88
w/o aux-loss2
1.12
0.90
1.82
0.88
1.85
0.89
ARROW-Preerain
1.09
0.91
1.71
0.91
1.77
0.91
Effect of Private Mixture-of-Experta To validate the capability of S&P MoE in captur- ing weather variations across different intervals, we replace S&P MoE with a FFN, as shown in Table 2 (w/o S&P MoF). The results indicate that removing the ability to capture interval-specific
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Published as a conference paper at ICLR 2026
atmospheric variations leads to performance degradation. This underscores the importance of both shared and specific presentations across multi-scale temporal dependencies in atmospheric dynam- ics.
Effeet of two auxiliary losses. To further demonstrate the effectiveness of the two auxiliary losses for S&P MoE, design experiments that remove each loss individually: w/o aux-loss; and w/o aux-loss2, as shown in 2 When aux-loss is moved, the model focuses solely on load balanc- ing across experts, preventing individual private experts from capturing distinct features. In contrast, removing aux-loss eliminates load balancing, causing the model to heavily rely on only a few ex- perts.
Effeet of Adaptive Rollout Strategy. To as- sess the impact of the rollout strategy, we com- pare ARROW (Adaptive in Fig. 3 with the three strategies: Random, which selects time intervals randomly during autoregression, b)
Adaptive
Rundomn
Greedy
1.95
2.5
2.4
Naive, which repeats 23 times with time in-
RMSE
terval 6h, and c) Greedy, adopted by Pangu- Weather (e.g.. 138h = 24h x + 12h + 6h). As shown in Fig. 3 the results for T2m and T850 at the 138-hour lead time suggest that the adaptive strategy, conditioned on the rent weather state, is crucial for robust forecast- ing. Although the greedy strategy alleviates er- ror accumulation, it lacks the ability to capture fine- une-grained atmospheric variations and therefore performs worse than the naive strategy. Most im- portantly, the adaptive strategy outperforms the random strategy, demonstrating that the AR sched- uler successfully estimates meaningful state-action values within the weather forecasting environ- ment.
1.85
2.3
2.2
1.75
(a) T2m
(b) T850
Figure 3: Effect of Adaptive Rollout Scheduler on T2m and T850 138-hour lead time.
4.4 CASE STUDIES
Two representative examples are analyzed to demonstrate ARROW's strong forecasting capability and its potential for downstream applications. To highlight forecasting performance under extreme weather events, we visualize the Siberian cold wave (as shown in Fig. 4 that occurred from January 22 to January 27, 2018, and its impact on East and Central China (purple circle) as well as several Central Asian countries (black circle). Based on the initial weather state, ARROW successfully predicted the trajectory of the cold wave and accurately captured the temperature variations in the marked regions. Notably, the red spot within the purple circle is shielded by topographic factors and remains unaffected by the cold wave. This detail precisely predicted by ARROW, demonstrating its potential for air quality (Liang et al. [2023] Tiin et al., (025) and traffic flow (Wu et al.) 2021 2023 2024) prediction tasks in which temperature serves as an important auxiliary covariate.
Weather (22 Jan 2018 12.00 UTC)
(27 Jan 2018 12,00 UTC)
Greand
S-lay Forzzel (27 Jus 2018 12:00 LTC))
Emoc (F (Focecast Truth)
20
10
10
:00
Figure 4: Visualization of T2m during the Siberian cold wave (unit: PC).
Next, we visualize changes in cloud cover from May 10 to May 11, 2018. Cloud cover prediction plays a crucial role eicision-making for photovoltaic power scheduling. As shown in Fig. 5 ARROW accurately predicted global cloud cover day in advance. In particular, indicated by the two black circles, ARROW successfully identified regions of low cloud cover, providing decision support for adjusting photovoltaic power generation in these areas.

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Published as a conference paper at ICLR 2026
Weather (10 May 2015 0:00 UTC)
Grund trali (LI May 2018 0.00 LTTC)
Fanocasi (11 May 2015 0.00 UTC)
Ener ('orecast Trust)
05
a6
B2
05
Figure 5: Visualization of TCC in China (unitless).
