Articles | Volume 26, issue 4
https://doi.org/10.5194/npg-26-381-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-26-381-2019
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
05 Nov 2019
Research article |
| 05 Nov 2019
| 05 Nov 2019
Generalization properties of feed-forward neural networks trained on Lorenz systems
Sebastian Scher
CORRESPONDING AUTHOR
Department of Meteorology and Bolin
Centre for Climate Research, Stockholm
University, Stockholm, Sweden
Gabriele Messori
Department of Meteorology and Bolin
Centre for Climate Research, Stockholm
University, Stockholm, Sweden
Department of Earth Sciences, Uppsala University, Uppsala, Sweden
Viewed
Total article views: 4,686 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 14 Jun 2019)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 2,805 | 1,787 | 94 | 4,686 | 97 | 87 |
- HTML: 2,805
- PDF: 1,787
- XML: 94
- Total: 4,686
- BibTeX: 97
- EndNote: 87
Total article views: 2,824 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 05 Nov 2019)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 2,094 | 646 | 84 | 2,824 | 85 | 77 |
- HTML: 2,094
- PDF: 646
- XML: 84
- Total: 2,824
- BibTeX: 85
- EndNote: 77
Total article views: 1,862 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 14 Jun 2019)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 711 | 1,141 | 10 | 1,862 | 12 | 10 |
- HTML: 711
- PDF: 1,141
- XML: 10
- Total: 1,862
- BibTeX: 12
- EndNote: 10
Viewed (geographical distribution)
Total article views: 4,686 (including HTML, PDF, and XML)
Thereof 3,913 with geography defined
and 773 with unknown origin.
Total article views: 2,824 (including HTML, PDF, and XML)
Thereof 2,544 with geography defined
and 280 with unknown origin.
Total article views: 1,862 (including HTML, PDF, and XML)
Thereof 1,369 with geography defined
and 493 with unknown origin.
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
Cited
29 citations as recorded by crossref.
- Surrogate modeling for the climate sciences dynamics with machine learning and data assimilation M. Bocquet 10.3389/fams.2023.1133226
- Online learning of both state and dynamics using ensemble Kalman filters M. Bocquet et al. 10.3934/fods.2020015
- Coupled online learning as a way to tackle instabilities and biases in neural network parameterizations: general algorithms and Lorenz 96 case study (v1.0) S. Rasp 10.5194/gmd-13-2185-2020
- DEEP LEARNING OF CHAOTIC SYSTEMS FROM PARTIALLY-OBSERVED DATA V. Churchill & D. Xiu 10.1615/JMachLearnModelComput.2022045602
- Enhancing African market predictions: Integrating quantum computing with Echo State Networks S. Seddik et al. 10.1016/j.sciaf.2024.e02299
- Can Machines Learn How Clouds Work? The Epistemic Implications of Machine Learning Methods in Climate Science S. Kawamleh 10.1086/714877
- A Comparison of Data‐Driven Approaches to Build Low‐Dimensional Ocean Models N. Agarwal et al. 10.1029/2021MS002537
- Using machine learning to correct model error in data assimilation and forecast applications A. Farchi et al. 10.1002/qj.4116
- A Toy Model to Investigate Stability of AI‐Based Dynamical Systems B. Balogh et al. 10.1029/2020GL092133
- Generalization properties of feed-forward neural networks trained on Lorenz systems S. Scher & G. Messori 10.5194/npg-26-381-2019
- Advances and prospects of deep learning for medium-range extreme weather forecasting L. Olivetti & G. Messori 10.5194/gmd-17-2347-2024
- Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network A. Chattopadhyay et al. 10.5194/npg-27-373-2020
- Optimizing Echo State Networks for Enhancing Large Prediction Horizons of Chaotic Time Series A. González-Zapata et al. 10.3390/math10203886
- WeatherBench: A Benchmark Data Set for Data‐Driven Weather Forecasting S. Rasp et al. 10.1029/2020MS002203
- Data‐Driven Super‐Parameterization Using Deep Learning: Experimentation With Multiscale Lorenz 96 Systems and Transfer Learning A. Chattopadhyay et al. 10.1029/2020MS002084
- Uncertainty Quantification When Learning Dynamical Models and Solvers With Variational Methods N. Lafon et al. 10.1029/2022MS003446
- A Neural-Network Based MPAS—Shallow Water Model and Its 4D-Var Data Assimilation System X. Tian et al. 10.3390/atmos14010157
- Machine learning for weather and climate are worlds apart D. Watson-Parris 10.1098/rsta.2020.0098
- How to Calibrate a Dynamical System With Neural Network Based Physics? B. Balogh et al. 10.1029/2022GL097872
- Variability of echo state network prediction horizon for partially observed dynamical systems A. Mahata et al. 10.1103/PhysRevE.108.064209
- A comparison of combined data assimilation and machine learning methods for offline and online model error correction A. Farchi et al. 10.1016/j.jocs.2021.101468
- Hyperparameter optimization for randomized algorithms: a case study on random features O. Dunbar et al. 10.1007/s11222-025-10587-w
- Online Model Error Correction With Neural Networks in the Incremental 4D‐Var Framework A. Farchi et al. 10.1029/2022MS003474
- Deep Emulators for Differentiation, Forecasting, and Parametrization in Earth Science Simulators M. Nonnenmacher & D. Greenberg 10.1029/2021MS002554
- Precipitation forecasting: from geophysical aspects to machine learning applications E. Oliveira et al. 10.3389/fclim.2023.1250201
- Representation learning with unconditional denoising diffusion models for dynamical systems T. Finn et al. 10.5194/npg-31-409-2024
- Dynamical analysis, geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor Y. Li et al. 10.1088/1674-1056/acd68b
- A sensitivity analysis of a regression model of ocean temperature R. Furner et al. 10.1017/eds.2022.10
- Data‐Driven Medium‐Range Weather Prediction With a Resnet Pretrained on Climate Simulations: A New Model for WeatherBench S. Rasp & N. Thuerey 10.1029/2020MS002405
28 citations as recorded by crossref.
