Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows
Abstract
In the past couple of years, there has been a proliferation in the use of machine learning approaches to represent subgrid-scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-driven closure model can cause instabilities and biases in modeling the overall effect of subgrid-scale processes, which in turn leads to inaccurate prediction. To tackle this issue, we exploit the data assimilation technique to correct the physics-based model coupled with the neural network as a surrogate for unresolved flow dynamics in multiscale systems. In particular, we use a set of neural network architectures to learn the correlation between resolved flow variables and the parametrizations of unresolved flow dynamics and formulate a data assimilation approach to correct the hybrid model during their online deployment. We illustrate our framework in a set of applications of the multiscale Lorenz 96 system for which the parametrization model for unresolved scales is exactly known, and the two-dimensional Kraichnan turbulence system for which the parametrization model for unresolved scales is not known a priori. Our analysis, therefore, comprises a predictive dynamical coremore »
- Publication Date:
- Research Org.:
- Oklahoma State Univ., Stillwater, OK (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1853026
- Grant/Contract Number:
- SC0019290
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Fluids (Online)
- Additional Journal Information:
- Journal Name: Physical Review Fluids (Online); Journal Volume: 6; Journal Issue: 5; Journal ID: ISSN 2469-990X
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Physics; Chaos; Control & applications of chaos; Geophysical fluid dynamics; Mixing in geophysical flows; Spatiotemporal chaos
Citation Formats
Pawar, Suraj, and San, Omer. Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows. United States: N. p., 2021.
Web. doi:10.1103/physrevfluids.6.050501.
Pawar, Suraj, & San, Omer. Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows. United States. https://doi.org/10.1103/physrevfluids.6.050501
Pawar, Suraj, and San, Omer. Wed .
"Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows". United States. https://doi.org/10.1103/physrevfluids.6.050501. https://www.osti.gov/servlets/purl/1853026.
@article{osti_1853026,
title = {Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows},
author = {Pawar, Suraj and San, Omer},
abstractNote = {In the past couple of years, there has been a proliferation in the use of machine learning approaches to represent subgrid-scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-driven closure model can cause instabilities and biases in modeling the overall effect of subgrid-scale processes, which in turn leads to inaccurate prediction. To tackle this issue, we exploit the data assimilation technique to correct the physics-based model coupled with the neural network as a surrogate for unresolved flow dynamics in multiscale systems. In particular, we use a set of neural network architectures to learn the correlation between resolved flow variables and the parametrizations of unresolved flow dynamics and formulate a data assimilation approach to correct the hybrid model during their online deployment. We illustrate our framework in a set of applications of the multiscale Lorenz 96 system for which the parametrization model for unresolved scales is exactly known, and the two-dimensional Kraichnan turbulence system for which the parametrization model for unresolved scales is not known a priori. Our analysis, therefore, comprises a predictive dynamical core empowered by (i) a data-driven closure model for subgrid-scale processes, (ii) a data assimilation approach for forecast error correction, and (iii) both data-driven closure and data assimilation procedures. We show significant improvement in the long-term prediction of the underlying chaotic dynamics with our framework compared to using only neural network parametrizations for future prediction. Moreover, we demonstrate that these data-driven parametrization models can handle the non-Gaussian statistics of subgrid-scale processes, and effectively improve the accuracy of outer data assimilation workflow loops in a modular nonintrusive way.},
doi = {10.1103/physrevfluids.6.050501},
journal = {Physical Review Fluids (Online)},
number = 5,
volume = 6,
place = {United States},
year = {Wed May 12 00:00:00 EDT 2021},
month = {Wed May 12 00:00:00 EDT 2021}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Dynamical Subgrid-Scale Parameterizations from Direct Numerical Simulations
journal, November 2006
- Frederiksen, Jorgen S.; Kepert, Steven M.
- Journal of the Atmospheric Sciences, Vol. 63, Issue 11
Accelerating Progress in Global Atmospheric Model Development through Improved Parameterizations: Challenges, Opportunities, and Strategies
journal, July 2010
- Jakob, Christian
- Bulletin of the American Meteorological Society, Vol. 91, Issue 7
A proposed modification of the Germano subgrid‐scale closure method
journal, March 1992
- Lilly, D. K.
- Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 3
Deep learning
journal, May 2015
- LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey
- Nature, Vol. 521, Issue 7553
Two-Dimensional Turbulence
journal, January 2012
- Boffetta, Guido; Ecke, Robert E.
