Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model
Not on the map. Why?
Abstract (arXiv)
Stochastic parameterizations account for uncertainty in the representation of unresolved sub-grid processes by sampling from the distribution of possible sub-grid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant structural assumptions that can limit their scalability. Machine learning models, including neural networks, are able to represent a wide range of distributions and build optimized mappings between a large number of inputs and sub-grid forcings. Recent research on machine learning parameterizations has focused only on deterministic parameterizations. In this study, we develop a stochastic parameterization using the generative adversarial network (GAN) machine learning framework. The GAN stochastic parameterization is trained and evaluated on output from the Lorenz '96 model, which is a common baseline model for evaluating both parameterization and data assimilation techniques. We evaluate different ways of characterizing the input noise for the model and perform model runs with the GAN parameterization at weather and climate timescales. Some of the GAN configurations perform better than a baseline bespoke parameterization at both timescales, and the networks closely reproduce the spatio-temporal correlations and regimes of the Lorenz '96 system. We also find that in general those models which produce skillful forecasts are also associated with the best climate simulations.
Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Sep 2019.
Builds on
No reference list yet.
Built on by
Citing papers per year: 2021: 10; 2022: 11; 2023: 7; 2024: 9; 2025: 4; 2026: 4.
45 papers.
Sort:
By area:
- 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
- 2021Will Artificial Intelligence supersede Earth System and Climate Models?cited by 37
- 2021Probabilistic Forecasting with Generative Networks via Scoring Rule Minimizationcited by 35
- 2022Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Modelscited by 28
- 2021Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observationscited by 20
- 2024DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models with 3D Diffusion Modelscited by 15
- 2021A comparison of combined data assimilation and machine learning methods for offline and online model error correctioncited by 13
- 2022Online model error correction with neural networks in the incremental 4D-Var frameworkcited by 13
- 2021The Need for Ethical, Responsible, and Trustworthy Artificial Intelligence for Environmental Sciencescited by 12
- 2023Broadband Ground Motion Synthesis via Generative Adversarial Neural Operators: Development and Validationcited by 12
- 2021Controlled abstention neural networks for identifying skillful predictions for regression problemscited by 9
- 2022On the modern deep learning approaches for precipitation downscalingcited by 9
33 more
- 2022A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterizationcited by 8
- 2023Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jetscited by 8
- 2023CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boostingcited by 7
- 2024CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilationcited by 7
- 2022A Machine Learning Tutorial for Operational Meteorology, Part I: Traditional Machine Learningcited by 6
- 2024CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilationcited by 6
- 2021Deep Learning Based Cloud Cover Parameterization for ICONcited by 5
- 2022Using Probabilistic Machine Learning to Better Model Temporal Patterns in Parameterizations: a case study with the Lorenz 96 modelcited by 5
- 2022Embed and Emulate: Learning to estimate parameters of dynamical systems with uncertainty quantificationcited by 5
- 2024Defining error accumulation in ML atmospheric simulatorscited by 5
- 2021Combining data assimilation and machine learning to estimate parameters of a convective-scale modelcited by 4
- 2021Controlled abstention neural networks for identifying skillful predictions for classification problemscited by 3
- 2022History-Based, Bayesian, Closure for Stochastic Parameterization: Application to Lorenz '96cited by 3
- 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
- 2023Navigating the Noise: Bringing Clarity to ML Parameterization Design with O(100) Ensemblescited by 3
- 2025Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Modelscited by 3
- 2025Controllable Probabilistic Forecasting with Stochastic Decomposition Layerscited by 3
- 2021Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilationcited by 2
- 2023Taylorformer: Probabilistic Modelling for Random Processes including Time Seriescited by 2
- 2022Semi-automatic tuning of coupled climate models with multiple intrinsic timescales: lessons learned from the Lorenz96 modelcited by 1
- 2022Statistical treatment of convolutional neural network super-resolution of inland surface wind for subgrid-scale variability quantificationcited by 1
- 2024Development of an offline and online hybrid model for the Integrated Forecasting Systemcited by 1
- 2024Towards Physically Consistent Deep Learning For Climate Model Parameterizationscited by 1
- 2025Regularization of ML models for Earth systems by using longer model timestepscited by 1
- 2026climt-paraformer: Stable Emulation of Convective Parameterization using a Temporal Memory-aware Transformercited by 1
- 2022Don't Waste Data: Transfer Learning to Leverage All Data for Machine-Learnt Climate Model Emulationcited by 0
- 2024Machine Learning for Stochastic Parametrisationcited by 0
- 2024Paraformer: Parameterization of Sub-grid Scale Processes Using Transformerscited by 0
- 2024Improving the Noise Estimation of Latent Neural Stochastic Differential Equationscited by 0
- 2025Trajectory learning for ensemble forecasts via the continuous ranked probability score: a Lorenz '96 case studycited by 0
- 2026Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizationscited by 0
- 2026Do AI Forecast Ensembles Sample the Correct Conditional Distribution?cited by 0
- 2026Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillationcited by 0
- 2026Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillation21 Sep 2026
- 2026Do AI Forecast Ensembles Sample the Correct Conditional Distribution?9 Aug 2026
- 2026Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations21 May 2026
- 2026climt-paraformer: Stable Emulation of Convective Parameterization using a Temporal Memory-aware Transformer22 Apr 2026
- 2025Controllable Probabilistic Forecasting with Stochastic Decomposition Layers21 Dec 2025
