Learning continuous models for continuous physics
Abstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discret...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-11-01
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| Series: | Communications Physics |
| Online Access: | https://doi.org/10.1038/s42005-023-01433-4 |
| _version_ | 1827770519845339136 |
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| author | Aditi S. Krishnapriyan Alejandro F. Queiruga N. Benjamin Erichson Michael W. Mahoney |
| author_facet | Aditi S. Krishnapriyan Alejandro F. Queiruga N. Benjamin Erichson Michael W. Mahoney |
| author_sort | Aditi S. Krishnapriyan |
| collection | DOAJ |
| description | Abstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications. |
| first_indexed | 2024-03-11T12:40:43Z |
| format | Article |
| id | doaj.art-776f47981bd7428aab296c6fe960eb7f |
| institution | Directory Open Access Journal |
| issn | 2399-3650 |
| language | English |
| last_indexed | 2024-03-11T12:40:43Z |
| publishDate | 2023-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Communications Physics |
| spelling | doaj.art-776f47981bd7428aab296c6fe960eb7f2023-11-05T12:20:38ZengNature PortfolioCommunications Physics2399-36502023-11-016111410.1038/s42005-023-01433-4Learning continuous models for continuous physicsAditi S. Krishnapriyan0Alejandro F. Queiruga1N. Benjamin Erichson2Michael W. Mahoney3University of California, BerkeleyGoogle ResearchLawrence Berkeley National LaboratoryUniversity of California, BerkeleyAbstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.https://doi.org/10.1038/s42005-023-01433-4 |
| spellingShingle | Aditi S. Krishnapriyan Alejandro F. Queiruga N. Benjamin Erichson Michael W. Mahoney Learning continuous models for continuous physics Communications Physics |
| title | Learning continuous models for continuous physics |
| title_full | Learning continuous models for continuous physics |
| title_fullStr | Learning continuous models for continuous physics |
| title_full_unstemmed | Learning continuous models for continuous physics |
| title_short | Learning continuous models for continuous physics |
| title_sort | learning continuous models for continuous physics |
| url | https://doi.org/10.1038/s42005-023-01433-4 |
| work_keys_str_mv | AT aditiskrishnapriyan learningcontinuousmodelsforcontinuousphysics AT alejandrofqueiruga learningcontinuousmodelsforcontinuousphysics AT nbenjaminerichson learningcontinuousmodelsforcontinuousphysics AT michaelwmahoney learningcontinuousmodelsforcontinuousphysics |