- Annual Review of Fluid Mechanics, Vol. 44, Issue 1
A Maximum Likelihood Ensemble Filter via a Modified Cholesky Decomposition for Non-Gaussian Data Assimilation
journal, February 2020
- Nino-Ruiz, Elias David; Mancilla-Herrera, Alfonso; Lopez-Restrepo, Santiago
- Sensors, Vol. 20, Issue 3
A deterministic formulation of the ensemble Kalman filter: an alternative to ensemble square root filters
journal, January 2008
- Sakov, Pavel; Oke, Peter R.
- Tellus A: Dynamic Meteorology and Oceanography, Vol. 60, Issue 2
Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach
journal, January 2018
- Pathak, Jaideep; Hunt, Brian; Girvan, Michelle
- Physical Review Letters, Vol. 120, Issue 2
Optimal reduced space for Variational Data Assimilation
journal, February 2019
- Arcucci, Rossella; Mottet, Laetitia; Pain, Christopher
- Journal of Computational Physics, Vol. 379
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
journal, February 2019
- Raissi, M.; Perdikaris, P.; Karniadakis, G. E.
- Journal of Computational Physics, Vol. 378
Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: A case study with the Lorenz 96 model
journal, July 2020
- Brajard, Julien; Carrassi, Alberto; Bocquet, Marc
- Journal of Computational Science, Vol. 44
The role of large-scale spatial patterns in the chaotic amplification of perturbations in a Lorenz’96 model
journal, January 2011
- Herrera, S.; Paz ó, D.; Ferná Ndez, J.
- Tellus A: Dynamic Meteorology and Oceanography, Vol. 63, Issue 5
Reynolds-averaged Navier–Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned
journal, April 2019
- Wu, Jinlong; Xiao, Heng; Sun, Rui
- Journal of Fluid Mechanics, Vol. 869
Stochastic parameterization for large eddy simulation of geophysical flows
journal, April 2007
- Duan, Jinqiao; Nadiga, Balasubramanya T.
- Proceedings of the American Mathematical Society, Vol. 135, Issue 04
A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems
journal, July 2020
- Tang, Meng; Liu, Yimin; Durlofsky, Louis J.
- Journal of Computational Physics, Vol. 413
Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation
journal, December 2016
- Houtekamer, P. L.; Zhang, Fuqing
- Monthly Weather Review, Vol. 144, Issue 12
Symmetries in the Lorenz-96 Model
journal, January 2019
- van Kekem, Dirk L.; Sterk, Alef E.
- International Journal of Bifurcation and Chaos, Vol. 29, Issue 01
Effects of stochastic parametrizations in the Lorenz '96 system
journal, January 2005
- Wilks, Daniel S.
- Quarterly Journal of the Royal Meteorological Society, Vol. 131, Issue 606
Dynamic Data Assimilation
book, January 2006
- Lewis, John M.; Lakshmivarahan, S.; Dhall, Sudarshan
- Cambridge University Press
A New Approach to Linear Filtering and Prediction Problems
journal, March 1960
- Kalman, R. E.
- Journal of Basic Engineering, Vol. 82, Issue 1
Deep learning to represent subgrid processes in climate models
journal, September 2018
- Rasp, Stephan; Pritchard, Michael S.; Gentine, Pierre
- Proceedings of the National Academy of Sciences, Vol. 115, Issue 39
Total variation diminishing Runge-Kutta schemes
journal, January 1998
- Gottlieb, Sigal; Shu, Chi-Wang
- Mathematics of Computation of the American Mathematical Society, Vol. 67, Issue 221
An adaptive covariance inflation error correction algorithm for ensemble filters
journal, January 2007
- Anderson, Jeffrey L.
- Tellus A: Dynamic Meteorology and Oceanography, Vol. 59, Issue 2
General Circulation Experiments with the Primitive Equations: i. the Basic Experiment*
journal, March 1963
- Smagorinsky, J.
