arXiv subjects

Kuilin Qin

Publications and source records attributed to Kuilin Qin.

3 recordsLinked to original sources

arXiv2026

Deep Neural Networks Inspired by Differential Equations

Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines. However, neural Networks persistently face challenges related to theoretical understanding, interpretability, and generalization. To address these issues, researchers are increasingly adopting a differential equations perspective to propose a unified theoretical framework and systematic design methodologies for neural networks. In this paper, we provide an extensive review of deep neural network architectures and dynamic modeling methods inspired by differential equations. We specifically examine deep neural network models and deterministic dynamical network constructs based on ordinary differential equations (ODEs), as well as regularization techniques and stochastic dynamical network models informed by stochastic differential equations (SDEs). We present numerical comparisons of these models to illustrate their characteristics and performance. Finally, we explore promising research directions in integrating differential equations with deep learning to offer new insights for developing intelligent computational methods that boast enhanced interpretability and generalization capabilities.

cs.LG↗

arXiv2026

Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

Operator learning is an emerging interdisciplinary field that integrates machine learning with scientific computing. By mapping infinite-dimensional function spaces, this approach provides an efficient surrogate modeling framework for high-dimensional partial differential equations (PDEs). Compared to traditional numerical solvers, it achieves a superior trade-off between computational complexity and approximation accuracy, demonstrating significant advantages in many-query tasks such as real-time prediction and parameter sweeps. Given the stringent accuracy requirements of both forward simulation and inverse inference, as well as the precision bottlenecks of existing operator learning methods in handling complex boundaries or long-term evolution, we propose the Starter-Iterator Neural Operator (SINO). Our framework reinterprets the initialization strategies and iterative formats of traditional iterative methods through neural networks, establishing an efficient approach for spectral-spatiotemporal collaborative modeling. Specifically, the frequency-domain initialization module captures globally stable low-frequency features, while the time-domain learning module focuses on optimizing local solution residuals, thereby effectively overcoming the inherent limitations of conventional single-domain modeling approaches. Extensive experiments on typical dynamical systems such as the Navier-Stokes equations and acoustic wave equations, as well as practical applications including super-resolution imaging and weather forecasting, demonstrate that SINO achieves outstanding performance in numerical accuracy, generalization capability, and robustness.

math.NA↗

arXiv2026

Noise-adapted Neural Operator for Robust Non-Line-of-Sight Imaging

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible. Computational imaging, especially non-line-of-sight (NLOS) imaging, the extraction of information from obscured or hidden scenes is achieved through the utilization of indirect light signals resulting from multiple reflections or scattering. The inherently weak nature of these signals, coupled with their susceptibility to noise, necessitates the integration of physical processes to ensure accurate reconstruction. This paper presents a parameterized inverse problem framework tailored for large-scale linear problems in 3D imaging reconstruction. Initially, a noise estimation module is employed to adaptively assess the noise levels present in transient data. Subsequently, a parameterized neural operator is developed to approximate the inverse mapping, facilitating end-to-end rapid image reconstruction. Our 3D image reconstruction framework, grounded in operator learning, is constructed through deep algorithm unfolding, which not only provides commendable model interpretability but also enables dynamic adaptation to varying noise levels in the acquired data, thereby ensuring consistently robust and accurate reconstruction outcomes. Furthermore, we introduce a novel method for the fusion of global and local spatiotemporal data features. By integrating structural and detailed information, this method significantly enhances both accuracy and robustness. Comprehensive numerical experiments conducted on both simulated and real datasets substantiate the efficacy of the proposed method. It demonstrates remarkable performance with fast scanning data and sparse illumination point data, offering a viable solution for NLOS imaging in complex scenarios.

cs.CV↗