Jinghao Cao

Jinghao Cao

We present a Fourier--Galerkin framework for the analysis and computation of subwavelength resonances in two-dimensional scattering problems in finite domains. Starting from the boundary integral formulation, we project the operator onto Fourier modes and derive an explicit finite-dimensional effective matrix whose singularity characterizes the resonant frequencies. In the subwavelength regime, we obtain asymptotic expansions of this matrix in terms of $ω$ and the material contrast, identifying the leading-order operators and their kernel structure. This reduction transforms the resonance problem into a low-dimensional nonlinear eigenvalue problem, avoiding large-scale discretizations and global root-search procedures. The entries of the effective matrix are explicitly computable and admit fast evaluation using FFT-based quadrature. The resulting approach provides an efficient and robust computational framework for resonances in general smooth geometries.

Ming Li, Xuejiao Hu, Xueqian Jin et al.

Omnidirectional depth estimation has received much attention from researchers in recent years. However, challenges arise due to camera soiling and variations in camera layouts, affecting the robustness and flexibility of the algorithm. In this paper, we use the geometric constraints and redundant information of multiple 360-degree cameras to achieve robust and flexible multi-view omnidirectional depth estimation. We implement two algorithms, in which the two-stage algorithm obtains initial depth maps by pairwise stereo matching of multiple cameras and fuses the multiple depth maps to achieve the final depth estimation; the one-stage algorithm adopts spherical sweeping based on hypothetical depths to construct a uniform spherical matching cost of the multi-camera images and obtain the depth. Additionally, a generalized epipolar equirectangular projection is introduced to simplify the spherical epipolar constraints. To overcome panorama distortion, a spherical feature extractor is implemented. Furthermore, a synthetic 360-degree dataset consisting of 12K road scene panoramas and 3K ground truth depth maps is presented to train and evaluate 360-degree depth estimation algorithms. Our dataset takes soiled camera lenses and glare into consideration, which is more consistent with the real-world environment. Experiments show that our two algorithms achieve state-of-the-art performance, accurately predicting depth maps even when provided with soiled panorama inputs. The flexibility of the algorithms is experimentally validated in terms of camera layouts and numbers.

Jinghao Cao, Qin Li, Mengnan Du et al.

We propose Physics-informed Attention-enhanced Fourier Neural Operator (PIANO) to solve the Nonlinear Force-Free Field (NLFFF) problem in solar physics. Unlike conventional approaches that rely on iterative numerical methods, our proposed PIANO directly learns the 3D magnetic field structure from 2D boundary conditions. Specifically, PIANO integrates Efficient Channel Attention (ECA) mechanisms with Dilated Convolutions (DC), which enhances the model's ability to capture multimodal input by prioritizing critical channels relevant to the magnetic field's variations. Furthermore, we apply physics-informed loss by enforcing the force-free and divergence-free conditions in the training process so that our prediction is consistent with underlying physics with high accuracy. Experimental results on the ISEE NLFFF dataset show that our PIANO not only outperforms state-of-the-art neural operators in terms of accuracy but also shows strong consistency with the physical characteristics of NLFFF data across magnetic fields reconstructed from various solar active regions. The GitHub of this project is available https://github.com/Autumnstar-cjh/PIANO

Chaofan Wu, Jiaheng Li, Jinghao Cao et al.

Accurate 3D perception is essential for autonomous driving. Traditional methods often struggle with geometric ambiguity due to a lack of geometric prior. To address these challenges, we use omnidirectional depth estimation to introduce geometric prior. Based on the depth information, we propose a Sketch-Coloring framework OmniDepth-Occ. Additionally, our approach introduces a cylindrical voxel representation based on polar coordinate to better align with the radial nature of panoramic camera views. To address the lack of fisheye camera dataset in autonomous driving tasks, we also build a virtual scene dataset with six fisheye cameras, and the data volume has reached twice that of SemanticKITTI. Experimental results demonstrate that our Sketch-Coloring network significantly enhances 3D perception performance.