- Monthly Weather Review, Vol. 91, Issue 3
Approximate deconvolution large eddy simulation of a stratified two-layer quasigeostrophic ocean model
journal, March 2013
- San, Omer; Staples, Anne E.; Iliescu, Traian
- Ocean Modelling, Vol. 63
Deep neural networks for data-driven LES closure models
journal, December 2019
- Beck, Andrea; Flad, David; Munz, Claus-Dieter
- Journal of Computational Physics, Vol. 398
A Machine Learning‐Based Global Atmospheric Forecast Model
journal, May 2020
- Arcomano, Troy; Szunyogh, Istvan; Pathak, Jaideep
- Geophysical Research Letters, Vol. 47, Issue 9
Modeling subgrid-scale forces by spatial artificial neural networks in large eddy simulation of turbulence
journal, May 2020
- Xie, Chenyue; Wang, Jianchun; E., Weinan
- Physical Review Fluids, Vol. 5, Issue 5
Assessment and Propagation of Model Uncertainty
journal, January 1995
- Draper, David
- Journal of the Royal Statistical Society: Series B (Methodological), Vol. 57, Issue 1
Turbulence model reduction by deep learning
journal, June 2020
- Heinonen, R. A.; Diamond, P. H.
- Physical Review E, Vol. 101, Issue 6
Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems
journal, April 2020
- Wu, Jin-Long; Kashinath, Karthik; Albert, Adrian
- Journal of Computational Physics, Vol. 406
Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion: Two-Dimensional Incompressible Flow. Part I
journal, August 1997
- Arakawa, Akio
- Journal of Computational Physics, Vol. 135, Issue 2
Structure functions in two-dimensional turbulence
journal, February 1992
- Grossmann, Siegfried; Mertens, Peter
- Zeitschrift für Physik B Condensed Matter, Vol. 88, Issue 1
Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
journal, May 2020
- Qian, Elizabeth; Kramer, Boris; Peherstorfer, Benjamin
- Physica D: Nonlinear Phenomena, Vol. 406
Statistical mechanics of two-dimensional and geophysical flows
journal, June 2012
- Bouchet, Freddy; Venaille, Antoine
- Physics Reports, Vol. 515, Issue 5
Hidden physics models: Machine learning of nonlinear partial differential equations
journal, March 2018
- Raissi, Maziar; Karniadakis, George Em
- Journal of Computational Physics, Vol. 357
Sampling the posterior: An approach to non-Gaussian data assimilation
journal, June 2007
- Apte, A.; Hairer, M.; Stuart, A. M.
- Physica D: Nonlinear Phenomena, Vol. 230, Issue 1-2
Theory-Guided Data Science: A New Paradigm for Scientific Discovery from Data
journal, October 2017
- Karpatne, Anuj; Atluri, Gowtham; Faghmous, James H.
- IEEE Transactions on Knowledge and Data Engineering, Vol. 29, Issue 10
Predictive large-eddy-simulation wall modeling via physics-informed neural networks
journal, March 2019
- Yang, X. I. A.; Zafar, S.; Wang, J. -X.
- Physical Review Fluids, Vol. 4, Issue 3
Spatially Extended Tests of a Neural Network Parametrization Trained by Coarse‐Graining
journal, August 2019
- Brenowitz, Noah D.; Bretherton, Christopher S.
- Journal of Advances in Modeling Earth Systems, Vol. 11, Issue 8
A turbulent eddy-viscosity surrogate modeling framework for Reynolds-averaged Navier-Stokes simulations
journal, September 2021
- Maulik, Romit; Sharma, Himanshu; Patel, Saumil
- Computers & Fluids, Vol. 227
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
journal, October 2016
- Ling, Julia; Kurzawski, Andrew; Templeton, Jeremy
- Journal of Fluid Mechanics, Vol. 807
Inertial Ranges in Two-Dimensional Turbulence
journal, January 1967
- Kraichnan, Robert H.
- Physics of Fluids, Vol. 10, Issue 7
Analysis Scheme in the Ensemble Kalman Filter
journal, June 1998
- Burgers, Gerrit; Jan van Leeuwen, Peter; Evensen, Geir
- Monthly Weather Review, Vol. 126, Issue 6
A proof of concept for scale-adaptive parametrizations: the case of the Lorenz '96 model: Proof for Scale-adaptive Parametrizations
journal, December 2017
- Vissio, Gabriele; Lucarini, Valerio
- Quarterly Journal of the Royal Meteorological Society, Vol. 144, Issue 710
Prognostic Validation of a Neural Network Unified Physics Parameterization
journal, June 2018
- Brenowitz, N. D.; Bretherton, C. S.