To demonstrate ARROW's capability to capture fine-grate fine-grained spatiotemporal dependencies other meteorological variables, we provide additional comparative case studies (see Appendix J
5 CONCLUSION
In this paper, we present ARROW, an adaptive rollout and routing method for global weather fore- casting. ARROW consists of two key components: Multi-Interva, Forecasting Model (MIFM) and an Adaptive Rollout scheduler (AR scheduler). Leveraging Ring Positional Encoding and Shared-Private Mixture-of-Experrts, the pre-trained MIFM effectively captures spatial and multi- scale temporal dependencies in atmospheric dynamics. The AR Scheduler is designed to select appropriate autoregressive rollout strategies. By alternately optimizing the comporal-diffrentt and performing multi-step fine-tuning on the pre-trained model, ARROW effectively suppresses cu- mulative errors under the learned policy. In the future, we plan to explore reinforcement learning for local weather forecasting and further investigate physics-guided approaches in this domain.
loss
LEKNOWLEDGEMENT
This work was partially supported by the National Natural Science Foundation of China (62372179). In addition, we thank Prof. S. Yang and Dr. S. Liu for their helpful discussions during this work.
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APPENDIX
A NOTATION
Table 3: Summary of Notations used in the paper
Symbol
Description
8
Time interval
P
Patch size in the tokenization
V
Number of Atmospheric variables
H
Latitude in the grid
W
Longitude in the grid
h
Token resolution (latitude), h (H/P) Token resolution (longitude), (W/P) Initial weather state
w
Xo
X,
Current Weather state in time
V
Weather forecasting environment with pre-trained ARROW and weather dataset
F
Rollout trajectory to Xx. G v) (7,,72, 7
GT
Return of the trajectory Gr Exer r + +
6
Adaptive Rollout Scheduler (AR Scheduler) Weather embedding used as the input the n-th Arch Block
(()
7(n)
Input representation to the S&P MoE in the n-th Arch Block The step in the trajectory r
t
7
The timestamp at the t-th in the trajectory r, = T[t]
B THE DETAILS OF RING POSITIONAL ENCODING
For clarity, we first introduce the formulation of ID Ring Positional Encoding, and then extend it to 2D Ring Positional Encoding.
ID Ring Positional Encoding. Suppose there a sequence X WXD {aı, ...... 2s} that forms circular structure. The distance between any two positions the sequence satisfies the following property:
W), Va (1, dis,,b min b), W la b|}.
(11)
where dis.,5 denotes the circular distance between positions a and on a periodic sequence of length W. defined the minimum of the direct distance and the wrap-around distance. Following the sine/cosine positional encoding (Vaswani et al. 2017 Xu et al. 2025). RPE should be this form:
1: 2T
S
2T
5
RPE sin(
1)
RPE = cos(
(12)
W
2
W 28
where: L, D. By computing the dot dot-product similarity, is straightforward to obtain
(Pm, Pa) = Σ cos
m n
2mi)
L ( 2
L
21
It can be proven to satisfy the property described in Eq.
2D Longitude Ring Positional Encoding, Inspired by the 2D sine/cosine positional encod- ing (Dosovitskiy al. 2020: Heo et al., 2024), the 1D RPE be naturally extended 2D. In practice, the input vector is split into two halves: one half assigned the one-dimensional circular positional encoding along the longitude direction, and the other half is assigned the one-dimensional
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0
1.00
1.0
0.95
0.8
5
0.90
0.6
10
0.85
10
0.4
15
0,80
15
0.2
0.75
0.70
25
0.65
25
-0.2
30
0.60
30
-0.4
10
20
30
10
20
30
(b)
Figure 6: Similarity matrix of normal positional encoding and ring positional encoding.
positional encoding along the latitude direction. Therefore, for any location grid, its positional encoding is given by:
(PE, pp) on an x
RPE A = sin( Pk
w
Ph.
2mi)
RPE = cos(
2mi)
(13)
w
4i
w
4i
Pk
w
P1
W
RPE = sin(
2mi)
RPE = cos
2mi)
(14)
4i
w
4i"
where i I,.... T. Note that properties of Eq. latitude has not the ring property after equirectangular projection.
12
are not applied 4 and 4i
Differences between Ring Positional Encoding and Conventional Positional Encoding. We vi- sually contrast RPE with conventional positional encoding in Fig. 6 The equation of conventional positional encoding shown as follows:
Pk.:: sin(k: 10000 #
(15)
P cos(k 10000 3).
Conventional ID positional encoding exhibits high similarity values (red circle in Fig. 6 (a)) between positions near the left endpoint, while showing low similarity (blue circle in Fig. (())
demonstrated:
(a)) between left-end and right-end regions. This fails to recognize endpoint adjacency, which contradicts Earth's 's longitudinal continuity where 180 and 180 are identical. Conversely, RPE
correctly maintains high similarity (blue circle (b)) between endpoints, accurately capturing eyclic spatial relationships essential for global meteorological data processing.
