Discovering interpretable physical models using symbolic regression and discrete exterior calculus
Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of machine learning to recover physical models from experiments and increase the accuracy of physical simulations, p...
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/ad1af2 |
| _version_ | 1797354164366344192 |
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| author | Simone Manti Alessandro Lucantonio |
| author_facet | Simone Manti Alessandro Lucantonio |
| author_sort | Simone Manti |
| collection | DOAJ |
| description | Computational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of machine learning to recover physical models from experiments and increase the accuracy of physical simulations, purely data-driven models have limited generalization and interpretability. To overcome these limitations, we propose a framework that combines symbolic regression (SR) and discrete exterior calculus (DEC) for the automated discovery of physical models starting from experimental data. Since these models consist of mathematical expressions, they are interpretable and amenable to analysis, and the use of a natural, general-purpose discrete mathematical language for physics favors generalization with limited input data. Importantly, DEC provides building blocks for the discrete analog of field theories, which are beyond the state-of-the-art applications of SR to physical problems. Further, we show that DEC allows to implement a strongly-typed SR procedure that guarantees the mathematical consistency of the recovered models and reduces the search space of symbolic expressions. Finally, we prove the effectiveness of our methodology by re-discovering three models of continuum physics from synthetic experimental data: Poisson equation, the Euler’s elastica and the equations of linear elasticity. Thanks to their general-purpose nature, the methods developed in this paper may be applied to diverse contexts of physical modeling. |
| first_indexed | 2024-03-08T13:45:34Z |
| format | Article |
| id | doaj.art-88976e14543f49868169dde366e2e9cc |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-03-08T13:45:34Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-88976e14543f49868169dde366e2e9cc2024-01-16T09:19:22ZengIOP PublishingMachine Learning: Science and Technology2632-21532024-01-015101500510.1088/2632-2153/ad1af2Discovering interpretable physical models using symbolic regression and discrete exterior calculusSimone Manti0https://orcid.org/0000-0002-4060-0620Alessandro Lucantonio1https://orcid.org/0000-0002-9807-5451Department of Mechanical and Production Engineering, Aarhus University , Aarhus, DenmarkDepartment of Mechanical and Production Engineering, Aarhus University , Aarhus, DenmarkComputational modeling is a key resource to gather insight into physical systems in modern scientific research and engineering. While access to large amount of data has fueled the use of machine learning to recover physical models from experiments and increase the accuracy of physical simulations, purely data-driven models have limited generalization and interpretability. To overcome these limitations, we propose a framework that combines symbolic regression (SR) and discrete exterior calculus (DEC) for the automated discovery of physical models starting from experimental data. Since these models consist of mathematical expressions, they are interpretable and amenable to analysis, and the use of a natural, general-purpose discrete mathematical language for physics favors generalization with limited input data. Importantly, DEC provides building blocks for the discrete analog of field theories, which are beyond the state-of-the-art applications of SR to physical problems. Further, we show that DEC allows to implement a strongly-typed SR procedure that guarantees the mathematical consistency of the recovered models and reduces the search space of symbolic expressions. Finally, we prove the effectiveness of our methodology by re-discovering three models of continuum physics from synthetic experimental data: Poisson equation, the Euler’s elastica and the equations of linear elasticity. Thanks to their general-purpose nature, the methods developed in this paper may be applied to diverse contexts of physical modeling.https://doi.org/10.1088/2632-2153/ad1af2symbolic regressiondiscrete exterior calculusmachine learningmodel identificationequation discovery |
| spellingShingle | Simone Manti Alessandro Lucantonio Discovering interpretable physical models using symbolic regression and discrete exterior calculus Machine Learning: Science and Technology symbolic regression discrete exterior calculus machine learning model identification equation discovery |
| title | Discovering interpretable physical models using symbolic regression and discrete exterior calculus |
| title_full | Discovering interpretable physical models using symbolic regression and discrete exterior calculus |
| title_fullStr | Discovering interpretable physical models using symbolic regression and discrete exterior calculus |
| title_full_unstemmed | Discovering interpretable physical models using symbolic regression and discrete exterior calculus |
| title_short | Discovering interpretable physical models using symbolic regression and discrete exterior calculus |
| title_sort | discovering interpretable physical models using symbolic regression and discrete exterior calculus |
| topic | symbolic regression discrete exterior calculus machine learning model identification equation discovery |
| url | https://doi.org/10.1088/2632-2153/ad1af2 |
| work_keys_str_mv | AT simonemanti discoveringinterpretablephysicalmodelsusingsymbolicregressionanddiscreteexteriorcalculus AT alessandrolucantonio discoveringinterpretablephysicalmodelsusingsymbolicregressionanddiscreteexteriorcalculus |