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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Preprints
https://doi.org/10.5194/gmd-2020-83
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-2020-83
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: development and technical paper 28 Apr 2020

Submitted as: development and technical paper | 28 Apr 2020

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This preprint is currently under review for the journal GMD.

A Mass- and Energy-Conserving Framework for Using Machine Learning to Speed Computations

Patrick Obin Sturm1,3 and Anthony S. Wexler1,2 Patrick Obin Sturm and Anthony S. Wexler
  • 1Air Quality Research Center, University of California, Davis, California 95616, USA
  • 2Departments of Mechanical and Aerospace Engineering, Civil and Environmental Engineering, and Land, Air and Water Resources, University of California, Davis, California 95616, USA
  • 3Institute of Mathematics, Technical University of Berlin, Berlin 10587, Germany

Abstract. Large air quality models and large climate models simulate the physical and chemical properties of the ocean, land surface and/or atmosphere to predict atmospheric composition, energy balance, and the future of our planet. All of these models employ some form of operator splitting, also called the method of fractional steps, in their structure, which enables each physical or chemical process to be simulated in a separate operator or module within the overall model. In this structure, each of the modules calculates property changes for a fixed period of time; that is, property values are passed into the module which calculates how they change for a period of time and then returns the new property values, all in round robin between the various modules of the model. Some of these modules require the vast majority of the computer resources consumed by the entire model so increasing their computational efficiency can either improve the model's computational performance or enable more realistic physical or chemical representations in the module, or a combination of these two. Recent efforts have attempted to replace these modules with ones that use machine learning tools to memorize the input-output relationships of the most time-consuming modules. One shortcoming of some of the original modules and their machine learned replacements is lack of adherence to conservation principles that are essential to model performance. In this work, we derive a mathematical framework for machine learned replacements that conserves properties, say mass, atoms, or energy, to machine precision. This framework can be used to develop machine learned operator replacements in environmental models.

Patrick Obin Sturm and Anthony S. Wexler

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Status: open (until 23 Jun 2020)
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Patrick Obin Sturm and Anthony S. Wexler

Model code and software

A MATLAB Script to Generate a Restricted Inverse (v0.2.0) P. Obin Sturm and A. S. Wexler https://doi.org/10.5281/zenodo.3733594

Photochemical Box Model in Julia P. Obin Sturm https://doi.org/10.5281/zenodo.3733503

Patrick Obin Sturm and Anthony S. Wexler

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Latest update: 31 May 2020
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Short summary
Large air quality and climate models calculate different physical and chemical phenomena in separate operators within the overall model, some of which are computationally intensive. Machine learning tools can memorize the behavior of these operators and replace them, but the replacements must still obey physical laws, like conservation principles. This work derives a mathematical framework for machine learning replacements that conserves properties, such as mass or energy, to machine precision.
Large air quality and climate models calculate different physical and chemical phenomena in...
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