C OPTIMIZATION LOSS
Clearly, a higher value of aux-loss; and a lower value of aux-loss2 are desirable. Therefore, the overall auxiliary loss function is defined
L.s = aux-loss; + a aux-loss2,
(16)
where a a weighting hyperparameter. In addition, to train ARROW to forecast atmospheric dy- namics random time intervals, conditioned on ö, we introduce randomized dynamics forecasting loss Ls as follows:
V ΣΣΣ
L5 ===
E P
(())L()( - A33
(17)
VHW
Here, w(v) denotes the mariabl-sseciffe loss weight Lam et al. 2023 Nguyen et al. 2024 L(i)
the latitude weighting factor, and Åş represents the predicted dynamics corresponding to the time interval. Finally, the overall loss function used during the pre-training stage summarized as:
Spee train
La + Laxx-
(18)
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D THE ALGORITHM OF ADAPTIVE ROLLOUT FINE-TUNING
D.1 ALGORITHM DETAILS
Considering the bi-level optimization in Eq. 10 we adopt the following algorithm to alternately optimize and Y
Algorithm 1: Adaptive Rollout Fine-tuning
Input: Weather forecasting environment V with Pre-trained ARROW and weather dataset, AR
Scheduler 6, replay buffer B, penalty coefficient w, max optimizing steps T Tiax.
alternating optimization rate C
Output: Fine-tuned ARROW, AR Scheduler
Initialize Weather Forecasting Environment V;;
Initialize Main DQN Qmain (s, a)) and Target DQN (8; d);
Initialize replay buffer B;
for each epoch do
Interact agent with environment and store (s, a, into B:
Refresh B with Qurget: for each iteration do
Uniformly sample mini-batch from B; Optimizing the Eq. as follows:
for each transition (8, a, s')) in the mini-batch do
11
Compute target value:
Vtarget - max 9targe(sss (oneerss',00) aa); eEA(e')
Update Qmain by minimizing Temporal difference loss:
Le (3trgget qmain (s,
15
if global step mod C = 0 then
16
Copy parameters: Quaget + Gmain:
Optimizing the Eq. 9 as follows:
18
AR Scheduler generates rollout trajectory I based on initial weather state:
r = (quaget, v. like == {6h, 18h, 42h, ... 120h):
20
Fine-tuning ARROW's prediction head with rollout loss on the trajectory
Stop the gradient of (Å,} for steps where Tmax [.]
21
Cagnps = Erer(e A Á,)?;
22
D.2 ALGORITIM STABILITY AND CONVERGENCE
Given that Adaptive Rollout Fine-tuning (Algorithm) I is an alternative optimization Eq. and Eq. [9] it is essential to verify the numerical stability of the algorithm. Therefore, provide the training curves of the multi-step fine-tuning loss and temporal difference loss (Fig. 7 both exhibit- ing clear convergence, Additionally, trend consistent with the convergence of the two losses. Since the reward is defined as the nega- tive RMSE (as described in Sec. 3.3 Reward Function), the objective of the AR Scheduler is to make the trajectory return approach zero. These results indicate that the AR Scheduler learns more effective rollout trajectories for weather prediction compared to random initialization.
also present the trajectory return, which shows upward
E
BASELINE DETAILS
E.1
IFS HRES
The IFS HRES (Roberts et al. 2018) (High Resolution Forecast System) is ECMWF's flagship de- terministic forecasting model, developed based on its core Integrated Forecasting System (IFS). represents of the world's most advanced global numerical weather prediction technologies for
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Multi-steps Fine-tuning Loss
Trajectory Return
0.26
Eq.
-0.010
w
00.012
|
0.015
0.22
0.20
My IV I
(w VM
M
-0.020
0.18
-0.025
Σ
00002
100
200
300
400 Step
500
600
700
100
200
300
400
500
600
700
Step
Temporal Difference Loss
Eq.
100
300
500
Step
Figure 7: The training curves of the temporal difference loss (Eq. 8), multi-step fine-tuning loss (Eq. 9.. and trajectory return collectively demonstrate that the AR Scheduler achieves convergence.
short-to-ne thort-to--ediim medium-range forecasting. By assimilating massive observational data data-including satel- lite, surface station, and radiosonde observations--hrouu advanced four-dimensional variational data assimilation (4D-Var), the model drives high-fidelity physical equations to generate global weather forecasts.
