Journal article
Data-driven discovery of Green’s functions with human-understandable deep learning
- Abstract:
- There is an opportunity for deep learning to revolutionize science and technology by revealing its findings in a human interpretable manner. We develop a novel data-driven approach for creating a human-machine partnership to accelerate scientific discovery. By collecting physical system responses, under carefully selected excitations, we train rational neural networks to learn Green's functions of hidden partial differential equation. These solutions reveal human-understandable properties and features, such as linear conservation laws, and symmetries, along with shock and singularity locations, boundary effects, and dominant modes. We illustrate this technique on several examples and capture a range of physics, including advection-diffusion, viscous shocks, and Stokes flow in a lid-driven cavity.
- Publication status:
- Accepted
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 2.8MB, Terms of use)
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- Publisher copy:
- 10.1038/s41598-022-08745-5
Authors
- Publisher:
- Springer Nature
- Journal:
- Scientific Reports More from this journal
- Volume:
- 12
- Article number:
- 4824
- Publication date:
- 2021-03-22
- Acceptance date:
- 2022-03-11
- DOI:
- EISSN:
-
2045-2322
Terms of use
- Copyright holder:
- Boullé et al
- Copyright date:
- 2021
- Rights statement:
- © The Author(s) 2022. Tis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. Te images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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