Learned Weather Forecasting: What Neural Networks Replaced, and What They Did Not

GraphCast has 36.7 million parameters. That is roughly a thousandth of a mid-sized language model, and it was trained in about four weeks on 32 Cloud TPU v4 devices. It produces a 10-day global forecast at 0.25 degree resolution across 37 vertical levels, hundreds of variable-level combinations in all, in under a minute on a single TPU. Against ECMWF's HRES, the deterministic system generally regarded as the best operational forecast in the world, it won on 90 percent of 1,380 verification targets (Lam et al., Science 382(6677), 1416–1421, 2023, arXiv:2212.12794).

The comparison that made this land was not accuracy. It was that HRES runs on a supercomputer for roughly an hour to produce one forecast, and GraphCast runs on one accelerator for under a minute to produce a better one.

Two years later, ECMWF put its own machine-learned model into operations on 25 February 2025, running alongside the physics-based Integrated Forecasting System it had been refining for four decades (ECMWF, 2025). The field did not resist the result; it absorbed it in about eighteen months.

Why this matters: Weather forecasting is the most mature, most carefully verified numerical simulation discipline in existence, with a sixty-year track record and a scoring culture that other fields envy. If a learned surrogate can beat it, the question of when learned models replace solvers stops being philosophical and becomes an engineering schedule. The answer, on close reading, is more specific and more interesting than "machine learning won".

TL;DR

• GraphCast beat ECMWF's HRES on 90 percent of 1,380 verification targets at 0.25 degrees over 10 days, with 36.7M parameters, in under a minute per forecast.
• GenCast beat the operational ensemble ENS on 97.2 percent of 1,320 targets, which is the harder and more consequential result, because ensembles are how forecasting expresses uncertainty (Price et al., Nature, 2025, arXiv:2312.15796).
• The move from deterministic to generative was not a refinement. A model trained on mean squared error learns the conditional mean of the atmosphere, which is smooth, so it systematically blurs fronts and understates extremes while scoring well on RMSE.
• These models are trained on ERA5 reanalysis, not observations. They learn to reproduce a physics model that was fitted to data, and they inherit its biases along with its skill.
• Machine learning replaced the forecast model, not the forecast system. Data assimilation, the expensive part that turns satellite radiances and radiosondes into an initial state, is still conventional. Remove it and GraphCast has nothing to start from.
• ECMWF reports its operational AIFS reduces the energy cost of producing a forecast by roughly a factor of 1,000 relative to the physics-based system.
• The unresolved problem is out-of-distribution climate. Conservation of mass and energy are learned approximately, not enforced, and a warming atmosphere moves the input distribution outside 45 years of training data.

At a Glance

The pipeline, with the part that changed marked off from the parts that did not.

flowchart LR
  Obs["Satellites, radiosondes,<br/>aircraft, buoys"] --> DA["Data assimilation<br/>still conventional"]
  DA --> Init["Analysis:<br/>gridded initial state"]
  Init --> Model["Learned forecast model<br/>GraphCast, GenCast, AIFS"]
  Model --> Roll["Autoregressive rollout<br/>6h or 12h steps"]
  Roll --> Out["10 to 15 day forecast<br/>deterministic or ensemble"]
  Roll -.->|"feeds its own output"| Model
  classDef blue fill:#1e40af,stroke:#3b82f6,stroke-width:1px,color:#fff
  classDef slate fill:#334155,stroke:#64748b,stroke-width:1px,color:#e2e8f0
  classDef purple fill:#6d28d9,stroke:#a78bfa,stroke-width:1px,color:#fff
  classDef teal fill:#0e7490,stroke:#22d3ee,stroke-width:1px,color:#fff
  class Obs,Init blue
  class DA slate
  class Model,Roll purple
  class Out teal

[IMAGE: Side-by-side global 500 hPa geopotential height fields at day 7, three panels: ERA5 truth, a deterministic MSE-trained model, and a diffusion ensemble member. The middle panel visibly smoother, with weaker gradients. Caption: "The conditional mean of the atmosphere is not a weather map."]