E.2 STORMER
Stormer (Nguyen et al. 2024) is a global weather prediction model based on the Transformer ar- chitecture (derived from DiT). Its training process consists of two phases: initial pre-training via single-step prediction to establish short-term forecasting capabilities, followed by critical multi-step fine-tuning that focuses on 4-step and 8-step prediction performance (including ablation studies validating its significance). During inference, Stormer adopts an innovative composite prediction strategy, generating weather forecasts by averaging outputs across multiple time intervals, thereby substantially improving forecast stability and accuracy. For example, the results of three 24-hour, six 12-hour, and twelve 6-hour predictions are ensembled produce the final 72h forecast.
E.3 KEISLER GRAPH NEURAL NETWOR
The Keisler Graph Neural Network (Keisler 2022 is an innovative global weather prediction model that pioneers the application of graph neural networks (GNNs) in this domain. Its architecture employs a bipartite graph neural network (featuring encoder and decoder components) coupled with specialized GNN processor.
E.4 GRAPHCAST
The GraphCast (Lam et al. 2023) is global weather forecasting model that leverages multi-scale graph to model the evolution of atmospheric variables over time. represents the Earth as a spheri- cal mesh of nodes connected by edges based geodesic proximity, and employs message-passing
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GNN architecture learn spatial and temporal dependencies. Similar with Keisler, GraphCast ploys a bipartite graph to construct the connection between the graph(mesh) and grid. By encoding sequence of past meteeooologccal states and predicting the next state in autoregressive manner, GraphCast achieves fast and accurate medium-range forecasts. significantly outperforms tradi- tional numerical weather prediction models and earlier deep learning approaches in both accuracy and inference speed.
E.5 PANGU- BEGGUWEETIEER
Pangu-Weather Weather et al. 2023) is model specialized in global high-resolution weather prediction. Built upon 3D Earth-Specint Transformer cerifeeture-tailoree to process the three-dimensional spatial characteristics of Earth's metcorological data (longitude, latitude, altitude)-tts core training strategy involves concurrently training three independent models. During inference, the system employs a greedy strategy for any target forecast horizon: it iteratively selects and utilizes the model with the largest available timestep (24h, 12h 6h) to efficiently achieve long-term forecasting.
E.6 FORECASTNET
FourCastNet (Pathak et al. 2022) is an advanced Al model specifically designed for global high- resolution weather forecasting. Built on Transformer architecture integrated with Adaptive Fourier Neural Operators (AFNO), it efficiently processes meteorological data across global 128 x 256 grid (WeatherBench dataset).
F METRICS
F.
ROOT MEAN SQUARED ERROR (RMSE)
The RMSE is calculated as follows:
T E EE
V H W
ΣΣΣ 1(i) (Xeods - Xeerss EE
RMSE T
(19)
V
where denotes the number of time steps, represents the number variables, and W corre- spond to the height and width of grids, respectively. L(-) is the latitude weighting factor (decreasing weight with increasing latitude). Here, Xt,,, and Xt,e, correspond ARROW's forecast and the ground truth for variable V at time and grid point (i.j).
F.2 ANOMALY CORRELATION COEFFICIENT (ACC)
The ACC computes the Pearson correlation coefficient between climatology-based anomalies & = Xx,m.is - Cr,w..ff and X = Xt,r.i.j - Cr,w,i.j where Cr,,..j represents the cli- matology for variable v at grid point (i,j) and time step t. The ACC defined as:
L()) L Xi.was
ACC corr T
4
(20)
& ..di (()x
This metric evaluates whether predicted anomalies (deviations from climatology) align spatially with true anomalies. Higher ACC values (closer 1) indicate superior model capability in capturing anomalous patterns, while lower values (near 0) reflect weaker performance.
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G EXPERIMENTS DETAILS
G.1 SOFTWARE AND HARDWARE ENVIRONMENT
All experiments conducted using PyTorch 2.1.0 and PyTorch Lightningg 2.1.1, executed on NVIDIA GeForce A800 GPUs (80 GB). We leverage mixed-preciste training and the Distributed Data Parallel (DDP) strategy. The software environment includes CUDA 11.8 and Python 3.11, running on Ubuntu 22.04.
