Aravinth Ravi | Search arXiv

arXiv2026

A Spectral Model-Informed Neural Network for Inverse Source Problems

In this paper, we propose an unsupervised, two-step model-informed deep learning framework for solving the inverse source problem. In the first step, boundary measurement data are transformed into an imaging function that encodes information about the shape and location of the unknown source. Leveraging this information, we derive a Fourier-based model equation in the spectral domain that relates the imaging function to the Fourier coefficients of the source function. In the second step, this model equation is incorporated into the training of a model-informed neural network to recover the parameters of interest. The proposed approach enables fast and accurate reconstruction of the source function while maintaining robustness to noise. The effectiveness of the method is demonstrated through numerical experiments in both two- and three-dimensional settings. For the two-dimensional case, we further compare our approach with the traditional least-squares method to validate its computational efficiency and reconstruction accuracy.

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arXiv2026

A Model-Informed Deep Learning Algorithm for Solving the Phaseless Inverse Scattering Problem

We study in this paper an unsupervised, two-step, model-informed deep learning framework for solving the phaseless inverse scattering problem. The objective is to reconstruct a compactly supported function that characterizes a scatterer from boundary measurements of the modulus of the total wave corresponding to multiple incident waves. In the first step, the phaseless data are transformed into an imaging function that is directly related to the underlying scatterer. Motivated by the contrast source method, we derive a coupled system of model equations using the Lippmann-Schwinger integral equation and a spectral-based equation involving the imaging function. In the second step, the unknown scatterer and contrast source function are each parameterized as independent feedforward neural networks, which are trained simultaneously at each iteration using the derived system of model equations. The Lippmann-Schwinger integral equation enforces the underlying physics as a model constraint, while the spectral-based equation incorporating the imaging function supplies geometric information on the shape and location of the unknown scatterer. The resulting framework achieves accurate and efficient reconstructions while maintaining robustness to measurement noise. Furthermore, transforming some aspects of the problem to the spectral domain enables an effective reduction in the computational cost, allowing us to recover the unknown scatterer quickly. Numerical experiments in both two- and three-dimensional settings demonstrate the effectiveness, stability, and practical potential of the proposed approach.

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