Before the Neural Networks

Numerical weather prediction is old and it worked. Richardson attempted a hand-computed forecast in 1922 and got a catastrophic answer for reasons later understood as a data-initialisation problem. The first successful numerical forecast ran on ENIAC in 1950. By the 1980s, operational centres were integrating the primitive equations on global grids, and by the 2010s, ECMWF's IFS was producing skilful forecasts to about a week ahead, with the useful horizon extending by roughly one day per decade, a trend so consistent it has its own name in the literature: the quiet revolution.

The cost structure never changed. Solving the discretised equations of atmospheric motion at 9 km resolution across the globe requires a supercomputer, an ensemble of 51 members at coarser resolution requires more of one, and improving resolution by a factor of two costs roughly an order of magnitude in compute.

The first credible learned challenger arrived in 2022. FourCastNet, built on adaptive Fourier neural operators, showed that a data-driven model could produce global forecasts at 0.25 degrees at all, running orders of magnitude faster than IFS while falling short of it on skill (Pathak et al., 2022, arXiv:2202.11214). The following year the gap closed. Pangu-Weather used a 3D Earth-specific transformer with separate models trained for different lead times, a hierarchical scheme designed specifically to limit the error accumulation that kills autoregressive rollouts, and reported stronger deterministic results than IFS across all tested variables (Bi et al., Nature 619, 533–538, 2023). GraphCast followed months later with the 1,380-target result.

timeline
    title Learned forecasting, 2022 to 2025
    2022 : FourCastNet shows 0.25 degree data-driven global forecasting is feasible
         : WeatherBench 2 gives the field a common scoring protocol
    2023 : Pangu-Weather beats IFS on all tested deterministic variables using a 3D transformer
         : GraphCast wins 90 percent of 1,380 targets against HRES; ECMWF begins running it experimentally
    2024 : GenCast produces ensembles that beat operational ENS on 97.2 percent of 1,320 targets
         : NeuralGCM couples a differentiable dynamical core to learned physics parameterisations
    2025 : ECMWF takes AIFS operational on 25 February, alongside IFS
         : Aurora, a 1.3B-parameter Earth-system foundation model, extends the recipe to air quality, waves and cyclone tracks

The compression is the striking part. Three years from "this is possible" to "this is operational at the institution with the most to lose from being wrong".

[IMAGE: Line chart of anomaly correlation coefficient for 500 hPa geopotential at day 5, plotted against year from 1980 to 2025, showing the long slow climb of physics-based IFS and then the learned models arriving above the curve after 2022. Caption: "Forty years of one-day-per-decade improvement, and then a step."]

How a Learned Forecast Model Actually Works

The task, stated precisely

The model learns a one-step map. Given the atmospheric state at time \(t\) and at \(t - 6\text{h}\), predict the state at \(t + 6\text{h}\):

Longer forecasts come from applying \(f_\theta\) to its own output. A 10-day forecast at 6-hour steps is forty applications, which is where all the difficulty lives.

The state \(X\) is a tensor over a 0.25 degree lat-lon grid, which is 721 × 1440 points, times 37 pressure levels, times the prognostic variables (geopotential, temperature, wind components, specific humidity) plus surface fields. That is on the order of \(10^8\) numbers per timestep, which explains why 36.7 million parameters is considered a small model here and also why memory footprint, not capacity, drove the architecture.

Training data is a physics model's output

This is the fact most often skipped and it changes the interpretation of every result.

The training target is ERA5: ECMWF's reanalysis, a physically consistent gridded reconstruction of the atmosphere from 1979 to the present, produced by assimilating the historical observational record into a fixed version of the IFS. It is the best available estimate of past atmospheric states, and it is model output, not measurement.