G.2 IMPLEMENTS DETAILS
Pre-training. In ARROW, the patch size is set 4 for tokenization. The core architecture comprises 16 Transformer layers, each with hidden size of 1024, and the attention mechanism employs 16 heads. The S&P MoE module includes I shared expert and private experts, with experts selected for each forward pass. The time intervals are configured as [6h, 12h, 24h]. enabling ARROW to perform multi-interval forecasting and allowing the AR Scheduler trajectory construction. During training, the model is trained with a batch size of 16 and initial learning rate of 0.0005, which follows cosine decay schedule after a 5-epoch warm-up phase. We adopt the Adam optimizer with 31 0.9, 82 0.95, and weight decay of le-5 to optimize the model parameters. We apply an early stopping mechanism with a patience of 10 epochs for optimization.
select temporal intervals for
Fine-tuning. In the AR Scheduler, the replay buffer size is set to 9000, with a refresh size of 2000 at the end of each epoch. The agent learning rate and multi-step fine-tuning learning rate set to 0.0002 and 1e-7, respectively. The alternating optimization interval is set to 10 steps. The target network Qtarget is synchronized with the main network Qmain every 10 steps. The maximum number of optimization steps for multi-step fine-tuning, denoted as Tmax. is set to 10 to adapt to error accumulation under the learned rollout strategy.
H ANALYSIS OF S&P MoE
To evaluate whether the routing behavior achieves both individual characteristics and global balance, we visualize the expert selec- tion distribution across different time intervals within one Arch Block of ARROW (left side of Fig. 2 Three key phenomena can be observed from Fig. (1) the overall load of S&P MoE
Rounting
350
300
230
am
balanced; (2) expert is simultaneously sponsible for all three intervals, indicating that the shared expert is sufficient
150
capture the commonalities across intervals; (3) each private expert predominantly handles specific inter- val while still being involved in a small number of other intervals. These findings support the design goals of S&P MoE: (i) capturing global commonalities shared across time intervals, (ii) learning distinct features specific to each time interval, and (iii) representing partial commonalities shared by subsets of intervals (as discussed in Sec. 3.2.2).
100
Private Experts index
Figure 8: The routing behavior of S&P MoE.
I ANALYSIS OF AR SCHEDULER
In this section, we analyze the behavior the AR Scheduler during inference on the 2018 test dataset and provide in-depth analysis of the learned adaptive rollout strategy.
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We first present the distribution of selected time intervals when making decisions for medium-ranee range (120h) and long-range (354h) forecasts in Fig. 9 Notably, the decision trajectories for 120h fore- casts rely more frequently the 6-hour interval than those for 354h. This is because the trajectory length for 120h forecasts is generally shorter (see Fig- TOp. allowing finer 6-hour intervals to capture detailed atmospheric dynamics without incurring significant accumulated error. In contrast, longer 354h trajectories cannot afford to use such short intervals due to greater potential for error accumu- lation. Thus, the AR Scheduler's ' interval selection behavior reflects reasonable trade-off between temporal resolution and error accumulation.
Time interval distribution at lead time 120h
Time interval distribution at lead time 354h
6h interval
24h interval
12 5%
24h interval
31.8%
36.5%
44.7%
12h interval
Figure 9: Decision interval distribution throughout 2018.
Trajectory longth distributionn lnad 120h
Trajectory length distribution 2018 lead time 354h
175
20
159
TmjectoryLLangh
Trajactory' Langth
20
Figure 10: Trajectory lengths for 120h and 354h lead times throughout 2018.
Then, further examine the AR Scheduler's decision trajectories for the 120h and 354h forecasts to investigate the rationale behind its interval choice under specific weather conditions. In Fig. [] present the weekly distribution of different intervals throughout 2018. Interestingly, the 6h inter- val shows a similar pattern in both the 120h and 354h forecasts, suggesting that the AR Scheduler considers fine- -ne-grained atmospheric dynamics be equally important during certain periods, regard- less of the lead time. Specifically, the black circles in Fig. [1 highlight periods of high frequency in selecting 6h interval.
To validate these decisions, plot the temporal changes in geopotential in the 850hPa (Z850) and 1000hPa pressure level (Z1000) at each time step. As shown in Fig. [2] the time points highlighted with black circles closely align with those in Fig. II These periods exhibit clear signs of regime shifts geopotential'ss 's variation height, characterized by pronounced curvature and turning points. Such transitions typically correspond significant changes in global low-pressure systems and often associated with severe weather phenomena, including strong winds, precipitation, and convec- tion. The identified transition period, from late August early September, marks seasonal shift:
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from summer to autumn in the Northern Hemisphere and from winter to spring in the Southern Hemisphere. This period is also associated with heightened tropical activity worldwide.
