FourCastNet: Fourier Forecasting Neural Network

• FourCastNet is a data-driven global weather forecast model that replaces traditional PDE time stepping with learned Fourier-domain updates for medium-range predictions.
• It employs Adaptive Fourier Neural Operators and patch embeddings to process 20 atmospheric variables on a 0.25° grid, ensuring high synoptic-scale accuracy.
• Its exceptional computational efficiency enables week-long forecasts in seconds, facilitating large ensemble runs, uncertainty quantification, and transfer learning applications.

FourCastNet, short for Fourier Forecasting Neural Network, is a global data-driven weather forecasting model that learns a mapping from a multivariate atmospheric state on a regular $0.25^\circ \times 0.25^\circ$ grid to the state six hours later, then rolls this mapping forward autoregressively to produce medium-range forecasts. Developed as a purely data-driven high-resolution weather model built around Adaptive Fourier Neural Operators (AFNOs), it targets numerical-weather-prediction-grade global forecasting while replacing explicit PDE time stepping with learned spectral-space updates; the original reports emphasize accurate week-long forecasts, strong performance on fast-timescale variables such as surface wind, precipitation, and atmospheric water vapor, and inference that is orders of magnitude faster than conventional NWP (Pathak et al., 2022, Kurth et al., 2022).

1. Origin, scope, and forecasting objective

FourCastNet emerged from the observation that operational NWP is constrained by high computational cost and strict time-to-solution limits, especially for global high-resolution forecasting. In response, FourCastNet was formulated as a purely data-driven Earth-system emulator trained on ERA5 reanalysis to forecast global weather at $0.25^\circ$ resolution. In its canonical form, the model predicts the full atmospheric state at $t+\Delta t$ from the state at $t$, with $\Delta t=6$ h, and then reuses its own output recursively for multi-day forecasts (Kurth et al., 2022).

The original formulation represents the weather state as $X(t)\in\mathbb{R}^{\ell\times h\times w}$ with $\ell=20$ prognostic variables and $(h,w)=(720,1440)$ grid points, or equivalently as a three-dimensional state $\mathbf{x}_t$ on a regular latitude–longitude grid. This setup places FourCastNet in the class of global surrogate models for medium-range forecasting rather than limited-area nowcasting systems or purely statistical post-processors. The intended application domain includes short- to medium-range prediction of large-scale circulation together with high-resolution, fast-timescale variables such as precipitation, surface winds, and atmospheric water vapor, and the original paper explicitly links these capabilities to tropical cyclones, extra-tropical cyclones, atmospheric rivers, and wind-energy planning (Pathak et al., 2022).

A central feature of the model’s positioning is computational asymmetry relative to physics-based forecasting. The original reports describe FourCastNet as producing a week-long forecast in less than 2 seconds and as being five orders-of-magnitude faster than NWP while approaching state-of-the-art accuracy. This speed is not only an implementation detail; it is intrinsic to the model’s scientific role, because it makes very large ensembles feasible and therefore shifts part of the forecasting problem from deterministic integration toward rapid probabilistic scenario generation (Pathak et al., 2022, Kurth et al., 2022).

2. AFNO architecture and mathematical formulation

The core recurrence is

$\mathbf{x}_{t+\Delta t}=f_\theta(\mathbf{x}_t),$

with outputs consisting of the same set of fields at $0.25^\circ$0 h, suitable for recursive rollout (Charlton-Perez et al., 2023). In the conference-scale description, the model takes $0.25^\circ$1 channels on a $0.25^\circ$2 grid, divides the grid into non-overlapping patches of size $0.25^\circ$3 with $0.25^\circ$4, and yields $0.25^\circ$5 tokens. Each token is then linearly projected to an embedding of dimension $0.25^\circ$6 (Kurth et al., 2022).

The distinctive element is the AFNO block. Each block performs spatial mixing through a global Fourier-domain convolution, followed by a per-token channel-mixing MLP, with residual connections and layer normalization. In one layer, the forward FFT is applied on each feature channel, the $0.25^\circ$7-dimensional channel vector at each retained frequency is partitioned into $0.25^\circ$8 blocks of size $0.25^\circ$9, and a learned complex block-diagonal matrix acts on each block before inverse FFT returns the representation to physical space. The subsequent MLP has hidden size $t+\Delta t$0 and GeLU activations (Kurth et al., 2022).

A compact expression used for one AFNO layer is

$t+\Delta t$1

where the Fourier-space multiplication is block-diagonal. Relative to CNNs, this realizes a global convolution in $t+\Delta t$2 rather than a local stencil, and relative to Transformers it avoids explicit $t+\Delta t$3 attention and the associated $t+\Delta t$4 token–token products (Kurth et al., 2022).