So the learned model is trained to reproduce the behaviour of a physics model that has been fitted to observations. It inherits ERA5's quality, which is high, and ERA5's biases, which are real. It also means that headline comparisons scored against ERA5 give a systematic advantage to a model trained on ERA5 over a physics model that was not, and scoring against independent station observations narrows the reported gap. This is an active methodological argument in the field rather than a settled point.

The architecture problem: acting globally without a global attention bill

Weather is a long-range phenomenon. A trough over the Pacific matters for Europe five days later. But attention over \(10^6\) grid points is not affordable, and a convolutional stack needs impractically many layers to propagate information across the globe.

GraphCast's answer is a multi-mesh: an icosahedral mesh refined to several resolutions, with the edges from all refinement levels present simultaneously in a single graph. The coarsest edges span thousands of kilometres and the finest span tens. Message passing on this union propagates information globally in a small, fixed number of steps, regardless of distance. The full model is an encoder that maps the lat-lon grid onto the mesh, sixteen rounds of message passing on the mesh, and a decoder back to the grid.

Pangu takes the transformer route instead, applying 3D windowed attention with an Earth-specific positional bias that encodes the fact that the atmosphere is a sphere with a vertical structure, not a flat torus. Both are solving the same problem: give every point a path to every other point without paying the quadratic bill.

The rollout problem and the curriculum

An autoregressive model fed its own output drifts. Errors compound, and small artefacts amplify into instabilities that look nothing like weather.

The fix is training-time, not architectural. GraphCast is trained with a curriculum that gradually increases the number of autoregressive steps in the loss, from one step up to twelve, so the model is explicitly optimised to remain stable when consuming its own predictions. Pangu attacks the same problem differently, training separate models for 1, 3, 6 and 24-hour steps and composing the largest available steps to reach a target lead time, which minimises the number of compositions and therefore the accumulation.

Neither approach guarantees stability. Both make it empirically reliable out to the lead times they were trained for, and neither is trustworthy far beyond them.

Why deterministic models blur, and what diffusion fixed

Train with a mean-squared-error loss and the optimum is the conditional mean:

The atmosphere at lead time 7 days is genuinely uncertain, so the conditional mean is an average over many possible futures, and averaging fields with sharp features in different places produces a field with no sharp features anywhere. The model is not making a mistake. It is correctly reporting the average of the possibilities, which is a smoother object than any of them.

For anyone forecasting a storm rather than a monthly mean, that is the wrong output. It understates gradients, softens fronts, and systematically under-predicts extremes, all while scoring better on RMSE than a sharp forecast that puts the front 100 km off.

GenCast solves this by changing the objective rather than the architecture. It is a conditional diffusion model: instead of predicting the next state, it learns to denoise a sample from the conditional distribution over next states. Each ensemble member is an independent sample, generated in about 8 minutes on a single TPU v5, at 12-hour steps out to 15 days across more than 80 surface and atmospheric variables. Against ECMWF's operational ENS, it had greater skill on 97.2 percent of 1,320 evaluation targets and improved forecasts of extremes, tropical cyclone tracks, and wind power production.

[IMAGE: Two rank histograms (Talagrand diagrams) side by side for a 50-member ensemble at day 7, one U-shaped indicating under-dispersion and one flat indicating calibration, with the CRPS value annotated on each. Caption: "Calibrated spread is the claim RMSE cannot make. A flat rank histogram means the truth falls where the ensemble said it would."]

That is the result that mattered. Beating a deterministic forecast requires a good mean. Beating an ensemble requires calibrated spread, meaning the ensemble's disagreement has to correctly reflect genuine uncertainty, and that is a much stronger claim about what the model learned.

