ML models that produce ensembles or full forecast distributions: generative models (diffusion, flow matching), CRPS-trained models, learned perturbations.
Simon Lang, Mihai Alexe, Mariana C. A. Clare et al.
· npj Artificial Intelligence
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AIFS-CRPS trains an ML ensemble model on a CRPS-based loss, outperforming the IFS ensemble for most medium-range variables and competing at subseasonal lead times.
ArchesWeather is a transformer deterministic model, and ArchesWeatherGen a flow-matching ensemble that beats IFS ENS and NeuralGCM on WeatherBench headline variables at academic compute cost.
Ankur Mahesh, William Collins, Boris Bonev et al.
· Geoscientific Model Development
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A 1.1-billion-parameter SFNO ensemble with bred vectors and perturbed parameters passes spectral tests and is calibrated, setting up ML huge ensembles of 1,000+ members.
Noah D. Brenowitz, Yair Cohen, Jaideep Pathak et al.
· Geophysical Research Letters, 52, e2024GL113656 (2025)
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Lagged ensembles give a parameter-free probabilistic comparison showing GraphCast and Pangu tie on CRPS, and that multi-step losses hurt probabilistic skill.
Ilan Price, Alvaro Sanchez-Gonzalez, Ferran Alet et al.
· Nature
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GenCast, a diffusion ensemble trained on reanalysis, beats ECMWF ENS on 97.4% of 1320 targets, with better tropical cyclone and wind power prediction, in 8 minutes.
Lizao Li, Rob Carver, Ignacio Lopez-Gomez et al.
· Science Advances
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SEEDS uses diffusion models to emulate operational weather ensembles, generating thousands of realistic members cheaply with improved reliability and extreme-event probabilities after bias correction.
Boris Bonev, Thorsten Kurth, Ankur Mahesh et al.
· arXiv
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FourCastNet 3 is a spherical-CNN probabilistic ensemble model that rivals diffusion models, forecasts 8-60x faster, and stays calibrated and spectrally realistic to 60 days.
Simon Lang, Mihai Alexe, Mariana C. A. Clare et al.
· npj Artificial Intelligence
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AIFS-CRPS trains an ML ensemble model on a CRPS-based loss, outperforming the IFS ensemble for most medium-range variables and competing at subseasonal lead times.
ArchesWeather is a transformer deterministic model, and ArchesWeatherGen a flow-matching ensemble that beats IFS ENS and NeuralGCM on WeatherBench headline variables at academic compute cost.
Martin Andrae, Tomas Landelius, Joel Oskarsson et al.
· arXiv
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Continuous Ensemble Forecasting samples diffusion ensemble trajectories in parallel without autoregressive rollout, achieving competitive global forecasts at arbitrary temporal resolution.
Ankur Mahesh, William Collins, Boris Bonev et al.
· Geoscientific Model Development
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A 1.1-billion-parameter SFNO ensemble with bred vectors and perturbed parameters passes spectral tests and is calibrated, setting up ML huge ensembles of 1,000+ members.
Noah D. Brenowitz, Yair Cohen, Jaideep Pathak et al.
· Geophysical Research Letters, 52, e2024GL113656 (2025)
·
Lagged ensembles give a parameter-free probabilistic comparison showing GraphCast and Pangu tie on CRPS, and that multi-step losses hurt probabilistic skill.
Joel Oskarsson, Tomas Landelius, Marc Peter Deisenroth et al.
· Advances in Neural Information Processing Systems 37
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Graph-EFM is a hierarchical graph latent-variable model that generates arbitrarily large spatially coherent ensembles in one forward pass per step, matching deterministic error levels.
Ilan Price, Alvaro Sanchez-Gonzalez, Ferran Alet et al.
· Nature
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GenCast, a diffusion ensemble trained on reanalysis, beats ECMWF ENS on 97.4% of 1320 targets, with better tropical cyclone and wind power prediction, in 8 minutes.
Lizao Li, Rob Carver, Ignacio Lopez-Gomez et al.
· Science Advances
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SEEDS uses diffusion models to emulate operational weather ensembles, generating thousands of realistic members cheaply with improved reliability and extreme-event probabilities after bias correction.
Score-based diffusion models super-resolve coarse NWP to satellite-resolution day-ahead solar irradiance, giving probabilistic forecasts with many samples.
Lei Xu, Nengcheng Chen, Chao Yang et al.
· Hydrology and earth system sciences
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Deep learning precipitation forecasting that jointly models input, target and model uncertainty via error propagation and weight sampling, giving tighter predictive uncertainty than prior joint approaches.
Yuan Hu, Lei Chen, Zhibin Wang et al.
· Journal of Advances in Modeling Earth Systems
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SwinVRNN learns VAE-based distribution perturbations within a Swin transformer recurrent model, giving better ensemble accuracy and spread than other perturbation methods on WeatherBench.
