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GenONet: A Generative operator Network for High-Resolution Precipitation Nowcasting

Mohammad Kian Golkar, Luciano Alves de Oliveira, Mohammad Khanjani

arXiv:2609.00544v1cs.LGphysics.ao-ph

TL;DR

Long-horizon precipitation nowcasting suffers from forecast degradation and increasing blur as storms evolve rapidly. The paper introduces GenONet, which combines a DeepONet generator with adversarial training and an MCE-based physics-informed loss. Evaluations report sharper, more coherent, and more temporally stable forecasts than baselines, with the regularizer improving physical consistency and skill in ablation experiments.

  • Problem

    Long-horizon precipitation nowcasting is difficult because deep learning forecasts can become blurry and lose structural fidelity as storm evolution continues.

  • Method

    GenONet uses a Spatio-Temporal U-DeepONet as a GAN generator, with a 3D discriminator and an MCE-derived physics-informed regularizer in secondary experiments.

  • Results

    GenONet produces sharper and more temporally consistent forecasts than baseline models, while physics-informed training improves predictive skill, especially at longer lead times.

  • Takeaways & Limitations

    The results support combining continuous-time operator learning with adversarial training and explicit physical constraints for high-resolution nowcasting.

  • Takeaways & Limitations

    Operational use is constrained by the computational intensity of the deep U-Net branch and 3D spatio-temporal discriminator, although the discriminator is excluded during inference.

Abstract

from arXiv · show

High-resolution precipitation nowcasting is critical for reducing the impacts of severe weather but remains difficult because of rapid storm evolution. Deep learning models have shown great promise for this task, but their predictive skill often deteriorates over longer forecast horizons. This leads to increasingly blurry forecasts that fail to capture the complex, non-linear evolution of storm systems. In order to address these limitations, we introduce Spatio-Temporal U-DeepONet (GenONet), a novel architecture for long-range precipitation forecasting up to 3 hours, specifically designed to produce sharp and physically consistent results. GenONet's architecture pioneers the use of a Deep Operator Network (DeepONet) as a generator within a Generative Adversarial Network (GAN) framework for this task. The DeepONet learns the continuous-time dynamics of precipitation, ensuring stability over long forecast horizons. Adversial training against a spatio-temporal discriminator compels the model to produce sharp, coherent forecasts, while a physics-informed loss regularizer, derived from the Moisture Conservation Equation, improves physical plausibility in our ablation setting. Quantitative evaluations show that our model achieves consistently higher scores on most of the metrics, especially for highintensity events and at longer lead times. Qualitatively, GenONet produces structurally coherent forecasts that maintain their integrity, whereas baseline models degrade into indistinct patterns. Finally, an ablation study confirms the benefit of this physics-informed loss, highlighting the strength of combining operator learning with adversarial training.

I. Introduction

High-resolution precipitation nowcasting is important but difficult because storm systems evolve nonlinearly and forecasts degrade over longer horizons. GenONet combines DeepONet-based continuous-time modeling, adversarial training, and physics-informed regularization to improve sharpness, stability, and physical plausibility.

  • Motivation: Precipitation nowcasting supports mitigation of flash floods, landslides, and disruptions to transportation and agriculture.It forecasts rainfall in the immediate future, usually 0–2 hours.
  • Motivation: Deep learning models learn complex nonlinear weather dynamics from historical radar archives and implicitly model storm growth and decay.CNNs, ConvLSTM, and U-Net architectures learn spatio-temporal relationships directly from radar data.
  • Motivation: GANs improve forecast sharpness and temporal consistency, but recursive frame-by-frame generation can accumulate errors and lose structural integrity at long lead times.Spatio-temporal discriminators evaluate entire predicted sequences rather than isolated frames.
  • Motivation: DeepONets learn operators between function spaces and can map an input radar sequence to future states across the forecast horizon through continuous-time modeling.Their branch and trunk networks encode input functions and query coordinates such as time and space.
  • Contribution: GenONet uses a DeepONet generator inside a GAN, with a spatio-temporal discriminator and an MCE-derived physics-informed loss evaluated in an ablation study.The model targets high-resolution precipitation forecasting up to 3 hours.
  • Contribution: GenONet produces sharper and more temporally consistent predictions than baseline models, while the physics-informed loss provides additional predictive-skill improvements at longer lead times.The paper frames this combination as the synergistic integration of operator learning, adversarial training, and explicit physical laws.