Seeing It in Motion

The training and inference paths differ in a way that is easy to miss:

sequenceDiagram
    participant D as ERA5 archive
    participant T as Training loop
    participant M as Model f(θ)
    participant I as Inference
    participant U as Forecast product
    D->>T: state pairs (t-1, t) and target (t+1)
    T->>M: one-step loss
    Note over T,M: curriculum grows rollout 1 → 12 steps
    T->>M: multi-step loss on own predictions
    M-->>T: gradients through the full rollout
    I->>M: operational analysis at t0
    M->>I: state at t0 + 6h
    Note over I,M: 40 applications for a 10-day forecast
    I->>U: deterministic field or ensemble members

And the architectural split between the two dominant families:

graph TD
  subgraph GC["Graph approach: GraphCast"]
    G1["Lat-lon grid<br/>721 x 1440 x 37"] --> G2["Encoder to multi-mesh"]
    G2 --> G3["16 rounds message passing<br/>edges at all refinement levels"]
    G3 --> G4["Decoder to grid"]
  end
  subgraph PW["Transformer approach: Pangu"]
    T1["3D patch embedding"] --> T2["Windowed attention<br/>Earth-specific bias"]
    T2 --> T3["Separate models per lead time"]
    T3 --> T4["Compose largest steps"]
  end
  classDef purple fill:#6d28d9,stroke:#a78bfa,stroke-width:1px,color:#fff
  classDef teal fill:#0e7490,stroke:#22d3ee,stroke-width:1px,color:#fff
  class G1,G2,G3,G4 purple
  class T1,T2,T3,T4 teal

[IMAGE: Diagram of the multi-mesh construction, showing an icosahedron refined through five levels with the edge sets from all levels overlaid on one sphere, colour-coded by refinement level. Caption: "Every refinement level's edges coexist, so one message-passing step moves information both 20 km and 5,000 km."]

Watch It Run

By the Numbers

Sources: GraphCast parameter count of 36.7M, training on 32 TPU v4 devices for approximately four weeks, and the 90 percent of 1,380 targets result (Lam et al., Science, 2023, arXiv:2212.12794); GenCast's 97.2 percent of 1,320 targets, 8-minute member generation and 80-plus variables (Price et al., Nature, 2025, arXiv:2312.15796); Pangu results (Bi et al., Nature 619, 2023); HRES at 9 km, ENS at 18 km, AIFS operational from 25 February 2025 and AIFS ENS at 51 members and 31 km, plus the roughly 1,000-fold energy reduction claim (ECMWF, 2025); Aurora's 1.3B parameters and multi-domain fine-tuning (Bodnar et al., Nature, 2025).

The energy figure comes from ECMWF describing its own system, so treat it as a vendor claim from an unusually credible vendor. The direction is not in dispute; the exact multiplier depends heavily on what is being counted.

[IMAGE: Grouped bar chart of forecast production cost, log scale, comparing HRES, ENS, GraphCast and GenCast on two axes: accelerator-hours per forecast and approximate energy per forecast, with the assimilation cost shown as a shared grey base under every bar. Caption: "The shared grey base is the part nobody replaced."]

A Concrete Example

Trace one 10-day forecast from the 00 UTC cycle on an arbitrary day, and watch where the time and the error go.

Step 1: the analysis. The conventional 4D-Var assimilation window ingests on the order of tens of millions of observations, mostly satellite radiances, and produces a gridded analysis: the best estimate of the atmospheric state at 00 UTC. This takes a substantial fraction of an hour on the supercomputer, and it is unchanged by any of the machine learning work described here. Call the output \(X^{0}\), a tensor of about \(10^8\) floats.

Step 2: the second input. GraphCast conditions on two states, so it also takes \(X^{-1}\), the analysis from 18 UTC the previous day. This gives the model a finite-difference estimate of tendency, which is how it infers motion without being told the equations.

Step 3: encode. The 721 × 1440 × 37 grid is mapped onto the multi-mesh. The finest mesh level has on the order of \(10^5\) nodes, roughly an order of magnitude fewer than the grid, so the encoder is also a compression.

Step 4: sixteen rounds of message passing. Each round updates every mesh node from its neighbours across all refinement levels. Because the coarsest edges span thousands of kilometres, a signal from the Pacific reaches Europe within the first few rounds rather than after hundreds of layers.