Nick Rittler, Carlo Graziani, Jiali Wang et al.
· arXiv
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Chains dimensional reduction with normalizing flows to produce conditional probabilistic forecasts of surface wind from 22 years of WRF simulation data.
Lorenzo Pacchiardi, Rilwan Adewoyin, Peter Dueben et al.
· Journal of Machine Learning Research, 25(45), 2024
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Generative networks trained with prequential scoring rules, avoiding adversarial training, improve probabilistic calibration on chaotic models and a global weather benchmark.
Mariana Clare, Omar Jamil, Cyril Morcrette
· Quarterly Journal of the Royal Meteorological Society
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Neural networks predict full probability density functions for WeatherBench geopotential and temperature at 3 and 5 days, stacked into a combined forecast that beats some NWP models.
Yang Liu, Jisk Jakob Attema, Wilco Hazeleger
· preprint
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Bayesian LSTMs give reliable probabilistic forecasts of the Lorenz 84 atmospheric analogue, staying near the attractor and beating VAR and persistence.
A conditional convolutional GAN forecasts 500 hPa height, 2 m temperature and precipitation over Europe for 24 h, and MC dropout yields a deep learning ensemble.
Sebastian Scher, Gabriele Messori
· Journal of Advances in Modeling Earth Systems
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Compares four ensemble generation methods for a neural weather model; retraining gives the largest gain, but ensembles remain less skillful than operational NWP.
Peter Grönquist, Tal Ben-Nun, Nikoli Dryden et al.
· arXiv
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Deep 3D U-Net variants estimate weather forecast ensemble spread from a small set of numerical simulations, reducing the compute needed for uncertainty quantification.
Sebastian Scher, Gabriele Messori
· Quarterly Journal of the Royal Meteorological Society
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A CNN trained on past forecasts assigns a confidence score to medium-range forecasts without running an ensemble; it is cheaper but less skilful than ensembles.
Ferran Alet, Tom R. Andersson, Ilan Price et al.
· Nature
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Operational AI ensemble WeatherNext Cyclones predicts tropical cyclone track, intensity and size to 15 days, gaining about 1 day of lead time over leading operational models.
Daniel Abdi, Isidora Jankov, Paul Madden et al.
· Artificial Intelligence for the Earth Systems, Vol. 5, No. 2, 2026, Article 250061
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HRRRCast is a ResNet-based emulator of the HRRR convection-allowing model over CONUS, with DDIM ensembles that beat HRRR at the 20 dBZ reflectivity threshold.
Erik Larsson, Joel Oskarsson, Tomas Landelius et al.
· arXiv
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Diffusion-LAM is a conditional diffusion model that generates probabilistic limited-area forecasts from boundary conditions, demonstrated on the MEPS regional ensemble dataset.
Yingkai Sha, Ryan A. Sobash, David John Gagne
· Artificial Intelligence for the Earth Systems, 3(2), p.e230094 (2024)
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Conditional GANs generate synthetic ensemble members from HRRR convection-allowing forecasts, and a CNN turns them into severe weather probabilities with up to 20% Brier skill score gain.
Score-based data assimilation with a memory-efficient score network is tested on a two-layer quasi-geostrophic atmosphere-like model, demonstrating scalability to high-dimensional geophysical systems.
Fenwick Cooper, Andrew T. T. McRae, Matthew Chantry et al.
· arXiv
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Trains a conditional GAN on ERA5 to generate downscaled 1 km precipitation ensembles over UK and US regions, competitive with IFS ensembles at 8–16 h lead.
Mohamed Aziz Bhouri, Liran Peng, Michael S. Pritchard et al.
· arXiv
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Multi-fidelity randomized prior networks combine physical parameterizations and storm-resolving runs to extrapolate to +4K warming, yielding more skillful climate projections with uncertainty.
Christian Lessig, Ilaria Luise, Bing Gong et al.
· arXiv
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Stochastic, task-independent atmosphere model learned by self-supervised representation learning; skillful for nowcasting, interpolation, model correction and downscaling without task-specific training.
Andrea Asperti, Fabio Merizzi, Alberto Paparella et al.
· arXiv
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Generative ensemble diffusion produces precipitation scenarios over Central Europe from ERA5 data, outperforming U-Net baselines after a learned post-processing step.
Fatemeh Farokhmanesh, Kevin Höhlein, Christoph Neuhauser et al.
· arXiv
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Neural field compactly represents non-linear mutual-information dependencies across a 1000-member weather forecast ensemble, enabling interactive volume-rendered visualization with lower memory and compute.
Julia Jeworrek, Gregory West, Roland B. Stull
· Weather and Forecasting
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Analog ensemble variant that applies past analog errors reduces dry bias and improves heavy 3-hourly precipitation reliability over British Columbia, and can forecast record values.