B. Generative Adversarial Networks for Realistic Nowcasting

The paper combines operator learning with adversarial generation to address smooth, unrealistic, and long-horizon precipitation forecasts. GenONet uses a U-DeepONet generator, a spatio-temporal discriminator, and an optional MCE-based regularizer.

  • Generative Adversarial Networks: GANs use adversarial competition between a generator and discriminator to produce forecasts that better match realistic precipitation distributions.This approach targets overly smooth deterministic predictions and preserves sharp spatial variability.
  • Deep Operator Networks: DeepONets learn mappings between infinite-dimensional function spaces using branch and trunk networks rather than fixed-dimensional input-output mappings.The branch encodes the input function, while the trunk processes output-domain coordinates.
  • Research Gap: Prior operator-learning models use U-Net or sequential branches but still rely on L2 losses and produce overly smooth outputs.The paper identifies the use of DeepONets as GAN generators as an unresolved gap for this application.
  • Proposed Method: GenONet adapts Spatio-Temporal U-DeepONet as a GAN generator for deterministic, high-resolution precipitation nowcasting.Its branch processes radar sequences, its trunk handles query coordinates, and a 3D discriminator guides sharp forecast generation.
  • Problem Definition: The forecasting problem is formulated as sequence-to-sequence prediction, with historical radar observations mapped to deterministic future precipitation fields.The primary task uses 15 five-minute input frames to predict 36 future frames, while a secondary task uses three 30-minute frames to predict six.

B. Data Source and Preprocessing

GenONet is built around DeepONet components that process radar sequences and future query coordinates, with adversarial training supplied by a 3D spatio-temporal discriminator. Its projection head produces precipitation fields for each future time step.

  • Data Source and Preprocessing: The model uses KNMI national radar composites sampled every 5 minutes from 2008–2018 and cropped to a 256×256 pixel, 256 km×256 km domain.The spatial resolution is 1 km per pixel.
  • Data Source and Preprocessing: Chronological splitting assigns 2008–2014 to training, 2015–2016 to validation, and 2017–2018 to testing.This prevents temporal overlap between training and test sequences and provides a stricter evaluation setting.
  • DeepONet Components: DeepONet approximates an operator with a branch network encoding the input function and a trunk network processing the query coordinate.The outputs form learned basis functions used to generate predictions.
  • Generator Architecture: GenONet's generator combines a specialized branch network, trunk network, and projection layer to map historical radar sequences to future precipitation fields.The branch uses a 3D CNN-enhanced U-Net, while the trunk processes future time coordinates.
  • Generator Architecture: The final projection head maps the combined representation to a single-channel precipitation field and repeats this process across future time steps.The resulting fields form the complete forecast sequence.
  • Adversarial Training: The GAN discriminator is a deep 3D CNN that distinguishes real video clips from generated ones using spatio-temporal convolutional blocks.Its blocks use 3×3×3 kernels and spatial downsampling, with normalization after the first layer.

D. Loss Functions

GenONet combines reconstruction and adversarial losses, with an optional physics-informed regularizer based on a simplified moisture conservation formulation. The regularizer uses atmospheric moisture-balance terms while acknowledging limitations in representing vertical transport.

  • Loss design: The generator combines reconstruction and adversarial losses to balance forecast accuracy with perceptual realism.The reconstruction loss includes MS-SSIM and weighted L1 components; L1 supports intensity accuracy, while MS-SSIM preserves precipitation-field structure and texture.
  • Physics-informed regularization: The physics-informed loss regularizes the DeepONet generator using a soft constraint derived from the atmospheric moisture conservation equation.It is added directly to the generator rather than embedded in the main architecture or discriminator, enabling targeted ablation.
  • Physics-informed regularization: Including the vertical moisture term slightly reduced categorical scores, supporting the simplified two-dimensional horizontal formulation for this task.The authors attribute this result to weak, noisy near-surface vertical velocity at radar scale and ERA5’s coarse vertical resolution.
  • Physics-informed regularization: The simplified formulation focuses on multi-level horizontal moisture advection using ERA5 winds and specific humidity derived from temperature, dew point, and pressure.Evapotranspiration and precipitation-related condensation provide additional source and sink terms.
  • Physics-informed regularization: The residual loss is computed as mean squared error across predicted frames and spatial grid points, with a scaling factor and physics weight balancing its contribution.The scaling factor brings advection terms into a range comparable to source and sink terms, while the physics hyperparameter balances regularization against other losses.