Step 5: decode and step. The decoder returns a residual on the lat-lon grid, added to \(X^{0}\) to give \(\hat{X}^{1}\), the state at 06 UTC. Elapsed accelerator time so far: a fraction of a second.

Step 6: repeat 39 times. \(\hat{X}^{2} = f_\theta(\hat{X}^{1}, X^{0})\), then \(\hat{X}^{3} = f_\theta(\hat{X}^{2}, \hat{X}^{1})\), and from step 3 onward the model has seen no real data at all. It is consuming exclusively its own output for the remaining 37 steps. Total wall-clock: under a minute.

Step 7: where the error is. Suppose the one-step RMSE on 500 hPa geopotential is small, on the order of a few metres. That error does not stay small, and it does not simply add. Atmospheric dynamics are chaotic, so an initial perturbation grows roughly exponentially with an e-folding time of a day or two in the mid-latitudes. Forty compounding steps through a chaotic map is why day-10 skill is so much worse than day-2 skill for every forecasting system ever built, learned or not. The curriculum that trains on twelve-step rollouts exists to make the model's own contribution to that growth as small as possible; it cannot suppress the atmosphere's.

Step 8: for GenCast, do it again 50 times. Each ensemble member is an independent diffusion sample, so 50 members at 8 minutes each is roughly 400 TPU-minutes, parallelisable to about 8 minutes wall-clock. The spread across those 50 trajectories is the forecast's statement about its own uncertainty, and the 97.2 percent result says that statement is better calibrated than the one a supercomputer-based ensemble makes.

[IMAGE: Error-growth curve showing RMSE of 500 hPa geopotential against lead time from 0 to 10 days, with the per-step model error shown as a thin band at the bottom and the total error growing roughly exponentially above it, annotated to show that the gap between them is atmospheric chaos rather than model deficiency. Caption: "The model contributes the thin band. The rest is the atmosphere."]

The arithmetic to hold onto: one forecast, forty compounding applications of a 36.7M-parameter function, under a minute, and the initial condition it started from cost more to produce than the forecast did.

Where It Breaks

The distribution shifts and nothing stops it

Conservation of mass, energy and momentum are not enforced by these architectures. They are approximately learned, because the training data approximately satisfies them. This is fine while the input stays inside the training distribution and offers no guarantee when it does not.

A warming climate is exactly that kind of shift. Forty-five years of ERA5 contain the atmosphere as it was, and a model asked about states outside that range is extrapolating with no physical constraint. Numerical models have the opposite property: their equations hold regardless of whether the state has been seen before, which is why climate projection remains a physics-model job and why nobody credible is proposing otherwise.

Rare events are rare in the training set too

A category-5 landfall in a specific basin, a record-breaking heat dome, a once-in-a-century atmospheric river. These have few analogues in the archive, and a model that learns from analogues has little to go on. Physics-based models get these partly right because the equations do not care how often something has happened before.

Both GraphCast and GenCast report improved severe-event skill on tropical cyclone tracks and atmospheric rivers, so the picture is not simply "learned models fail on extremes". But the mechanism by which they succeed is different, and it degrades further out in the tail than the physics-based mechanism does.

The verification argument

Most headline results score against ERA5. That is standard practice, and it advantages a model trained on ERA5 over one that was not. Scoring against independent station observations tends to narrow the reported gaps, and the field has been openly arguing about how much. WeatherBench 2 exists partly to make this comparison honest by fixing the protocol (Rasp et al., 2023, arXiv:2308.15560).

There is a second and subtler version. RMSE rewards smoothness. A deterministic learned model that blurs will beat a sharper forecast that displaces a front slightly, even though a forecaster would prefer the sharp one. Choosing scores that penalise blurring, such as spectral energy retention or CRPS for ensembles, changes the ranking, which is why the shift to probabilistic evaluation was substantive rather than cosmetic.

The dependency on the system it did not replace

The initial condition still comes from conventional 4D-Var assimilation, which is a large fraction of the operational compute budget and all of the observational infrastructure. Every "1,000 times cheaper" claim is about the forecast step, sitting on top of an assimilation step it does not change.

