Treffer: Numerical method-informed DeepONet for refractivity inversion in waveguides.

This work applies deep learning methods to estimate vertical refractive index profiles in elongated waveguides. We use the DeepONet architecture to learn an inverse operator that maps signal measurements from a known source to the refractive index profile. The forward model is the one-way Helmholtz equation. A variational autoencoder is employed to augment the input data used for training the inverse operator. The obtained solution is then refined using the automatically differentiable forward model. Computational experiments are performed for tropospheric and underwater tomography problems, including experiments on real data. The numerical results confirm the effectiveness of the proposed approach. A Python 3 (JAX) implementation of the proposed method is publicly available. This work is an extended version of the ICCS-2025 conference paper (Lytaev, 2025). • Generative models allow to define the solution space for the inverse problem. • DeepONet is used to train the inverse operator from the data and the forward model. • A differentiable forward model allows refining the solution obtained using DeepONet. [ABSTRACT FROM AUTHOR]