E. Experimental Setup

The experiments use PyTorch training on an NVIDIA A100 cluster with separately tuned generator and discriminator optimization settings. Training includes adaptive learning-rate scheduling, 50 epochs, batch size 8, and short video clips for adversarial discrimination.

  • Training protocol: Models were implemented in PyTorch and trained on a high-performance computing cluster equipped with an NVIDIA A100 GPU.The primary task and physics-informed ablation followed the same stated protocol for robustness and reproducibility.
  • Optimization: The generator and discriminator used learning rates of 1e-4 and 4e-4, respectively, with β values of (0.5, 0.999).A generator weight decay of 0.0001 was added for regularization.
  • Optimization: ReduceLROnPlateau schedulers halve each optimizer’s learning rate after three consecutive validation epochs without improvement.Training lasted 50 epochs with batch size 8, constrained by the memory footprint of the 3D model.
  • Adversarial training: The spatio-temporal discriminator receives video clips consisting of three consecutive frames.The discriminator therefore evaluates short temporal sequences rather than isolated images.

F. Baseline Models and Evaluations Metrics

GenONet is compared with five representative precipitation-forecasting models using continuous-field, event-based, and neighborhood-scale metrics. The evaluation includes a strong generative baseline and rainfall-threshold contingency measures.

  • Baseline models: The comparison includes UNet, SmaAtUNet, GAN-UNet, RainNet, and DGMR.DGMR is a generative adversarial baseline trained and evaluated under the same chronological protocol and extended to the full 180-minute horizon.
  • Continuous-field metrics: MAE measures pixel-wise error, while SSIM evaluates preservation of perceptual and structural features in continuous precipitation fields.These metrics assess complementary aspects of forecast quality.
  • Event-based metrics: Event-based metrics are computed after binarizing forecasts and observations at rainfall thresholds such as 0.1, 0.5, and 2 mm/h.The resulting contingency table supports categorical verification, including the Critical Success Index for correctly predicted rain events.

IV. Results

The results section assesses GenONet through baseline comparisons and qualitative visualizations, followed by an ablation study of the physics-informed loss regularizer.

  • Baseline comparison: GenONet is evaluated against baseline models using both quantitative metrics and qualitative visualizations.The assessment is followed by a targeted ablation study examining the influence of the physics-informed loss regularizer.
  • Ablation study: The ablation study systematically examines the effectiveness of the physics-informed loss regularizer.Its purpose is to isolate the influence of adding the physical constraint.

A. Quantitative Evaluation

GenONet generally maintains stronger precipitation forecast skill than baseline models, with its advantages becoming clearer at longer lead times and higher rainfall intensities. It also better preserves spatial structure while remaining competitive on pixel-wise error.

  • GenONet attains competitive-to-superior CSI and HSS across most rainfall thresholds and lead times, with advantages widening at longer horizons.DGMR is competitive at short lead times but degrades markedly at longer horizons and higher intensities.
  • At the 2 mm/h threshold, GenONet’s CSI advantage is clearest, and its performance degrades more slowly after 60 minutes.All models lose skill as lead time extends, but the gap between GenONet and baselines widens.
  • A high CSI combined with low FAR gives GenONet a better balance between detecting true precipitation events and avoiding false alarms.Lower FAR indicates fewer forecasts of precipitation events that do not occur.
  • GenONet maintains higher FSS at long lead times, especially at higher intensity thresholds where baseline scores approach zero.The FSS results indicate better preservation of spatially coherent and properly located precipitation fields.
  • GenONet retains the highest SSIM at longer lead times, while all models remain comparably grouped on MAE across the 180-minute horizon.Its slower SSIM decline indicates better preservation of spatial structure, texture, and organization.

B. Qualitative Analysis

Qualitative forecasts show that GenONet better preserves sharp, coherent precipitation structures over the 180-minute horizon than the baseline models. Pixel-wise-loss models become blurry, while GAN-UNet remains sharper but temporally fragmented and physically unrealistic.