Work on end-to-end learned assimilation exists, including efforts to produce an analysis directly from observations, and it is genuinely hard: the observations are heterogeneous, irregularly spaced, and each carries an instrument-specific error model that 4D-Var handles explicitly. Until that is solved, learned forecasting is a component inside a conventional system rather than a replacement for one.

Resolution and the things below the grid

At 0.25 degrees, which is roughly 28 km at the equator, a thunderstorm is a sub-grid phenomenon. Convection, boundary-layer turbulence and orographic effects are all parameterised in physics models and simply absent as explicit processes in a model that learns at that grid. Aurora's fine-tuning to 0.1 degrees and ECMWF's operational work push this down, and the compute cost rises with it, which is the same wall physics models hit.

Alternative Designs

NeuralGCM deserves more than a table row, because it is the design that most directly addresses the out-of-distribution objection (Kochkov et al., Nature, 2024, arXiv:2311.07222). It keeps a real dynamical core, written to be differentiable, and replaces only the parameterisations of unresolved physics with learned components. Conservation properties come from the core rather than from the data, and the learned parts handle exactly what the physics models were always weakest at. It gives up some of the pure-learned speed and buys back a structural guarantee.

How It Is Used in Practice

ECMWF's operational deployment is the case worth studying, because the choices are conservative in instructive ways. AIFS runs alongside IFS rather than replacing it, both are published, and forecasters are given both. The ensemble version, AIFS ENS, runs 51 members at 31 km, coarser than the physics ensemble's resolution, and ECMWF says so plainly rather than reporting only the members-and-lead-time figures that look best.

The applications where speed changes the product rather than just the bill are the interesting ones. Large ensembles become affordable, and ensemble size is one of the strongest levers on probabilistic skill. Rapid re-forecasting on new observations becomes possible within a decision window. Scenario sweeps for energy trading, aviation routing and grid operation, which previously required choosing which questions to ask, can now ask all of them.

The operational caution is also real. A learned model that fails does not fail gracefully: a physics model producing nonsense usually violates something checkable, while a learned model producing nonsense produces a smooth, plausible, wrong field. Operational centres run consistency checks precisely because the failure mode is quiet.

[IMAGE: Timeline strip showing a single operational day, with the assimilation window, analysis production, physics forecast run, and learned forecast run drawn to scale on the same horizontal axis. Caption: "The learned forecast is the thin sliver. The wide block to its left did not change."]

Insights Worth Remembering

1. The result is about the forecast model, not the forecast system. Data assimilation, observation processing and the satellite infrastructure are untouched, and they are most of the cost and all of the connection to reality. Learned forecasting is currently a very good component inside a conventional pipeline.

2. Mean squared error and weather are structurally mismatched. MSE's optimum is the conditional mean, and the conditional mean of a chaotic field is smooth. Deterministic learned models are not blurring by accident; they are correctly reporting an average nobody wanted. The move to diffusion changed the estimand, not the accuracy.

3. Beating an ensemble is a much stronger claim than beating a deterministic forecast. A good mean requires learning dynamics. Calibrated spread requires learning the shape of the uncertainty, which is a statement about what the model represents internally, not just what it outputs.

4. Thirty-six million parameters was enough. The scaling intuitions from language models transfer poorly here. The bottleneck was architecture, specifically getting global information flow without a quadratic bill, and training procedure, specifically rollout stability, not capacity.

5. Training on reanalysis means training on model output. The learned models inherit ERA5's biases and are evaluated, usually, against ERA5. That is not a scandal, it is a caveat, and it means the reported margins over physics models are upper bounds on the margin against reality.

6. Autoregressive rollout is the whole difficulty. Forty compounding applications through a chaotic system is why day-10 forecasts are hard for everyone. The multi-step curriculum exists to minimise the model's own contribution to error growth, which is the only part it can control.

