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Training physics‐based machine‐learning parameterizations with gradient‐free ensemble Kalman methods

Lopez-Gomez, Ignacio and Christopoulos, Costa and Ervik, Haakon Ludvig Langeland and Dunbar, Oliver R. A. and Cohen, Yair and Schneider, Tapio (2022) Training physics‐based machine‐learning parameterizations with gradient‐free ensemble Kalman methods. Journal of Advances in Modeling Earth Systems . Art. No. e2022MS003105. ISSN 1942-2466. doi:10.1029/2022ms003105. (In Press)

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Most machine learning applications in Earth system modeling currently rely on gradient-based supervised learning. This imposes stringent constraints on the nature of the data used for training (typically, residual time tendencies are needed), and it complicates learning about the interactions between machine-learned parameterizations and other components of an Earth system model. Approaching learning about process-based parameterizations as an inverse problem resolves many of these issues, since it allows parameterizations to be trained with partial observations or statistics that directly relate to quantities of interest in long-term climate projections. Here we demonstrate the effectiveness of Kalman inversion methods in treating learning about parameterizations as an inverse problem. We consider two different algorithms: unscented and ensemble Kalman inversion. Both methods involve highly parallelizable forward model evaluations, converge exponentially fast, and do not require gradient computations. In addition, unscented Kalman inversion provides a measure of parameter uncertainty. We illustrate how training parameterizations can be posed as a regularized inverse problem and solved by ensemble Kalman methods through the calibration of an eddy-diffusivity mass-flux scheme for subgrid-scale turbulence and convection, using data generated by large-eddy simulations. We find the algorithms amenable to batching strategies, robust to noise and model failures, and efficient in the calibration of hybrid parameterizations that can include empirical closures and neural networks.

Item Type:Article
Related URLs:
URLURL TypeDescription implementing ensemble Kalman methods implementing EDMF scheme from Shen et al. (2022) used for model training
Lopez-Gomez, Ignacio0000-0002-7255-5895
Christopoulos, Costa0000-0002-8552-465X
Ervik, Haakon Ludvig Langeland0000-0003-2912-5774
Dunbar, Oliver R. A.0000-0001-7374-0382
Cohen, Yair0000-0002-9615-2476
Schneider, Tapio0000-0001-5687-2287
Additional Information:© 2022 American Geophysical Union. Accepted manuscript online: 10 August 2022. Manuscript accepted: 08 August 2022. Manuscript revised: 22 June 2022. Manuscript received: 24 March 2022. We thank Daniel Z. Huang and Zhaoyi Shen for insightful discussions, and Julien Brajard and an anonymous reviewer for prompting a clearer and more precise formulation of the problem and methods discussed in this study. I.L. was supported by a fellowship from the Resnick Sustainability Institute at Caltech, and an Amazon AI4Science fellowship. H.L.L.E was supported by an Aker scholarship and a Fulbright fellowship. This research was additionally supported by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program, by the National Science Foundation (grant AGS-1835860), by the Defense Advanced Research Projects Agency (Agreement No. HR00112290030), and by the Heising-Simons Foundation. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The software package implementing ensemble Kalman methods can be accessed at, the one implementing the EDMF scheme at, and the software used to calibrate the EDMF scheme may be accessed at The data from Shen et al. (2022) used for model training is available at
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Resnick Sustainability InstituteUNSPECIFIED
Amazon AI4Science FellowshipUNSPECIFIED
Aker Scholarship FoundationUNSPECIFIED
Fulbright FoundationUNSPECIFIED
Schmidt Futures ProgramUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)HR00112290030
Heising-Simons FoundationUNSPECIFIED
Subject Keywords:Machine learning; Earth system mode;l Subgrid-scale process; Parameterization; Data assimilation; Model calibration
Record Number:CaltechAUTHORS:20220810-402975000
Persistent URL:
Official Citation:Lopez-Gomez, I., Christopoulos, C., Langeland Ervik, H. L., Dunbar, O. R. A., Cohen, Y., & Schneider, T. (2022). Training physics-based machine-learning parameterizations with gradient-free ensemble Kalman methods. Journal of Advances in Modeling Earth Systems, 14, e2022MS003105.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:116228
Deposited By: George Porter
Deposited On:11 Aug 2022 22:32
Last Modified:11 Aug 2022 22:32

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