- Surrogate modeling for the climate sciences dynamics with machine learning and data assimilation M. Bocquet 10.3389/fams.2023.1133226
- Online learning of both state and dynamics using ensemble Kalman filters M. Bocquet et al. 10.3934/fods.2020015
- Coupled online learning as a way to tackle instabilities and biases in neural network parameterizations: general algorithms and Lorenz 96 case study (v1.0) S. Rasp 10.5194/gmd-13-2185-2020
- DEEP LEARNING OF CHAOTIC SYSTEMS FROM PARTIALLY-OBSERVED DATA V. Churchill & D. Xiu 10.1615/JMachLearnModelComput.2022045602
- Enhancing African market predictions: Integrating quantum computing with Echo State Networks S. Seddik et al. 10.1016/j.sciaf.2024.e02299
- Can Machines Learn How Clouds Work? The Epistemic Implications of Machine Learning Methods in Climate Science S. Kawamleh 10.1086/714877
- A Comparison of Data‐Driven Approaches to Build Low‐Dimensional Ocean Models N. Agarwal et al. 10.1029/2021MS002537
- Using machine learning to correct model error in data assimilation and forecast applications A. Farchi et al. 10.1002/qj.4116
- A Toy Model to Investigate Stability of AI‐Based Dynamical Systems B. Balogh et al. 10.1029/2020GL092133
- Generalization properties of feed-forward neural networks trained on Lorenz systems S. Scher & G. Messori 10.5194/npg-26-381-2019
- Advances and prospects of deep learning for medium-range extreme weather forecasting L. Olivetti & G. Messori 10.5194/gmd-17-2347-2024
- Data-driven predictions of a multiscale Lorenz 96 chaotic system using machine-learning methods: reservoir computing, artificial neural network, and long short-term memory network A. Chattopadhyay et al. 10.5194/npg-27-373-2020
- Optimizing Echo State Networks for Enhancing Large Prediction Horizons of Chaotic Time Series A. González-Zapata et al. 10.3390/math10203886
- WeatherBench: A Benchmark Data Set for Data‐Driven Weather Forecasting S. Rasp et al. 10.1029/2020MS002203
- Data‐Driven Super‐Parameterization Using Deep Learning: Experimentation With Multiscale Lorenz 96 Systems and Transfer Learning A. Chattopadhyay et al. 10.1029/2020MS002084
- Uncertainty Quantification When Learning Dynamical Models and Solvers With Variational Methods N. Lafon et al. 10.1029/2022MS003446
- A Neural-Network Based MPAS—Shallow Water Model and Its 4D-Var Data Assimilation System X. Tian et al. 10.3390/atmos14010157
- Machine learning for weather and climate are worlds apart D. Watson-Parris 10.1098/rsta.2020.0098
- How to Calibrate a Dynamical System With Neural Network Based Physics? B. Balogh et al. 10.1029/2022GL097872
- Variability of echo state network prediction horizon for partially observed dynamical systems A. Mahata et al. 10.1103/PhysRevE.108.064209
- A comparison of combined data assimilation and machine learning methods for offline and online model error correction A. Farchi et al. 10.1016/j.jocs.2021.101468
- Hyperparameter optimization for randomized algorithms: a case study on random features O. Dunbar et al. 10.1007/s11222-025-10587-w
- Online Model Error Correction With Neural Networks in the Incremental 4D‐Var Framework A. Farchi et al. 10.1029/2022MS003474
- Deep Emulators for Differentiation, Forecasting, and Parametrization in Earth Science Simulators M. Nonnenmacher & D. Greenberg 10.1029/2021MS002554
- Precipitation forecasting: from geophysical aspects to machine learning applications E. Oliveira et al. 10.3389/fclim.2023.1250201
- Representation learning with unconditional denoising diffusion models for dynamical systems T. Finn et al. 10.5194/npg-31-409-2024
- Dynamical analysis, geometric control and digital hardware implementation of a complex-valued laser system with a locally active memristor Y. Li et al. 10.1088/1674-1056/acd68b
- A sensitivity analysis of a regression model of ocean temperature R. Furner et al. 10.1017/eds.2022.10
Latest update: 02 Apr 2025
Short summary
Neural networks are a technique that is widely used to predict the time evolution of physical systems. For this the past evolution of the system is shown to the neural network – it is
trained– and then can be used to predict the evolution in the future. We show some limitations in this approach for certain systems that are important to consider when using neural networks for climate- and weather-related applications.
Neural networks are a technique that is widely used to predict the time evolution of physical...