7. Conservation laws that are learned rather than enforced are a liability outside the training distribution. This is the strongest argument for hybrid designs like NeuralGCM, and the reason nobody serious proposes replacing climate models with pure learned surrogates.

8. The field absorbed the result in about eighteen months. From GraphCast's publication to ECMWF's operational AIFS is a remarkably short interval for a discipline that verifies everything. That speed is itself evidence: weather has a scoring culture rigorous enough to settle the argument quickly.

Open Questions

Can data assimilation be learned end to end? This is the question that determines whether learned forecasting becomes a complete system or stays a component. The difficulty is measured rather than speculative: observations are heterogeneous, irregular, and carry instrument-specific error models that 4D-Var handles explicitly. Several groups are working on producing an analysis directly from observations, and no approach has yet matched operational assimilation quality.

How badly do these models degrade under climate shift? It is established that conservation is learned rather than enforced, and it is not established how quickly skill decays as the input distribution moves. Retrospective tests on the warmest years in the archive give a hint and are not decisive, because those years are inside the training data. This is likely to be answered slowly, by the climate.

Is the hybrid design the endpoint or a transitional one? NeuralGCM's argument is that keeping a differentiable dynamical core buys structural guarantees cheaply. The counter-argument is that every constraint imposed by hand is a constraint that could have been learned given more data. Which wins is genuinely open, and the answer probably differs by timescale: hybrids look stronger the further out you forecast.

Does the verification advantage from training on reanalysis fully explain the reported margins? Studies scoring against independent observations narrow the gaps, and the size of the remaining margin is disputed. A properly designed observation-based comparison across all the major learned and physics-based systems would settle it and has not been done at the scale required.

Does the recipe generalise beyond weather? Aurora's fine-tuning to air quality, ocean waves and cyclone tracks suggests the pretrain-then-specialise pattern works across Earth-system domains. Whether it works in domains with far less data than the atmosphere has, which is most of them, is unproven and is the more consequential question for AI-for-science generally.

Sources and Further Reading

1. Lam, R., Sanchez-Gonzalez, A., Willson, M., et al. (2023). "Learning skillful medium-range global weather forecasting." Science 382(6677), 1416–1421. arXiv:2212.12794
2. Price, I., Sanchez-Gonzalez, A., Alet, F., et al. (2025). "Probabilistic weather forecasting with machine learning." Nature. arXiv:2312.15796
3. Bi, K., Xie, L., Zhang, H., Chen, X., Gu, X., & Tian, Q. (2023). "Accurate medium-range global weather forecasting with 3D neural networks." Nature 619, 533–538. nature.com
4. Pathak, J., Subramanian, S., Harrington, P., et al. (2022). "FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators." arXiv:2202.11214
5. Bodnar, C., Bruinsma, W. P., Lucic, A., et al. (2025). "A foundation model for the Earth system." Nature. nature.com
6. Kochkov, D., Yuval, J., Langmore, I., et al. (2024). "Neural general circulation models for weather and climate." Nature 632, 1060–1066. arXiv:2311.07222
7. Rasp, S., Hoyer, S., Merose, A., et al. (2023). "WeatherBench 2: A benchmark for the next generation of data-driven global weather models." arXiv:2308.15560
8. ECMWF (2025). "ECMWF's AI forecasts become operational." ecmwf.int
9. ECMWF. "AIFS ENS becomes operational." ECMWF Newsletter 185. ecmwf.int
10. Li, Z., Kovachki, N., Azizzadenesheli, K., et al. (2021). "Fourier Neural Operator for Parametric Partial Differential Equations." ICLR 2021. arXiv:2010.08895
11. Hersbach, H., et al. (2020). "The ERA5 global reanalysis." Quarterly Journal of the Royal Meteorological Society 146(730), 1999–2049.
12. Bauer, P., Thorpe, A., & Brunet, G. (2015). "The quiet revolution of numerical weather prediction." Nature 525, 47–55.

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