Time interval distribution week 2018 lead 120h
distribution per week 354h
Eh interval
350
interval
300
24h Interval
593
300
300
200
102
Week
Weeli
Figure 11: The weekly interval distribution AR scheduler decision trajectories throughout 2018.
Change of Geopotential at 850hPa and 1000hPa over time
106
171
2,1000
136
Distribution shift of Geopotential
1:2
178
07:00
05.13
48.52
6927
05.00
09-21
08.06
18:00
1011
10:30
Figure 12: The changes of geopotenital at 850hPa and 1000hPa pressure level at each time step.
To further verify the meteorological context from August 25 to September 5, 2018, we retrieved historical weather reports from that period:
On August 27, 2018, Hurricane Lane rapidly weakened into tropical storm as it approached the Hawaïaan Islands.
Typhoon Jebi, which formed August 26 and was officially named August 27, made landfall Japan's Kansai region on September It became one the most destructive typhoons to impact Japan in 2018.
Tropical Storm Gordon developed around August 30, affecting regions such as Florida, the Gulf Coast, Arkansas, and Mississippi. It brought heavy rainfall, toppled trees, and caused widespread power outages.
These reports confirm the presence of multiple extreme weather events during that period. Since such events demand more fine-grained modeling accurately capture atmospheric dynamics, the AR scheduler's frequent use of 6-hour intervals demonstrates its ability to correlate trajectory deci- sions with real-world weather patterns.
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J CASE STUDIES ON PREDICTION COMPARISONS
Fig. 13 presents qualitative comparison global weather forecasts at 234-hour lead time across several models. Among them, ARROW demonstrates outstanding predictive accuracy and spatial coherence across all variables, closely matching the Ground Truth. It captures fine- grained patterns in T2m, U10, V10, Z500), and T850 with minimal artifacts and excellent global consistency. In trast, Pangu-weather and FourCastNet exhibit noticeable spatial noise and over-smoothed patterns, especially over oceanic and polar regions, leading to reduced fidelity in key meteorological features. Stormer shows even more pronounced distortions and patchy inconsistencies, particularly in wind fields and geopotential contours, which compromises forecast reliability, Overall, ARROW not only recovers finer structures but also achieves superior global balance, making it reliable for long- term weather forecasts.
Incaal Staee
ARHOW
Figure 13: 222h lead time forecast comparison of different models.
We also provide forecast comparisons at other lead times to highlight ARROW's strong performance in global weather forecasting.
Paage oodber
Suerer
ARSOO
Tro
Figure 14: 126h lead time forecast comparison of different models.
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Iebill Stae
sedber
AMK0W
Oreallout
Figure 15: 222h lead time forecast comparison of different models.
TourCatNic
ARROW
Truk
Figure 16: 354h lead time forecast comparison of different models.
K THE IMPORTANCE OF WEATHER PREDICTION FOR DOWNSTREAM APPLICATIONS
Time series forecasting Yi al.
2024
Guo et al.
2024 Jiang al. 2025
Liu et al. 2025a Miao
et al. 2026; Zhang et al. 2025 Li et all 2025 Wu et al. 2025 2026) is ubiquitous in roal-world
applications. It typically involves predicting target variables with the support of auxiliary covari-
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Table 4: Overall prediction performance comparison of other variables. The best and second-best results are highlighted in bold and underline, respectively.
