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Published May 24, 2022 | Submitted
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Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods


Modeling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned from data (using kernel flows, a variant of cross-validation), then the resulting data-driven models are not only faster than equation-based models but are easier to train than neural networks such as the long short-term memory neural network. In addition, they are also more accurate and predictive than the latter. When trained on geophysical observational data, for example, the weekly averaged global sea-surface temperature, considerable gains are also observed by the proposed technique in comparison to classical partial differential equation-based models in terms of forecast computational cost and accuracy. When trained on publicly available re-analysis data for the daily temperature of the North-American continent, we see significant improvements over classical baselines such as climatology and persistence-based forecast techniques. Although our experiments concern specific examples, the proposed approach is general, and our results support the viability of kernel methods (with learned kernels) for interpretable and computationally efficient geophysical forecasting for a large diversity of processes.

Additional Information

This material is based upon work supported by the U.S. Department of Energy (DOE), Office of Science, Office of Advanced Scientific Computing Research, under Contract DE-AC02-06CH11357. This research was funded in part and used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. R. M. acknowledges support from the Margaret Butler Fellowship at the Argonne Leadership Computing Facility. B. H. thanks the European Commission for funding through the Marie Curie fellowship STALDYS-792919 (Statistical Learning for Dynamical Systems). H. O. gratefully acknowledges support by the Air Force Office of Scientific Research under award number FA9550-18-1-0271 (Games for Computation and Learning) and MURI (FA9550-20-1-0358). This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. DOE or the United States Government. Authors' Contributions. B.H. prepared code and analysis, wrote portions of the paper. R.M. designed the investigation, prepared code and documentation, performed analyses, generated visualizations, wrote paper. H.O. prepared code and analysis, wrote portions of the paper. Data Accessibility. The data that support the findings of this study are openly available in Github at https://github.com/Romit-Maulik/POD_RKHS.

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August 20, 2023
October 24, 2023