Model descriptions in the later literature emphasize an encode–process–decode interpretation. A synthesized technical report describes FourCastNet as combining a global Fourier Neural Operator block, a Vision-Transformer-style patch embedding, and several residual-connected layers of Adaptive FNO plus transformer blocks. The same report describes a training loss consisting of a weighted sum of pointwise MSE and spectral MSE so that both grid-scale and modal accuracy are enforced:

$t+\Delta t$5

with $t+\Delta t$6–$t+\Delta t$7 as a tunable spectral-penalty weight (Charlton-Perez et al., 2023). This suggests a recurring theme in FourCastNet work: synoptic fidelity is pursued through explicit control of spectral structure rather than through local finite-volume consistency.

3. Data, optimization, and high-performance implementation

The original large-scale training setup uses ERA5 reanalysis at $t+\Delta t$8 resolution, with data from 1979–2017 for training and 2018 onward for testing, sampled every 6 h and comprising 20 channels including winds, temperature, geopotential, humidity, surface pressure, and related surface fields (Kurth et al., 2022). Other FourCastNet summaries describe closely related ERA5 ranges such as 1979–2018 and similar variable sets on 10 pressure levels plus surface fields, but the common denominator is global six-hourly ERA5 supervision at quarter-degree resolution (Charlton-Perez et al., 2023).

The training protocol in the original systems paper is split into pre-training and fine-tuning. Pre-training minimizes a single-step $t+\Delta t$9 loss,

$t$0

and fine-tuning uses two-step teacher forcing,

$t$1

The reported setup uses 80 pre-training epochs, mixed-precision Adam, batch sizes from 32 up to 768, and an NVIDIA DALI pipeline that reads HDF5, normalizes each variable, and adds small Gaussian noise as data augmentation (Kurth et al., 2022).

At the systems level, FourCastNet was explicitly engineered for extreme-scale training. The model was optimized and scaled on Selene, Perlmutter, and JUWELS Booster up to 3,808 NVIDIA A100 GPUs, with 140.8 petaFLOPS peak mixed-precision performance. On JUWELS Booster with 3,072 A100 GPUs, training to 80 epochs was reported at 67.4 minutes, whereas a 32-GPU baseline would take approximately 40 h. The implementation used model parallelism across feature channels for FFT and block MLP computation, data parallelism across the batch, NCCL-backed all-reduce for gradients, CUDA Graphs to eliminate CPU launch latency, and torch.jit.script for fusing elementwise layers (Kurth et al., 2022).

Inference efficiency is a defining empirical result. For a 100-member 24 h forecast, FourCastNet on 8 A100 GPUs was reported at 12.41 node-seconds on Selene, compared with 984,000 node-seconds for IFS L91 at 18 km, corresponding to an 80,000-times faster node-seconds basis. The same comparison gives energy use of $t$2 J for FourCastNet against $t$3 J for IFS, ანუ a 10,000-times energy-efficiency advantage (Kurth et al., 2022).

4. Forecast skill, case studies, and event-based evaluation

On standard benchmark metrics, FourCastNet consistently shows strong medium-range skill, particularly for large-scale flow. A synthesized comparison reports that the anomaly correlation coefficient for 500 hPa height exceeds $t$4 at day 3, exceeds $t$5 at day 5, and is approximately $t$6 at day 10 on WeatherBench, with corresponding RMSE of approximately $t$7 m at day 5 and $t$8 m at day 10 (Charlton-Perez et al., 2023). The original systems paper reports for $t$9 at 72 h an RMSE of approximately $\Delta t=6$0 m and ACC of approximately $\Delta t=6$1 for FourCastNet at 25 km, compared with approximately $\Delta t=6$2 m and $\Delta t=6$3 for downsampled IFS at 200 km (Kurth et al., 2022). The earlier FourCastNet paper further states that the model matches IFS for large-scale variables at short lead times while outperforming IFS for small-scale fields such as precipitation and 10 m wind in the first 48 h (Pathak et al., 2022).

Case studies complicate any simple claim that FourCastNet already supersedes physics-based operational forecasting. In the Storm Ciarán evaluation, FourCastNet, Pangu-Weather, GraphCast, and FourCastNet-v2 all accurately captured the synoptic-scale structure of the cyclone, including the cloud head, warm sector, warm conveyor belt jet, and the storm’s placement relative to the upper-level jet exit. At 48 h lead, FourCastNet’s minimum MSLP forecast was 954–955 hPa versus 954 hPa in analysis. However, FourCastNet underestimated peak 10 m winds at approximately $\Delta t=6$4 m/s versus approximately $\Delta t=6$5 m/s in IFS HRES and approximately $\Delta t=6$6 m/s in ERA5, produced frontal-fracture and warm-conveyor-belt jets that were 4–6 m/s weaker at 850 hPa, did not resolve the sharp bent-back warm front, and did not produce a clear warm-core seclusion at maturity (Charlton-Perez et al., 2023).

