arXiv subjects

Yunwen Yin

Publications and source records attributed to Yunwen Yin.

3 recordsLinked to original sources

arXiv2025

Regularity of solutions to degenerate normalized $p$-Laplacian equation with general variable exponents

In this paper, we consider a kind of degenerate normalized $p$-Laplacian equation with general variable exponents. We establish local $C^{1,α'}$ regularity of viscosity solutions by making use of the compactness argument, scaling techniques and the localized oscillating method. In addition, we also obtain almost optimal pointwise $C^{1,τ} $ regularity for degenerate free transmission problem related to normalized $ p$-Laplacian. Our argument is based on a new improved oscillation-type estimate combined with a localized analysis.

math.AP↗

arXiv2024

Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problem

In this paper, we consider a deep learning approach to the limited aperture inverse obstacle scattering problem. It is well known that traditional deep learning relies solely on data, which may limit its performance for the inverse problem when only indirect observation data and a physical model are available. A fundamental question arises in light of these limitations: is it possible to enable deep learning to work on inverse problems without labeled data and to be aware of what it is learning? This work proposes a deep decomposition method (DDM) for such purposes, which does not require ground truth labels. It accomplishes this by providing physical operators associated with the scattering model to the neural network architecture. Additionally, a deep learning based data completion scheme is implemented in DDM to prevent distorting the solution of the inverse problem for limited aperture data. Furthermore, apart from addressing the ill-posedness imposed by the inverse problem itself, DDM is the first physics-aware machine learning technique that can have interpretability property for the obstacle detection. The convergence result of DDM is theoretically investigated. We also prove that adding small noise to the input limited aperture data can introduce additional regularization terms and effectively improve the smoothness of the learned inverse operator. Numerical experiments are presented to demonstrate the validity of the proposed DDM even when the incident and observation apertures are extremely limited.

math.NA↗

arXiv2024

A novel direct imaging method for passive inverse obstacle scattering problem

This paper investigates the inverse scattering problem of recovering a sound-soft obstacle using passive measurements taken from randomly distributed point sources. The randomness introduced by these sources poses significant challenges, leading to the failure of classical direct sampling methods that rely on scattered field measurements. To address this issue, we introduce the Doubly Cross-Correlating Method (DCM), a novel direct imaging scheme that consists of two major steps. Initially, DCM creates a cross-correlation between two passive measurements. This specially designed cross-correlation effectively handles the uncontrollability of incident sources and connects to the active scattering model via the Helmholtz-Kirchhoff identity. Subsequently, this cross-correlation is used to create a correlation-based imaging function that can qualitatively identify the obstacle. The stability and resolution of DCM are theoretically analyzed. Extensive numerical examples, including scenarios with two closely positioned obstacles and multiscale obstacles, demonstrate that DCM is computationally efficient, stable, and fast.

math.NA↗