Analytic field solution for machine learning integrating physics model and data driven approach
We derive analytical formulas for machine learning that merge a physics model with a data driven approach. We use a path integral method to find a field solution that calculates machine learning statistics while considering the physics model’s uncertainty, data limitations, geometry complexity, and...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2025-05-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0229813 |
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| _version_ | 1849692865058308096 |
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| author | Xiaobin Wang April Wang |
| author_facet | Xiaobin Wang April Wang |
| author_sort | Xiaobin Wang |
| collection | DOAJ |
| description | We derive analytical formulas for machine learning that merge a physics model with a data driven approach. We use a path integral method to find a field solution that calculates machine learning statistics while considering the physics model’s uncertainty, data limitations, geometry complexity, and mixed probability distributions due to field interactions. The formulas are exact and smoothly combine the physics model with observational data. The numerical realization of analytical expressions produces an interpretable, generative machine learning algorithm. We show the different machine learning options and their performances through examples of machine learning fields over complex geometries with interacting “hidden” nodes under data limitations, model uncertainty, and measurement noise constraints. |
| format | Article |
| id | doaj-art-29d15c53ef164ddc9d1eccd64047472f |
| institution | DOAJ |
| issn | 2158-3226 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj-art-29d15c53ef164ddc9d1eccd64047472f2025-08-20T03:20:36ZengAIP Publishing LLCAIP Advances2158-32262025-05-01155055029055029-810.1063/5.0229813Analytic field solution for machine learning integrating physics model and data driven approachXiaobin Wang0April Wang1Donaldson Company, 1400 W 94th Street, Bloomington, Minnesota 55431, USANorthwestern University, 633 Clark Street, Evanston, Illinois 60208, USAWe derive analytical formulas for machine learning that merge a physics model with a data driven approach. We use a path integral method to find a field solution that calculates machine learning statistics while considering the physics model’s uncertainty, data limitations, geometry complexity, and mixed probability distributions due to field interactions. The formulas are exact and smoothly combine the physics model with observational data. The numerical realization of analytical expressions produces an interpretable, generative machine learning algorithm. We show the different machine learning options and their performances through examples of machine learning fields over complex geometries with interacting “hidden” nodes under data limitations, model uncertainty, and measurement noise constraints.http://dx.doi.org/10.1063/5.0229813 |
| spellingShingle | Xiaobin Wang April Wang Analytic field solution for machine learning integrating physics model and data driven approach AIP Advances |
| title | Analytic field solution for machine learning integrating physics model and data driven approach |
| title_full | Analytic field solution for machine learning integrating physics model and data driven approach |
| title_fullStr | Analytic field solution for machine learning integrating physics model and data driven approach |
| title_full_unstemmed | Analytic field solution for machine learning integrating physics model and data driven approach |
| title_short | Analytic field solution for machine learning integrating physics model and data driven approach |
| title_sort | analytic field solution for machine learning integrating physics model and data driven approach |
| url | http://dx.doi.org/10.1063/5.0229813 |
| work_keys_str_mv | AT xiaobinwang analyticfieldsolutionformachinelearningintegratingphysicsmodelanddatadrivenapproach AT aprilwang analyticfieldsolutionformachinelearningintegratingphysicsmodelanddatadrivenapproach |