Maximiliano A. Sacco, Manuel Pulido, Juan J. Ruiz et al.
· arXiv
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A CNN estimates state-dependent forecast error covariance from one model run for hybrid data assimilation, matching ensemble Kalman filter performance on Lorenz96 with small ensembles.
Jussi Leinonen, Ulrich Hamann, Daniele Nerini et al.
· arXiv
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A latent diffusion model for radar precipitation nowcasting gives more diverse, well-calibrated ensembles than DGMR and PySTEPS, with more accurate predictions.
Seth Bassetti, Brian Hutchinson, Claudia Tebaldi et al.
· arXiv
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Diffusion model conditioned on monthly temperature or precipitation generates realistic daily fields matching Earth system model heat waves and dry spells at a fraction of the cost.
Fan Meng, Yichen Yao, Zhibin Wang et al.
· Environmental Research Letters
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Machine learning gives probabilistic tropical cyclone intensity forecasts with intervals, and its point forecasts outperform an operational statistical-dynamical model over 2010–2020.
Nachiketa Acharya, Kyle Joseph Chen Hall
· MAUSAM
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Probabilistic Output Extreme Learning Machine builds multi-model ensembles for Indian summer monsoon rainfall, aiming to avoid overconfidence and Gaussian assumptions. No quantitative skill score given.
Peter Mlakar, Janko Merše, Jana Faganeli Pucer
· arXiv
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Normalizing-flow neural post-processing jointly calibrates ensemble temperature forecasts across locations and lead times, reaching state-of-the-art on the EUPPBench station benchmark.
Weiming Hu, Mohammadvaghef Ghazvinian, William Eric Chapman et al.
· Monthly Weather Review
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A U-Net postprocesses 4 km West-WRF precipitation reforecasts into censored shifted gamma distributions, beating analog, regression and meta-Gaussian benchmarks at all lead times.
Martin János Mayer, Bence Bíró, Botond Szücs et al.
· Applied Energy
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Neural networks map reanalysis weather to PV, wind and load, generating 42-year synthetic ensembles for Hungary; Dunkelflaute events and a variance-correction step are analysed.
Tilmann Gneiting, Sebastian Lerch, Benedikt Schulz
· Solar Energy
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Proposes a probabilistic clear-sky benchmark and neural post-processing methods for NWP-based solar irradiance forecasts, with proper scoring and calibration checks.
Weiming Hu, Guido Cervone, George S. Young et al.
· Boundary-Layer Meteorology
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Deep-learning latent space replaces hand-tuned similarity weights in analog ensembles for near-surface wind and solar forecasts, improving RMSE in Pennsylvania.
Fan Meng, Kun‐Lin Yang, Yichen Yao et al.
· International Journal of Intelligent Systems
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PTCIF gives probabilistic 6-24 h tropical cyclone intensity forecasts from multimodal data, with prediction intervals comparable to forecast centres on deterministic scores.
Zhihan Gao, Xingjian Shi, Boran Han et al.
· Advances in Neural Information Processing Systems 36
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PreDiff is a latent diffusion precipitation nowcasting model with a physics-based knowledge alignment step that enforces domain constraints on SEVIR radar forecasts.
François Rozet, Gilles Louppe
· Advances in Neural Information Processing Systems 36
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Score-based data assimilation learns a generative prior over state trajectories and applies observations only at inference, enabling zero-shot observation scenarios for long dynamical-system trajectories.
Zhong Yi Wan, Ricardo Baptista, Yi-fan Chen et al.
· Advances in Neural Information Processing Systems 36
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A two-stage statistical downscaling method combines optimal-transport debiasing with diffusion upsampling, enabling unpaired 8x and 16x super-resolution on fluid flows relevant to weather and climate.
Eva‐Maria Walz, Alexander Henzi, Johanna F. Ziegel et al.
· arXiv
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EasyUQ converts single-valued model output into calibrated predictive distributions via isotonic regression, with a smooth variant and weather forecast examples; the method is general across models.
Adds a stochastic noise generation step to a deep network for ensemble urban radar rainfall nowcasts, matching optical flow skill over a full year at 5-minute resolution.
Jieyu Chen, Tim Janke, Florian Steinke et al.
· Annals of Applied Statistics (2024), 18, 159-183
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Generative neural network post-processing of ensemble forecasts captures multivariate dependencies better than copula methods for German station temperature and wind.
Weiming Hu, Guido Cervone, George S. Young et al.
· Research Square
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Deep-learning latent similarity metric for analog ensembles outperforms the original AnEn in RMSE, bias and CRPS for wind and solar forecasts in Pennsylvania.
Antoine P. Delaunay, Hannah M. Christensen
· Geophysical Research Letters
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A CNN gives skilful probabilistic MJO forecasts whose uncertainty tracks instantaneous predictability, using predicted standard deviation and Monte Carlo dropout.