- Geophysical Research Letters, Vol. 45, Issue 12
Assessing the scales in numerical weather and climate predictions: will exascale be the rescue?
journal, February 2019
- Neumann, Philipp; Düben, Peter; Adamidis, Panagiotis
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2142
Ensemble Kalman Filter for Assimilating Experimental Data into Large-Eddy Simulations of Turbulent Flows
journal, December 2019
- Labahn, Jeffrey W.; Wu, Hao; Harris, Shaun R.
- Flow, Turbulence and Combustion, Vol. 104, Issue 4
Uncertainty in Model Climate Sensitivity Traced to Representations of Cumulus Precipitation Microphysics
journal, January 2016
- Zhao, Ming; Golaz, J. -C.; Held, I. M.
- Journal of Climate, Vol. 29, Issue 2
An Improved Strategy for the Evaluation of Cloud Parameterizations in GCMS
journal, October 2003
- Jakob, Christian
- Bulletin of the American Meteorological Society, Vol. 84, Issue 10
A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
journal, January 2020
- Pawar, Suraj; San, Omer; Rasheed, Adil
- Theoretical and Computational Fluid Dynamics, Vol. 34, Issue 4
Gradient-based learning applied to document recognition
journal, January 1998
- Lecun, Y.; Bottou, L.; Bengio, Y.
- Proceedings of the IEEE, Vol. 86, Issue 11
Earth observation satellite sensors for biodiversity monitoring: potentials and bottlenecks
journal, September 2014
- Kuenzer, Claudia; Ottinger, Marco; Wegmann, Martin
- International Journal of Remote Sensing, Vol. 35, Issue 18
Shallow neural networks for fluid flow reconstruction with limited sensors
journal, June 2020
- Erichson, N. Benjamin; Mathelin, Lionel; Yao, Zhewei
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2238
Super-resolution reconstruction of turbulent flows with machine learning
journal, May 2019
- Fukami, Kai; Fukagata, Koji; Taira, Kunihiko
- Journal of Fluid Mechanics, Vol. 870
Coupled online learning as a way to tackle instabilities and biases in neural network parameterizations: general algorithms and Lorenz 96 case study (v1.0)
journal, January 2020
- Rasp, Stephan
- Geoscientific Model Development, Vol. 13, Issue 5
Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics
journal, June 2020
- Vlachas, P. R.; Pathak, J.; Hunt, B. R.
- Neural Networks, Vol. 126
Ensemble-Based State Estimator for Aerodynamic Flows
journal, July 2018
- da Silva, Andre F. C.; Colonius, Tim
- AIAA Journal, Vol. 56, Issue 7
Predictions of turbulent shear flows using deep neural networks
journal, May 2019
- Srinivasan, P. A.; Guastoni, L.; Azizpour, H.
- Physical Review Fluids, Vol. 4, Issue 5
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
journal, November 2019
- Lee, Kookjin; Carlberg, Kevin T.
- Journal of Computational Physics
Theory-Guided Machine Learning in Materials Science
journal, June 2016
- Wagner, Nicholas; Rondinelli, James M.
- Frontiers in Materials, Vol. 3
Could Machine Learning Break the Convection Parameterization Deadlock?
journal, June 2018
- Gentine, P.; Pritchard, M.; Rasp, S.
- Geophysical Research Letters, Vol. 45, Issue 11
Data-assisted reduced-order modeling of extreme events in complex dynamical systems
journal, May 2018
- Wan, Zhong Yi; Vlachas, Pantelis; Koumoutsakos, Petros
- PLOS ONE, Vol. 13, Issue 5
Towards a mesoscale eddy closure
journal, January 2008
- Eden, Carsten; Greatbatch, Richard J.
- Ocean Modelling, Vol. 20, Issue 3
A dynamic subgrid‐scale eddy viscosity model
journal, July 1991
- Germano, Massimo; Piomelli, Ugo; Moin, Parviz
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7
Turbulence Modeling in the Age of Data
journal, January 2019
- Duraisamy, Karthik; Iaccarino, Gianluca; Xiao, Heng
- Annual Review of Fluid Mechanics, Vol. 51, Issue 1
Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network
journal, June 2020
- Cheng, M.; Fang, F.; Pain, C. C.
- Computer Methods in Applied Mechanics and Engineering, Vol. 365
Atmospheric Predictability and Two-Dimensional Turbulence
journal, March 1971
- Leith, C. E.
- Journal of the Atmospheric Sciences, Vol. 28, Issue 2
High-order methods for decaying two-dimensional homogeneous isotropic turbulence
journal, June 2012
- San, Omer; Staples, Anne E.