Other extreme-event assessments are less favorable. In a three-case comparison against HRES, GraphCast, and PanguWeather, FourCastNet had the largest RMSE during the 2021 Pacific Northwest heatwave and the 2021 North American winter storm; it was also excluded from direct heat-index analysis for the 2023 South Asian humid heatwave because it does not forecast any humidity field at or near the surface, its lowest-level humidity being at 850 hPa (Pasche et al., 2024). During the South Asian monsoon, an observations-focused assessment reported over the Indian domain a $\Delta t=6$7 RMSE of $\Delta t=6$8 K at 1 day, $\Delta t=6$9 K at 3 days, $X(t)\in\mathbb{R}^{\ell\times h\times w}$0 K at 7 days, and $X(t)\in\mathbb{R}^{\ell\times h\times w}$1 K at 15 days, together with national-average precipitation RMSE of $X(t)\in\mathbb{R}^{\ell\times h\times w}$2, $X(t)\in\mathbb{R}^{\ell\times h\times w}$3, and $X(t)\in\mathbb{R}^{\ell\times h\times w}$4 mm day$X(t)\in\mathbb{R}^{\ell\times h\times w}$5 at 1-, 3-, and 7-day lead, and extreme-event hit rates for daily precipitation events exceeding 50 mm of $X(t)\in\mathbb{R}^{\ell\times h\times w}$6, $X(t)\in\mathbb{R}^{\ell\times h\times w}$7, and $X(t)\in\mathbb{R}^{\ell\times h\times w}$8 at the same leads. The same assessment reported an underestimation of mesoscale eddy kinetic energy at 100 hPa by approximately $X(t)\in\mathbb{R}^{\ell\times h\times w}$9–$\ell=20$0 dex for total wavenumbers greater than 50 and a mean 7-day cyclone-track error of 560 km for Cyclone Tauktae (Gupta et al., 2 Sep 2025).

Taken together, these studies indicate a stable pattern. FourCastNet is strong at steering flow, synoptic organization, and large-scale anomaly evolution, but its representation of warning-critical mesoscale structure, extreme tails, and some compound-impact variables remains mixed. This suggests that benchmark skill alone does not settle the operational question.

5. Extensions, derivatives, and reuse of the learned representation

A substantial literature has treated FourCastNet not only as a forecaster but also as a backbone for correction, remapping, uncertainty quantification, and transfer. The DL-Corrector-Remapper framework extends FourCastNet with an AFNO-based continuous Fourier decoder and a non-uniform inverse discrete Fourier transform so that outputs can be evaluated directly at sparse observational locations. Under dual supervision from sparse observations and gridded ERA5 fields, DLCR reduced MSE by 20–30% over a U-Net post-processor and by more than 40% over naive interpolation across lead times, while preserving the large-scale structure of the original FourCastNet forecast (Ge et al., 2022).

Precipitation forecasting motivated a different extension. A conditional GAN replacing the FourCastNet precipitation head was trained to sharpen fine-scale precipitation structure and improve extremes. At 18 h lead, the baseline FourCastNet and an $\ell=20$1-only model undershot ERA5 power spectral density by up to an order of magnitude at wavenumbers above 20, while the adversarial-plus-$\ell=20$2 model nearly matched ERA5 PSD up to approximately $\ell=20$3. The same study reported that baseline FourCastNet underestimated heavy precipitation tails by 20–30%, whereas the GAN model matched ERA5 percentiles within the 1-$\ell=20$4 variability envelope of the test set, while remaining comparable to state-of-the-art NWP in ACC at 1–2 day lead times (Duncan et al., 2022).

Several works target the computational barrier of retraining or stabilizing the model. FourCastNeXt introduced on-the-fly data augmentation, deep-norm initialization, smaller patch size, a learned temporal flow field, and multi-step fine-tuning, and reported comparable accuracy at approximately 5% of the original FourCastNet compute footprint, quantified as 140 V100-GPU hours versus a normalized 3072 V100-GPU-hour equivalent for the baseline (Guo et al., 2024). In data assimilation, FourCastNet has been embedded into a 3DVar cycle with sparse noisy ERA5 observations, where year-long filtering remained accurate with RMSE approximately $\ell=20$5–$\ell=20$6 for a 2° thinning and ACC remaining at least approximately $\ell=20$7 for $\ell=20$8 over a 2023 assimilation window (Adrian et al., 2024). A related weakly constrained 4DVar formulation replaced the model operator with FourCastNet and reported better hurricane-tracking accuracy and uncertainty quantification than both an unstabilized FourCastNet forecast and an EnKF benchmark (Dinenis et al., 4 Mar 2025).