Ashesh Chattopadhyay, Jaideep Pathak, Ebrahim Nabizadeh et al.
· Environmental Data Science
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A convolutional VAE pretrained on imperfect quasi-geostrophic simulations and transfer-learned on noisy observations gives stable stochastic long-term rollouts with accurate climatology.
Extends WeatherBench with probabilistic metrics, an IFS ensemble baseline and three probabilistic ML models; Monte Carlo dropout underestimates uncertainty and no ML model matches IFS.
Yingkai Sha, David John Gagne, Gregory West et al.
· Monthly Weather Review
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Hybrid analog-ensemble and CNN post-processing of GEFS precipitation raises CRPSS about 10% over quantile-mapped baseline out to 7 days in British Columbia.
Anna Vaughan, Will Tebbutt, J. Scott Hosking et al.
· Geoscientific model development
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Convolutional conditional neural processes provide off-grid multisite temperature and precipitation downscaling over Europe, beating existing methods and improving extreme precipitation representation.
Conditional GAN and dense networks postprocess COSMO-E and IFS cloud cover ensembles over Switzerland, with cGAN producing realistic scenarios without copula or shuffle templates.
Jonathan A. Weyn, Dale R. Durran, Rich Caruana et al.
· Sub-Seasonal Forecasting With a Large Ensemble of Deep-Learning Weather Prediction Models. Journal of Advances in Modeling Earth Systems, 2021
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A CNN-based cubed-sphere ensemble of 32 deep-learning weather models gives 2-6 week forecasts that are only modestly worse than the ECMWF S2S ensemble over land.
Azam Moosavi, Vishwas Rao, Adrian Sandu
· Journal of Computational Science
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Proposes machine learning algorithms for uncertainty quantification in numerical weather prediction models; no abstract is available to confirm details.
Camille Besombes, Olivier Pannekoucke, Corentin Lapeyre et al.
· Nonlinear processes in geophysics
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Wasserstein GAN with a CNN generator learns a 64-dimensional latent space of synthetic PLASIM climate states, reproducing leading EOF statistics and geostrophic balance.
Jennie Molinder, Sebastian Scher, Erik Olof Nilsson et al.
· Energies
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Quantile regression forests give probabilistic icing-related production-loss forecasts for Swedish wind parks, improved by physical icing model inputs.
David B. Huberman, Brian J. Reich, Howard D. Bondell
· Environmental and Ecological Statistics
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Proposes a neural conditional-density estimator with case-control sampling for tropical cyclone intensity forecasting, outperforming other ML conditional-distribution methods in simulations and Atlantic storm data.
Salvatore Candido, Aakanksha Singh, Luca Delle Monache
· Geophysical Research Letters
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Distilling an analog ensemble into a deep network postprocesses ECMWF stratospheric wind forecasts, cutting latency to near zero and beating ENS wind-speed error by 20% against balloon data.
Combines random feature map forecasting with ensemble Kalman filter data assimilation, learning sequentially from noisy observations to give long forecast skill, reliable ensembles and closure for multiscale chaotic systems.
Maxime Taillardat, Olivier Mestre
· Nonlinear processes in geophysics
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Operational quantile regression forests and ensemble copula coupling improve station temperature and gridded hourly rainfall forecasts in France, better capturing cold and heat waves than raw ensembles.
Charlie Kirkwood, Theo Economou, Henry Odbert et al.
· Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences
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Quantile regression forests post-process and combine multiple NWP models across lead times into calibrated probabilistic road surface temperature forecasts.
Alessandro Fanfarillo, Behrooz Roozitalab, Weiming Hu et al.
· GeoInformatica
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Deep generative models replace stored archives in the analog ensemble method, cutting memory needs by orders of magnitude for probabilistic NWP post-processing at stations.
David John Gagne, Hannah M. Christensen, Aneesh C. Subramanian et al.
· Journal of Advances in Modeling Earth Systems
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Trains a GAN as a stochastic sub-grid parameterization for the Lorenz '96 model; some configurations beat a bespoke scheme at weather and climate timescales.
Loris Foresti, Ioannis Vasileios Sideris, Daniele Nerini et al.
· Weather and Forecasting
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Neural networks and quantile trees nowcast precipitation growth and decay in Swiss Alps radar archive, with persistence inputs cutting RMSE by 20-30% in mountains.
Describes a parallel HPC system generating probabilistic weather forecasts with the data-driven analog ensemble method, scaling ensemble generation across nodes.
Martin Felder, Frank Sehnke, Kay Ohnmeiß et al.
· Advances in geosciences
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Neural network predicts probability distributions over discretised power bins for wind farm forecasts, matching deterministic MAE with lower CRPS and avoiding costly NWP ensembles.