{"ID":2866831,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.18479","arxiv_id":"2509.18479","title":"Machine learning approach to single-shot multiparameter estimation for the non-linear Schrödinger equation","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.18479","url_pdf":"https://arxiv.org/pdf/2509.18479v1","authors":"[\"Louis Rossignol\",\"Tangui Aladjidi\",\"Myrann Baker-Rasooli\",\"Quentin Glorieux\"]","published":"2025-09-23T00:32:37Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.CV\",\"physics.optics\"]","methods":"[]","has_code":false}