Metheds
Clinatolog
IFS
Kiisle
GraphCasi
Pangu-meather
FourczsNNet
Sturmar
ARROW
5-day
1.55
0.55
3.00
0.55
2.16
0.75
2.39
0.70
2.81
0.55
2,50
01:00
1.35
0.55
T500
T-day
3,183
2.64
0.64
3,50
0.34
2.63
0.56
3.08
0.50
3.44
0.39
2.75
0.61
2.56
0.65
14-day
4.19
3,69
5-day
264.95
0.58
665 25
0.61
335.55
0.51
371.96
1.75
461.5
0.00
250,00
1386
272.62
0.57
2350
T-day
351.363
413.4
0.71
581.8
464.00
0.61
499.99
0.55
563.56
0.44
431.48
0.68
405.3
0.71
9-day
14-dry
776.05
0.06
670,00
0.14
704.10
11.13
727.57
110
061.08
0.15
62599
0.22
5-day
5.49
0.78
5,39
0.49
5.90
0.72
6.55
0.67
7.51
0.57
5.81
0.26
5.45
0.76
U500
8:53
1441a
18.04
0.04
10.08
0.13
10.57
0.13
10.91
0.10
10.53
0114
9.55
0.30
9-day
9.28
0.35
11.30
0.12
8.99
0.30
9.97
0.19
10.00
0.13
9.22
0.33
8.57
0.38
14-day
13.04
0.01
10.12
0.08
10.50
1.06
13.00
1104
101.5
10.77
9.70
0.11
110000
9-day
Tday
4.5
0.54
6.44
0.12
4.77
0.29
5.30
0.21
5.56
0.15
4.59
0.33
4.56
0.38
144byy
7.78
0.04
5.35
0.09
5.71
0.00
5.80
5.57
5.66
0.86
5-day
V1000
Tdday
4.554
0.18
5.31
4.49
0.49
4.19
0.5%
9-day
3.22
0.39
6.52
0.09
5,07
0.36
5.60
0.16
5.85
0.11
5.16
0,30
4.79
0.34
Note: Climatology is derived from historical averages and therefore yields a constant RMSE across all Larget lead times throughout the year. delinition, not applicable Climatology. IFS results exclude forecasts beyond days as as TCC variable. Missing resalts both cases are denoted by
ates (Li et al. 2026), which often play a crucial role in forecasting accuracy. For example, wind power generation forecasting relies on local wind direction and speed, air pollutant prediction de- pends on temperature and humidity (Liang et al. 2023 Hettige et al., 2024 Feng et al. 2025 Tian
itt al. 2025), and landslide forecasting closely associated with extreme weather conditions (Quu
et al. 2025 Consequently, meteorological forecasting acts as an upstream task for these appli-
cations, and its accuracy critical to the performance of wide range of downstream forecasting
tasks Wang et al. (2020).
25


Reviews:
[{"review_id": "OlZ2T3BFsI", "reviewer": "Reviewer_WNTA", "summary": "This work proposes ARROW, an Adaptive-Rollout Multi-scale temporal Routing method for Global Weather Forecasting. It includes a multi-interval forecasting model that forecasts weather across different time intervals, Ring Positional Encoding that encodes the circular spatial information, and an adaptive rollout scheduler, which selects the most suitable time interval to forecast.", "questions": "See above.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "- Strong motivation to address circular spatial representation of Earth and innovative rollout design.\n- Clear paper writing and easy to follow.\n- Clear code and present the data downloading and model running.", "weaknesses": "- Limited baselines. Is it to compare with GraphCast and GenCast from Google? These two show powerful performance in global weather forecasting.\n- Lack uncertainty. Is it possible to study uncertainty in predictions, since weather evolution is an inherently uncertain process? The probabilistic methods may be a possibility.\n-  Any further explanations on loss functions in Eq. (7)?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "cn4A2elEAn", "reviewer": "Reviewer_inGq", "summary": "A novel data-driven global weather forecasting model that introduces a Reinforcement Learning-based Adaptive Rollout Scheduler for flexible time steps and a Multi-Interval Forecasting Model (MIFM) with a Shared-Private Mixture-of-Experts, achieving state-of-the-art accuracy.", "questions": "1.Policy Interpretation: Provide an in-depth analysis of the learned AR Scheduler policy. How do its chosen time steps ($\\delta$) correlate with quantifiable meteorological indicators (e.g., instability, magnitude of change in Z500)?\n\n2.Optimization Details: Provide more detail on the RL hyperparameters and comment on the stability and convergence of the challenging alternating optimization paradigm used to train the model and the policy jointly.\n\n3.RPE vs. Advanced PE: Given the rise of more advanced positional encoding techniques like Rotary Positional Encoding (RoPE) which are effective in capturing relative relationships, did the authors consider or test a comparison between RPE and methods like RoPE, especially since RoPE could potentially be adapted to model relative positions within the spatial grid? What specific limitations of RoPE (or similar methods) make RPE a superior or more suitable choice for the geophysical context of global weather forecasting?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "1.Novel use of Reinforcement Learning (Q-learning) to formulate and solve the autoregressive prediction process as a sequential decision-making problem, directly addressing the inflexibility of fixed-step forecasting.\n\n2.Introduces a Shared-Private Mixture-of-Experts (S&P MoE) for efficient, unified modeling of multi-scale temporal dependencies, and uses Ring Positional Encoding (RPE) for physically-informed spatial modeling of the Earth's spherical geometry.", "weaknesses": "1.Lack of AR Scheduler Insight: Insufficient analysis on the learned policy of the Adaptive Rollout Scheduler. It is unclear how the policy chooses time steps (e.g., $6\\text{h}$ vs. $24\\text{h}$) in response to specific weather conditions, which limits interpretability.