- Computers & Fluids, Vol. 63
A nonlinear dynamical perspective on model error: A proposal for non-local stochastic-dynamic parametrization in weather and climate prediction models
journal, January 2001
- Palmer, T. N.
- Quarterly Journal of the Royal Meteorological Society, Vol. 127, Issue 572
Subgrid modelling for geophysical flows
journal, January 2013
- Frederiksen, Jorgen S.; O'Kane, Terence J.; Zidikheri, Meelis J.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 371, Issue 1982
Middle atmosphere dynamical sources of the semiannual oscillation in the thermosphere and ionosphere: MIDDLE ATMOSPHERE SOURCES OF THE T-I SAO
journal, January 2017
- Jones, M.; Emmert, J. T.; Drob, D. P.
- Geophysical Research Letters, Vol. 44, Issue 1
Subgrid-Scale Parameterization with Conditional Markov Chains
journal, August 2008
- Crommelin, Daan; Vanden-Eijnden, Eric
- Journal of the Atmospheric Sciences, Vol. 65, Issue 8
A Non-Gaussian Ensemble Filter Update for Data Assimilation
journal, November 2010
- Anderson, Jeffrey L.
- Monthly Weather Review, Vol. 138, Issue 11
A Monte Carlo Implementation of the Nonlinear Filtering Problem to Produce Ensemble Assimilations and Forecasts
journal, December 1999
- Anderson, Jeffrey L.; Anderson, Stephen L.
- Monthly Weather Review, Vol. 127, Issue 12
A deep learning enabler for nonintrusive reduced order modeling of fluid flows
journal, August 2019
- Pawar, S.; Rahman, S. M.; Vaddireddy, H.
- Physics of Fluids, Vol. 31, Issue 8
Deep learning for physical processes: incorporating prior scientific knowledge
journal, December 2019
- de Bézenac, Emmanuel; Pajot, Arthur; Gallinari, Patrick
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 12
Prediction of turbulent heat transfer using convolutional neural networks
journal, November 2019
- Kim, Junhyuk; Lee, Changhoon
- Journal of Fluid Mechanics, Vol. 882
Extensive chaos in the Lorenz-96 model
journal, December 2010
- Karimi, A.; Paul, M. R.
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 20, Issue 4
Parameterised non-intrusive reduced order methods for ensemble Kalman filter data assimilation
journal, November 2018
- Xiao, D.; Du, J.; Fang, F.
- Computers & Fluids, Vol. 177
Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence
journal, May 2019
- Xie, Chenyue; Wang, Jianchun; Li, Ke
- Physical Review E, Vol. 99, Issue 5
Cloud parameterization for climate modeling: Status and prospects
journal, October 1989
- Randall, David A.
- Atmospheric Research, Vol. 23, Issue 3-4
Moisture Vertical Structure, Column Water Vapor, and Tropical Deep Convection
journal, June 2009
- Holloway, Christopher E.; Neelin, J. David
- Journal of the Atmospheric Sciences, Vol. 66, Issue 6
Combining machine learning with knowledge-based modeling for scalable forecasting and subgrid-scale closure of large, complex, spatiotemporal systems
journal, May 2020
- Wikner, Alexander; Pathak, Jaideep; Hunt, Brian
- Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 30, Issue 5
A stable and scale-aware dynamic modeling framework for subgrid-scale parameterizations of two-dimensional turbulence
journal, November 2017
- Maulik, Romit; San, Omer
- Computers & Fluids, Vol. 158
Harmonizing models and observations: Data assimilation in Earth system science
journal, June 2020
- Li, Xin; Liu, Feng; Fang, Miao
- Science China Earth Sciences, Vol. 63, Issue 8
Deep learning and process understanding for data-driven Earth system science
journal, February 2019
- Reichstein, Markus; Camps-Valls, Gustau; Stevens, Bjorn
- Nature, Vol. 566, Issue 7743
Subgrid modelling for two-dimensional turbulence using neural networks
journal, November 2018
- Maulik, R.; San, O.; Rasheed, A.
- Journal of Fluid Mechanics, Vol. 858
Theory-Guided Data Science for Climate Change
journal, November 2014
- Faghmous, James H.; Banerjee, Arindam; Shekhar, Shashi
- Computer, Vol. 47, Issue 11
State estimation in wall-bounded flow systems. Part 3. The ensemble Kalman filter
journal, August 2011
- Colburn, C. H.; Cessna, J. B.; Bewley, T. R.
