Data-driven model reconstruction for nonlinear wave dynamics
The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly used deep-learning approaches suffer from a lack of interpretability of the trained models. Here, we present an interpretable machine learning framework for analyzing the nonlinear evolution dynamics of...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/2jh8-p5y2 |
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| _version_ | 1849425080592891904 |
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| author | Ekaterina Smolina Lev Smirnov Daniel Leykam Franco Nori Daria Smirnova |
| author_facet | Ekaterina Smolina Lev Smirnov Daniel Leykam Franco Nori Daria Smirnova |
| author_sort | Ekaterina Smolina |
| collection | DOAJ |
| description | The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly used deep-learning approaches suffer from a lack of interpretability of the trained models. Here, we present an interpretable machine learning framework for analyzing the nonlinear evolution dynamics of optical wave packets in complex wave media. We use sparse regression to reduce microscopic discrete lattice models to simpler effective continuum models, which can accurately describe the dynamics of the wave packet envelope. We apply our approach to valley-Hall domain walls in honeycomb photonic lattices of laser-written waveguides with Kerr-type nonlinearity and different boundary shapes. The reconstructed equations accurately reproduce the linear dispersion and nonlinear effects, including self-steepening and self-focusing. This scheme is proven free of the a priori limitations imposed by the underlying hierarchy of scales traditionally employed in asymptotic analytical methods. It represents a powerful interpretable machine learning technique of interest for advancing design capabilities in photonics and framing the complex interaction-driven dynamics in various topological materials. |
| format | Article |
| id | doaj-art-07eca312858843aeb680a6dca8d3b98a |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-07eca312858843aeb680a6dca8d3b98a2025-08-20T03:29:53ZengAmerican Physical SocietyPhysical Review Research2643-15642025-06-017202331410.1103/2jh8-p5y2Data-driven model reconstruction for nonlinear wave dynamicsEkaterina SmolinaLev SmirnovDaniel LeykamFranco NoriDaria SmirnovaThe use of machine learning to predict wave dynamics is a topic of growing interest, but commonly used deep-learning approaches suffer from a lack of interpretability of the trained models. Here, we present an interpretable machine learning framework for analyzing the nonlinear evolution dynamics of optical wave packets in complex wave media. We use sparse regression to reduce microscopic discrete lattice models to simpler effective continuum models, which can accurately describe the dynamics of the wave packet envelope. We apply our approach to valley-Hall domain walls in honeycomb photonic lattices of laser-written waveguides with Kerr-type nonlinearity and different boundary shapes. The reconstructed equations accurately reproduce the linear dispersion and nonlinear effects, including self-steepening and self-focusing. This scheme is proven free of the a priori limitations imposed by the underlying hierarchy of scales traditionally employed in asymptotic analytical methods. It represents a powerful interpretable machine learning technique of interest for advancing design capabilities in photonics and framing the complex interaction-driven dynamics in various topological materials.http://doi.org/10.1103/2jh8-p5y2 |
| spellingShingle | Ekaterina Smolina Lev Smirnov Daniel Leykam Franco Nori Daria Smirnova Data-driven model reconstruction for nonlinear wave dynamics Physical Review Research |
| title | Data-driven model reconstruction for nonlinear wave dynamics |
| title_full | Data-driven model reconstruction for nonlinear wave dynamics |
| title_fullStr | Data-driven model reconstruction for nonlinear wave dynamics |
| title_full_unstemmed | Data-driven model reconstruction for nonlinear wave dynamics |
| title_short | Data-driven model reconstruction for nonlinear wave dynamics |
| title_sort | data driven model reconstruction for nonlinear wave dynamics |
| url | http://doi.org/10.1103/2jh8-p5y2 |
| work_keys_str_mv | AT ekaterinasmolina datadrivenmodelreconstructionfornonlinearwavedynamics AT levsmirnov datadrivenmodelreconstructionfornonlinearwavedynamics AT danielleykam datadrivenmodelreconstructionfornonlinearwavedynamics AT franconori datadrivenmodelreconstructionfornonlinearwavedynamics AT dariasmirnova datadrivenmodelreconstructionfornonlinearwavedynamics |