\n\n2.Limited Architectural Novelty: The concept of using multi-interval/lead-time based forecasting (the basis of MIFM) is not entirely new, with prior work (e.g., MetNet) having explored similar ideas.\n\n3.Inference Time Trade-off Unclear: The paper lacks discussion and comparison of the total inference time or computational cost of ARROW against fast baselines (like Pangu-weather). The adaptive nature might lead to more model calls and slower overall prediction.\n\n4.The core physical motivation for Ring Positional Encoding (RPE) needs clearer explanation and justification beyond just latitude circularity.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "rF47Z9heIs", "reviewer": "Reviewer_pyNv", "summary": "This paper introduces ARROW, an Adaptive Rollout and Routing framework for global weather forecasting (GWF).\nThe authors address two long-standing issues in data-driven GWF:Insufficient modeling of multi-scale spatiotemporal dependencies, as most methods independently train single-interval forecasting models (SIFMs).Rigid autoregressive rollout schemes, which use fixed or greedy intervals regardless of atmospheric dynamics.\nTo overcome these, ARROW integrates two key innovations:Multi-Interval Forecasting Model (MIFM) with a Shared–Private Mixture-of-Experts (S&P MoE) architecture and Ring Positional Encoding (RPE) for Earth’s spherical geometry.Adaptive Rollout Scheduler (AR Scheduler) trained via Deep Q-learning to dynamically select forecasting intervals conditioned on the current weather state.", "questions": "* In the AR Scheduler Fine-tuning strategy, what exactly does the term “environment” refer to? Could you please provide a more detailed explanation of its definition and role within the fine-tuning framework?\n\n* Regarding fine-tuning strategies, how does the proposed Adaptive Rollout compare with other approaches such as Pangu-Weather’s rollout scheme, Fengwu’s replay-buffer-based fine-tuning, Fuxi’s multi-timescale cascaded fine-tuning, and GraphCast’s multi-step fine-tuning?\n\n* How would the AR Scheduler Fine-tuning strategy perform when combined with the Pangu-Weather model? Given that the Pangu-Weather GitHub repository provides multi-step model checkpoints, would it be possible to test AR Scheduler Fine-tuning in conjunction with these checkpoints? I am particularly interested in seeing how the results would compare.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "* The paper is well-written, with a clear problem statement and a well-organized structure.\n\n* The authors propose a Ring Positional Encoding (RPE) that is more suitable for global prediction tasks. Theoretically, in the 1D case, the encoding ensures that points closer on the circular domain remain close in the RPE space. The visualization further demonstrates that along the latitude, points near the boundaries are represented with shorter distances, capturing the circular nature of global coordinates.\n\n* The paper introduces a Shared-Private Mixture of Experts architecture, which enables a single model to produce predictions at multiple temporal resolutions within one iterative step.\n\n* The authors further propose an AR Scheduler Fine-tuning strategy that adaptively selects the number of rollout steps during inference. It employs a Deep Q-Network (DQN) to estimate the state–action value function, and an Adaptive Rollout Fine-tuning Algorithm is designed to jointly optimize the DQN and the environment.", "weaknesses": "* The experiments are conducted under a limited data setting — using a resolution of 128×256 and only six variables. It is recommended to follow Pangu-Weather by maintaining a 25 km resolution and using 13-level variables, which would make the results in Table 1 more convincing.\n\n* Pangu-Weather performs predictions via multi-step rollouts of several models, but the paper does not clarify whether such multi-model rollouts were considered or compared in the experiments.\n\n* There is insufficient experimental evidence to illustrate how the Adaptive Rollout Scheduler (Fine-tuning) actually operates. Its mechanism is only reflected in the RMSE values in Table 3, without showing the distribution of selected rollout lengths or how the scheduler adapts to different cases.\n\n* Similarly, the paper lacks sufficient analysis to demonstrate how the Shared & Private Mixture of Experts (S&P-MoE) functions. Although the ablation setting is described in Section 2, there is no analysis of the routing behavior or how experts are dynamically selected in different situations.\n\n* In the case study, the paper does not compare its predictions against other methods, making it difficult to assess whether the proposed approach provides improved capture of fine-grained atmospheric variations compared to existing models.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)