# A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem

arXiv: https://arxiv.org/abs/2212.08736 · HTML: https://mlsanity.com/paper/2212.08736/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 58 references that are in the map.
- First posted on arXiv 16 Dec 2022.

## Builds on (most cited first, 6 of 6)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [SwitchNet: a neural network model for forward and inverse scattering problems](https://mlsanity.com/paper/1810.09675/) (2018)
- [A mathematical motivation for complex-valued convolutional networks](https://mlsanity.com/paper/1503.03438/) (2015)
- [Solving Inverse Wave Scattering with Deep Learning](https://mlsanity.com/paper/1911.13202/) (2019)

## Built on by (most cited first, 8 of 8)

- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems](https://mlsanity.com/paper/2409.16471/) (2024)
- [A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problems](https://mlsanity.com/paper/2305.00250/) (2023)
- [Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models](https://mlsanity.com/paper/2408.02866/) (2024)
- [Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problem](https://mlsanity.com/paper/2403.19470/) (2024)
- [Instance-Wise Adaptive Sampling for Dataset Construction in Approximating Inverse Problem Solutions](https://mlsanity.com/paper/2509.04583/) (2025)
- [GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries](https://mlsanity.com/paper/2509.24117/) (2025)
- [A Warm-basis Method for Bridging Learning and Iteration: a Case Study in Fluorescence Molecular Tomography](https://mlsanity.com/paper/2510.05926/) (2025)

## Abstract (arXiv)

We consider the inverse acoustic obstacle problem for sound-soft star-shaped obstacles in two dimensions wherein the boundary of the obstacle is determined from measurements of the scattered field at a collection of receivers outside the object. One of the standard approaches for solving this problem is to reformulate it as an optimization problem: finding the boundary of the domain that minimizes the L2 distance between computed values of the scattered field and the given measurement data. The optimization problem is computationally challenging since the local set of convexity shrinks with increasing frequency and results in an increasing number of local minima in the vicinity of the true solution. In many practical experimental settings, low frequency measurements are unavailable due to limitations of the experimental setup or the sensors used for measurement. Thus, obtaining a good initial guess for the optimization problem plays a vital role in this environment. We present a neural network warm-start approach for solving the inverse scattering problem, where an initial guess for the optimization problem is obtained using a trained neural network. We demonstrate the effectiveness of our method with several numerical examples. For high frequency problems, this approach outperforms traditional iterative methods such as Gauss-Newton initialized without any prior (i.e., initialized using a unit circle), or initialized using the solution of a direct method such as the linear sampling method. The algorithm remains robust to noise in the scattered field measurements and also converges to the true solution for limited aperture data. However, the number of training samples required to train the neural network scales exponentially in frequency and the complexity of the obstacles considered. We conclude with a discussion of this phenomenon and potential directions for future research.