  • UNet, SmaAt-UNet, and RainNet lose detail over time, becoming diffuse and indistinct by T+120 minutes.Their forecasts smooth sharp gradients, underestimate high-intensity cores, and lose the coherent precipitation band structure.
  • GAN-UNet produces sharper forecasts than the other baselines but fails to preserve temporal coherence and structural accuracy.Its resulting patterns are described as fragmented and physically unrealistic.
  • GenONet’s qualitative comparison supports its ability to maintain structurally coherent precipitation forecasts at extended lead times.The comparison covers representative forecasts through 180 minutes.

C. Ablation Study on Physics-Informed Regularization

The physics-informed loss improves moisture-conservation consistency and categorical forecast skill when appropriately weighted, with the largest reported benefits at higher intensities. However, excessive weighting destabilizes training, while the simplified horizontal formulation remains preferable to adding the vertical term.

  • The mean MCE residual decreases from 3.63 × 10⁻⁵ s⁻¹ without physics regularization to 2.15 × 10⁻⁵ s⁻¹ at λ = 1.0.This indicates that the physics-informed loss guides predictions toward better moisture conservation.
  • At 0.5 mm/h, adding physics improves CSI from 0.3540 to 0.3599 and HSS from 0.4537 to 0.4589, while FAR decreases from 0.4945 to 0.4820.At 2 mm/h, FAR drops from 0.6227 to 0.5570 and CSI rises from 0.1606 to 0.1666.
  • The physics-regularized model has higher CSI and HSS and lower FAR across the examined 0.1, 0.5, and 2 mm/h thresholds.The reported benefit is most pronounced for the highest intensity threshold.
  • Physics regularization is insensitive to the ERA5 downscaling choice because Kriging and bilinear interpolation yield comparable skill across thresholds.This finding indicates that the regularizer does not depend on Kriging-induced fine-scale structure.
  • Categorical skill peaks at λ = 0.33 for selected metrics, whereas MAE and mean MCE residual reach minima at λ = 1.0.The sensitivity analysis therefore shows a nonmonotonic tradeoff between physical consistency and data-driven accuracy.
  • Excessive physics weighting degrades both forecast skill and physical consistency, with HSS at 0.5 mm/h falling to 0.0530 at λ = 5.0.MAE rises to 0.3097 and the MCE residual increases again at large λ.
  • The horizontal-only physics formulation outperforms or matches the extended horizontal-plus-vertical formulation, supporting the simplified 2D choice.The vertical term did not improve skill and slightly reduced categorical scores.

D. Uncertainty Quantification

Monte Carlo dropout equips GenONet with ensemble-based predictive uncertainty estimates for operational risk assessment. Compared with DGMR under the same evaluation setup, GenONet achieves lower mean CRPS and larger ensemble spread.

  • Monte Carlo dropout forms GenONet’s predictive ensemble by keeping generator dropout active during inference and sampling multiple stochastic forward passes.The ensemble is used to compute CRPS and ensemble spread.
  • GenONet attains a mean CRPS of 0.0677 versus 0.221 for DGMR, with ensemble spread of 0.023 versus 0.015.Both models were evaluated using the same ensemble size, test subset, and CRPS estimator.
  • DGMR’s ensemble members remain nearly identical while its CRPS decreases from 0.44 at +5 minutes to 0.10 at +180 minutes.The reported behavior reflects progressive weakening of DGMR forecasts at long lead times.

V. Discussion

GenONet’s performance is attributed to combining DeepONet-based temporal modeling, adversarial training, and physics-informed regularization, while computational cost and simplified physical constraints remain operational boundaries.

  • GenONet improves sharpness, temporal stability, and physical consistency compared to leading deep learning baselines.
  • The physics-informed loss improves categorical skill scores and physical consistency in the reported ablation setting.
  • Adversarial training contributes to sharp, realistic forecasts that retain structural similarity at longer lead times.The spatiotemporal 3D discriminator encourages generated sequences to be statistically indistinguishable from real radar data.
  • GenONet’s deep U-Net branch and 3D spatio-temporal discriminator make training computationally intensive, although the discriminator is excluded during inference.The primary compression target is therefore the U-Net branch of the generator.
  • An extension adding vertical moisture transport from ERA5 pressure-level data did not improve skill at the radar scale.The authors attribute this result to weak and noisy near-surface vertical velocity and related scale limitations.
  • GenONet’s clearest advantage is categorical skill for higher-intensity events at longer lead times.
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