Learned 1-D passive scalar advection to accelerate chemical transport modeling: a case study with GEOS-FP horizontal wind fields

Manho Park aDepartment of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, Urbana, IL

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Zhonghua Zheng bDepartment of Earth and Environmental Sciences, The University of Manchester, Manchester M13 9PL, United Kingdom

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Nicole Riemer cDepartment of Atmospheric Sciences, University of Illinois Urbana-Champaign, Urbana, IL

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Christopher W. Tessum aDepartment of Civil and Environmental Engineering, University of Illinois Urbana-Champaign, Urbana, IL

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Abstract

We developed and applied a machine-learned discretization for one-dimensional (1-D) horizontal passive scalar advection, which is an operator component common to all chemical transport models (CTMs). Our learned advection scheme resembles a second-order accuracy, three-stencil numerical solver, but differs from a traditional solver in that coefficients for each equation term are output by a neural network rather than being theoretically-derived constants. We subsampled higher-resolution simulation results—resulting in up to 16× larger grid size and 64× larger timestep—and trained our neural network-based scheme to match the subsampled integration data. In this way, we created an operator that is low-resolution (in time or space) but can reproduce the behavior of a high-resolution traditional solver. Our model shows high fidelity in reproducing its training dataset (a single 10-day 1-D simulation) and is similarly accurate in simulations with unseen initial conditions, wind fields, and grid spacing. In many cases, our learned solver is more accurate than a low-resolution version of the reference solver, but the low-resolution reference solver achieves greater computational speedup (500× acceleration) over the high-resolution simulation than the learned solver is able to (18× acceleration). Surprisingly, our learned 1-D scheme—when combined with a splitting technique—can be used to predict 2-D advection, and is in some cases more stable and accurate than the low-resolution reference solver in 2-D. Overall, our results suggest that learned advection operators may offer a higher-accuracy method for accelerating CTM simulations as compared to simply running a traditional integrator at low resolution.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Christopher W. Tessum, ctessum@illinois.edu

Abstract

We developed and applied a machine-learned discretization for one-dimensional (1-D) horizontal passive scalar advection, which is an operator component common to all chemical transport models (CTMs). Our learned advection scheme resembles a second-order accuracy, three-stencil numerical solver, but differs from a traditional solver in that coefficients for each equation term are output by a neural network rather than being theoretically-derived constants. We subsampled higher-resolution simulation results—resulting in up to 16× larger grid size and 64× larger timestep—and trained our neural network-based scheme to match the subsampled integration data. In this way, we created an operator that is low-resolution (in time or space) but can reproduce the behavior of a high-resolution traditional solver. Our model shows high fidelity in reproducing its training dataset (a single 10-day 1-D simulation) and is similarly accurate in simulations with unseen initial conditions, wind fields, and grid spacing. In many cases, our learned solver is more accurate than a low-resolution version of the reference solver, but the low-resolution reference solver achieves greater computational speedup (500× acceleration) over the high-resolution simulation than the learned solver is able to (18× acceleration). Surprisingly, our learned 1-D scheme—when combined with a splitting technique—can be used to predict 2-D advection, and is in some cases more stable and accurate than the low-resolution reference solver in 2-D. Overall, our results suggest that learned advection operators may offer a higher-accuracy method for accelerating CTM simulations as compared to simply running a traditional integrator at low resolution.

© 2024 American Meteorological Society. This is an Author Accepted Manuscript distributed under the terms of the default AMS reuse license. For information regarding reuse and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Christopher W. Tessum, ctessum@illinois.edu
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