- 2025Trajectory learning for ensemble forecasts via the continuous ranked probability score: a Lorenz '96 case study29 Aug 2025
- 2025Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models25 Jun 2025
- 2025Regularization of ML models for Earth systems by using longer model timesteps23 Mar 2025
- 2024Improving the Noise Estimation of Latent Neural Stochastic Differential Equations23 Dec 2024
- 2024Paraformer: Parameterization of Sub-grid Scale Processes Using Transformers21 Dec 2024
- 2024CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation26 Oct 2024
- 2024DiffESM: Conditional Emulation of Temperature and Precipitation in Earth System Models with 3D Diffusion Models17 Sep 2024
33 more
- 2024Towards Physically Consistent Deep Learning For Climate Model Parameterizations6 Jun 2024
- 2024Defining error accumulation in ML atmospheric simulators23 May 2024
- 2024CGNSDE: Conditional Gaussian Neural Stochastic Differential Equation for Modeling Complex Systems and Data Assimilation10 Apr 2024
- 2024Development of an offline and online hybrid model for the Integrated Forecasting System6 Mar 2024
- 2024Machine Learning for Stochastic Parametrisation12 Feb 2024
- 2023Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jets25 Oct 2023
- 2023Navigating the Noise: Bringing Clarity to ML Parameterization Design with O(100) Ensembles28 Sep 2023
- 2023Broadband Ground Motion Synthesis via Generative Adversarial Neural Operators: Development and Validation7 Sep 2023
- 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution31 Jul 2023
- 2023Taylorformer: Probabilistic Modelling for Random Processes including Time Series30 May 2023
- 2023CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting16 Apr 2023
- 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review18 Mar 2023
- 2022Statistical treatment of convolutional neural network super-resolution of inland surface wind for subgrid-scale variability quantification30 Nov 2022
- 2022Embed and Emulate: Learning to estimate parameters of dynamical systems with uncertainty quantification3 Nov 2022
- 2022History-Based, Bayesian, Closure for Stochastic Parameterization: Application to Lorenz '9626 Oct 2022
- 2022Online model error correction with neural networks in the incremental 4D-Var framework25 Oct 2022
- 2022Don't Waste Data: Transfer Learning to Leverage All Data for Machine-Learnt Climate Model Emulation8 Oct 2022
- 2022Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Models25 Aug 2022
- 2022A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization19 Aug 2022
- 2022Semi-automatic tuning of coupled climate models with multiple intrinsic timescales: lessons learned from the Lorenz96 model11 Aug 2022
- 2022On the modern deep learning approaches for precipitation downscaling2 Jul 2022
- 2022A Machine Learning Tutorial for Operational Meteorology, Part I: Traditional Machine Learning15 Apr 2022
- 2022Using Probabilistic Machine Learning to Better Model Temporal Patterns in Parameterizations: a case study with the Lorenz 96 model28 Mar 2022
- 2021Deep Learning Based Cloud Cover Parameterization for ICON21 Dec 2021
- 2021The Need for Ethical, Responsible, and Trustworthy Artificial Intelligence for Environmental Sciences15 Dec 2021
- 2021Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization15 Dec 2021
- 2021Combining data assimilation and machine learning to estimate parameters of a convective-scale model7 Sep 2021
- 2021Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations8 Aug 2021
- 2021A comparison of combined data assimilation and machine learning methods for offline and online model error correction23 Jul 2021
- 2021Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation15 Jun 2021
- 2021Controlled abstention neural networks for identifying skillful predictions for classification problems16 Apr 2021
- 2021Controlled abstention neural networks for identifying skillful predictions for regression problems16 Apr 2021
- 2021Will Artificial Intelligence supersede Earth System and Climate Models?22 Jan 2021
- 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
- 2021Will Artificial Intelligence supersede Earth System and Climate Models?cited by 37
- 2021Probabilistic Forecasting with Generative Networks via Scoring Rule Minimizationcited by 35
- 2022Physically Constrained Generative Adversarial Networks for Improving Precipitation Fields from Earth System Modelscited by 28
- 2021Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observationscited by 20
- 2021A comparison of combined data assimilation and machine learning methods for offline and online model error correctioncited by 13
- 2022Online model error correction with neural networks in the incremental 4D-Var frameworkcited by 13
- 2021The Need for Ethical, Responsible, and Trustworthy Artificial Intelligence for Environmental Sciencescited by 12
- 2023Broadband Ground Motion Synthesis via Generative Adversarial Neural Operators: Development and Validationcited by 12
- 2021Controlled abstention neural networks for identifying skillful predictions for regression problemscited by 9
- 2022On the modern deep learning approaches for precipitation downscalingcited by 9
- 2022A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterizationcited by 8
12 most cited of 43 All 43 (JSON)
- 2026Learning Prognostic Variables for AI Convective Parameterizations via Symbolic Distillation21 Sep 2026
- 2026Do AI Forecast Ensembles Sample the Correct Conditional Distribution?9 Aug 2026
- 2026Decomposing Ensemble Spread in Lorenz '96 With Learned Stochastic Parameterizations21 May 2026
- 2026climt-paraformer: Stable Emulation of Convective Parameterization using a Temporal Memory-aware Transformer22 Apr 2026
- 2025Controllable Probabilistic Forecasting with Stochastic Decomposition Layers21 Dec 2025
- 2025Trajectory learning for ensemble forecasts via the continuous ranked probability score: a Lorenz '96 case study29 Aug 2025
- 2025Regularization of ML models for Earth systems by using longer model timesteps23 Mar 2025
- 2024Improving the Noise Estimation of Latent Neural Stochastic Differential Equations23 Dec 2024
- 2024Paraformer: Parameterization of Sub-grid Scale Processes Using Transformers21 Dec 2024
- 2024CGKN: A Deep Learning Framework for Modeling Complex Dynamical Systems and Efficient Data Assimilation26 Oct 2024
- 2024Towards Physically Consistent Deep Learning For Climate Model Parameterizations6 Jun 2024
- 2024Defining error accumulation in ML atmospheric simulators23 May 2024
12 newest of 43 All 43 (JSON)