Machine learning approach to single-shot multiparameter estimation for the non-linear Schrödinger equation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911171258351616 |
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| author | Rossignol, Louis Aladjidi, Tangui Baker-Rasooli, Myrann Glorieux, Quentin |
| author_facet | Rossignol, Louis Aladjidi, Tangui Baker-Rasooli, Myrann Glorieux, Quentin |
| contents | The nonlinear Schrödinger equation (NLSE) is a fundamental model for wave dynamics in nonlinear media ranging from optical fibers to Bose-Einstein condensates. Accurately estimating its parameters, which are often strongly correlated, from a single measurement remains a significant challenge. We address this problem by treating parameter estimation as an inverse problem and training a neural network to invert the NLSE mapping. We combine a fast numerical solver with a machine learning approach based on the ConvNeXt architecture and a multivariate Gaussian negative log-likelihood loss function. From single-shot field (density and phase) images, our model estimates three key parameters: the nonlinear coefficient $n_2$, the saturation intensity $I_{sat}$, and the linear absorption coefficient $α$. Trained on 100,000 simulated images, the model achieves a mean absolute error of $3.22\%$ on 12,500 unseen test samples, demonstrating strong generalization and close agreement with ground-truth values. This approach provides an efficient route for characterizing nonlinear systems and has the potential to bridge theoretical modeling and experimental data when realistic noise is incorporated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Machine learning approach to single-shot multiparameter estimation for the non-linear Schrödinger equation Rossignol, Louis Aladjidi, Tangui Baker-Rasooli, Myrann Glorieux, Quentin Quantum Physics Computer Vision and Pattern Recognition Optics The nonlinear Schrödinger equation (NLSE) is a fundamental model for wave dynamics in nonlinear media ranging from optical fibers to Bose-Einstein condensates. Accurately estimating its parameters, which are often strongly correlated, from a single measurement remains a significant challenge. We address this problem by treating parameter estimation as an inverse problem and training a neural network to invert the NLSE mapping. We combine a fast numerical solver with a machine learning approach based on the ConvNeXt architecture and a multivariate Gaussian negative log-likelihood loss function. From single-shot field (density and phase) images, our model estimates three key parameters: the nonlinear coefficient $n_2$, the saturation intensity $I_{sat}$, and the linear absorption coefficient $α$. Trained on 100,000 simulated images, the model achieves a mean absolute error of $3.22\%$ on 12,500 unseen test samples, demonstrating strong generalization and close agreement with ground-truth values. This approach provides an efficient route for characterizing nonlinear systems and has the potential to bridge theoretical modeling and experimental data when realistic noise is incorporated. |
| title | Machine learning approach to single-shot multiparameter estimation for the non-linear Schrödinger equation |
| topic | Quantum Physics Computer Vision and Pattern Recognition Optics |
| url | https://arxiv.org/abs/2509.18479 |