Learning Physically Interpretable Atmospheric Models from Data with WSINDy
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911037702275072 |
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| author | Minor, Seth Messenger, Daniel A. Dukic, Vanja Bortz, David M. |
| author_facet | Minor, Seth Messenger, Daniel A. Dukic, Vanja Bortz, David M. |
| contents | The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing atmospheric phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm can learn effective atmospheric models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00738 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Physically Interpretable Atmospheric Models from Data with WSINDy Minor, Seth Messenger, Daniel A. Dukic, Vanja Bortz, David M. Geophysics Machine Learning Computational Physics 35D30, 86-08, 86-10 The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing atmospheric phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm can learn effective atmospheric models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension. |
| title | Learning Physically Interpretable Atmospheric Models from Data with WSINDy |
| topic | Geophysics Machine Learning Computational Physics 35D30, 86-08, 86-10 |
| url | https://arxiv.org/abs/2501.00738 |