The learned atmospheric representation has also been reused outside direct forecasting. In global vegetation modeling, a pre-trained FourCastNet backbone was fine-tuned for NDVI estimation at $\ell=20$9 resolution using meteorological inputs only, improving test performance over a scratch-trained FCN variant from RMSE $(h,w)=(720,1440)$0, $(h,w)=(720,1440)$1 $(h,w)=(720,1440)$2 to RMSE $(h,w)=(720,1440)$3, $(h,w)=(720,1440)$4 $(h,w)=(720,1440)$5 on 2013 data (Janetzky et al., 2024). This suggests that FourCastNet’s representation captures transferable structure relevant to Earth-system processes beyond conventional weather verification.

6. Model-family evolution, known limitations, and open questions

Subsequent FourCastNet-family work has moved in three main directions: geometry-aware operators, probabilistic forecasting, and stabilization of long rollouts. In medium-range deterministic comparison, FourCastNet v2, described as using a spherical FNO, was reported at day-5 and day-10 $(h,w)=(720,1440)$6 ACC of approximately $(h,w)=(720,1440)$7 and $(h,w)=(720,1440)$8, compared with approximately $(h,w)=(720,1440)$9 and $\mathbf{x}_t$0 for the original FourCastNet, approximately $\mathbf{x}_t$1 and $\mathbf{x}_t$2 for GraphCast, and approximately $\mathbf{x}_t$3 and $\mathbf{x}_t$4 for Pangu-Weather (Charlton-Perez et al., 2023). FourCastNet 3 then recast the family as a purely convolutional geometric model on the sphere for probabilistic ensemble forecasting, reporting CRPS below IFS-ENS, calibration with spread-skill ratio approximately 1, no small-scale spectral blow-up up to 60 days, and a 90-day global forecast at $\mathbf{x}_t$5, 6-hourly resolution in under 20 seconds on a single H100 GPU (Bonev et al., 16 Jul 2025).

Long-horizon behavior remains an active issue. A study of autoregressive deep-learning climate models at $\mathbf{x}_t$6 resolution found that single-step FourCastNet training often led to runaway error over 10-year rollouts, whereas multi-step training with $\mathbf{x}_t$7 or $\mathbf{x}_t$8 dramatically reduced long-term RMSE. Stable configurations were associated with moderate hidden dimension $\mathbf{x}_t$9 or $\mathbf{x}_{t+\Delta t}=f_\theta(\mathbf{x}_t),$0, smaller prognostic sets, and careful seed selection; even then, some seeds failed, indicating substantial random-seed sensitivity (Gallusser et al., 5 May 2025). This is consistent with data-assimilation studies that treat FourCastNet as accurate over short forecast cycles but unstable in long free-running mode unless regularly corrected by observations (Adrian et al., 2024).

Another limitation concerns distribution shift in a warming climate. An evaluation of FourCastNet V2 Small over boreal winters 2020–2025 found a cosine-weighted global land cold bias of $\mathbf{x}_{t+\Delta t}=f_\theta(\mathbf{x}_t),$1 K at 2-day lead and $\mathbf{x}_{t+\Delta t}=f_\theta(\mathbf{x}_t),$2 K at 9-day lead, with a global hot-tail bias at the 0.9 quantile of approximately $\mathbf{x}_{t+\Delta t}=f_\theta(\mathbf{x}_t),$3 K. The authors attribute this to a training-climate anchoring effect: the model, trained on 1979–2015 ERA5, remains biased toward cooler historical conditions and is most biased in the hottest forecasts, where training exposure to modern extreme heat is limited (Landsberg et al., 26 Sep 2025). A plausible implication is that raw FourCastNet-family forecasts may require explicit bias correction or augmented training before they are used for future-climate or climate-change-adjacent applications.

The broader controversy is therefore not whether FourCastNet can forecast weather skillfully—it can—but what kind of meteorological competence its current training paradigm produces. The accumulated evidence shows high synoptic skill, exceptional computational efficiency, and rapidly expanding utility in post-processing, assimilation, and transfer learning. It also shows systematic difficulty with narrow frontal gradients, peak near-surface winds, some compound hazards, surface-level humidity availability, mesoscale kinetic energy, and extrapolation beyond the historical training distribution (Charlton-Perez et al., 2023, Pasche et al., 2024). For operational meteorology, FourCastNet is best understood not as a completed replacement for physics-based NWP, but as a high-performance learned forecast operator whose strengths are already scientifically consequential and whose limitations remain technically specific.