- Journal of Fluid Mechanics, Vol. 682
The maximum likelihood ensemble filter performances in chaotic systems
journal, January 2008
- Carrassi, Alberto; Vannitsem, Stephane; Zupanski, Dusanka
- Tellus A: Dynamic Meteorology and Oceanography, Vol. 61, Issue 5
Machine Learning for Fluid Mechanics
journal, September 2019
- Brunton, Steven L.; Noack, Bernd R.; Koumoutsakos, Petros
- Annual Review of Fluid Mechanics, Vol. 52, Issue 1
The Analog Data Assimilation
journal, October 2017
- Lguensat, Redouane; Tandeo, Pierre; Ailliot, Pierre
- Monthly Weather Review, Vol. 145, Issue 10
Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data
journal, March 2017
- Wang, Jian-Xun; Wu, Jin-Long; Xiao, Heng
- Physical Review Fluids, Vol. 2, Issue 3
Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization
journal, January 2020
- Bocquet, Marc; Brajard, Julien; Carrassi, Alberto
- Foundations of Data Science, Vol. 2, Issue 1
Continuous data assimilation reduced order models of fluid flow
journal, December 2019
- Zerfas, Camille; Rebholz, Leo G.; Schneier, Michael
- Computer Methods in Applied Mechanics and Engineering, Vol. 357
Filter accuracy for the Lorenz 96 model: Fixed versus adaptive observation operators
journal, June 2016
- Law, K. J. H.; Sanz-Alonso, D.; Shukla, A.
- Physica D: Nonlinear Phenomena, Vol. 325
Reconstruction of unsteady viscous flows using data assimilation schemes
journal, July 2016
- Mons, V.; Chassaing, J. -C.; Gomez, T.
- Journal of Computational Physics, Vol. 316
Deep neural networks for data-driven LES closure models
journal, December 2019
- Beck, Andrea; Flad, David; Munz, Claus-Dieter
- Journal of Computational Physics, Vol. 398
Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics
journal, June 2020
- Vlachas, P. R.; Pathak, J.; Hunt, B. R.
- Neural Networks, Vol. 126
Neural networks based subgrid scale modeling in large eddy simulations
journal, January 2003
- Sarghini, F.; de Felice, G.; Santini, S.
- Computers & Fluids, Vol. 32, Issue 1
Reynolds-averaged Navier–Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned
journal, April 2019
- Wu, Jinlong; Xiao, Heng; Sun, Rui
- Journal of Fluid Mechanics, Vol. 869
Perspective on machine learning for advancing fluid mechanics
journal, October 2019
- Brenner, M. P.; Eldredge, J. D.; Freund, J. B.
- Physical Review Fluids, Vol. 4, Issue 10
Spatio-temporal interpolation of altimeter-derived SSH fields using analog data assimilation: A case-study in the south china sea
conference, July 2017
- Lguensat, Redouane; Sun, Miao; Chen, Ge
- 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS)
The role of large-scale spatial patterns in the chaotic amplification of perturbations in a Lorenz’96 model
journal, January 2011
- Herrera, S.; Paz ó, D.; Ferná Ndez, J.
- Tellus A: Dynamic Meteorology and Oceanography, Vol. 63, Issue 5
Maximum Likelihood Ensemble Filter: Theoretical Aspects
journal, June 2005
- Zupanski, Milija
- Monthly Weather Review, Vol. 133, Issue 6
A proof of concept for scale-adaptive parameterizations: the case of the Lorenz '96 model
text, January 2016
- Vissio, Gabriele; Lucarini, Valerio
- arXiv
Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model
preprint, January 2017
- Shi, Xingjian; Gao, Zhihan; Lausen, Leonard
- arXiv
Super-resolution reconstruction of turbulent flows with machine learning
text, January 2018
- Fukami, Kai; Fukagata, Koji; Taira, Kunihiko
- arXiv
Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
text, January 2019
- Erichson, N. Benjamin; Mathelin, Lionel; Yao, Zhewei
- arXiv
Data-driven modelling of nonlinear spatio-temporal fluid flows using a deep convolutional generative adversarial network
text, January 2020
- Cheng, M.; Fang, F.; Pain, C. C.
- arXiv
Recurrent Neural Network Architecture Search for Geophysical Emulation
preprint, January 2020
- Maulik, Romit; Egele, Romain; Lusch, Bethany
- arXiv