arXiv subjects

Jinghao Cao

Publications and source records attributed to Jinghao Cao.

17 recordsLinked to original sources

arXiv2026

Diffusion-corrected Autoregressive Fourier Neural Operator for Droplet Evolution Prediction

Predicting droplet evolution in material jetting, or Inkjet Printing (IJP), is essential for maintaining printing quality. However, long-horizon forecasts remain challenging due to error accumulation and the complex coupling of process variables. In this work, we introduce the Diffusion-corrected Auto-Regressive Fourier Neural Operator (DiffARFNO), a two-stage framework that combines an autoregressive Fourier-MIONet with a conditional Denoising Diffusion Implicit Model (DDIM) corrector. Fourier-MIONet is trained as a coarse predictor and deployed autoregressively for long-horizon forecasting. In the second stage, a DDIM-based conditional corrector refines the coarse prediction within each sliding window through efficient iterative denoising. By combining coarse predictions from Fourier-MIONet with a DDIM corrector that restores fine details, DiffARFNO aims to provide high-fidelity predictions for long-horizon forecasts. Extensive experiments on droplet datasets from ANSYS Fluent demonstrate that DiffARFNO significantly outperforms existing state-of-the-art models.

cs.LG↗

arXiv2026

Fourier--Galerkin Methods for Subwavelength Resonances in two-dimensional Acoustic Metamaterials

We present a Fourier--Galerkin asymptotic framework for the analysis and computation of subwavelength resonances in two-dimensional scattering problems in finite domains. Starting from the boundary integral formulation, we apply a Fourier--Galerkin discretization to derive an explicit finite-dimensional effective matrix whose kernel characterizes the resonant frequencies. In the subwavelength regime, we obtain asymptotic expansions of this matrix in terms of $\omega$ 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.

math.NA↗

arXiv2026

Hybrid Centralized Distributed Control for Lifelong MAPF over Wireless Connections

In lifelong multi-agent path finding (MAPF) with many robots, unreliable wireless links and stochastic executions are the norm. Existing approaches typically either rely on centralized planning under idealized communication, or run fully distributed local controllers with fixed communication patterns; they rarely couple communication scheduling with policy learning, and thus struggle when bandwidth is scarce or packets are frequently dropped. We address this joint control--communication problem and propose a hybrid centralized--distributed scheme: a centralized cloud policy sends small residual corrections only when selected, while a lightweight on-board Gated recurrent unit (GRU) policy provides a safe default fallback when wireless connection is not available.

eess.SY↗

arXiv2025

Physics-informed Attention-enhanced Fourier Neural Operator for Solar Magnetic Field Extrapolations

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

cs.LG↗

arXiv2025

Exceptional point enhanced small particle detection in systems of subwavelength resonators

This paper considers the effects of small highly contrasted particles on the subwavelength resonances of a system of high-contrast resonators, with an application to sensing. The key technique is a multiple scattering expansion of the capacitance matrix associated with the perturbed system. At leading order, the perturbation of the scattering resonances is characterized by the associated term of the truncated multiple scattering expansion. When an exceptional point is present in the resonance structure, the perturbation critically affects the subwavelength resonances, which improves the sensitivity of a sensing task in the presence of noise. Numerical experiments demonstrate the use of the proposed reconstruction techniques.

math.AP↗

arXiv2025

Fast Singular-Kernel Convolution on General Non-Smooth Domains via Truncated Fourier Filtering

The rapid and accurate evaluation of convolutions with singular kernels plays crucial roles in a wide range of scientific and engineering applications. Building on the recently introduced Truncated Fourier Filtering method for smooth kernels, this work presents a fast, high-order numerical methodology that extends the approach to singular kernels and non-smooth domains. The method relies on truncated Fourier expansions of a prescribed order for the characteristic function of the integration domain, as well as expansions for the products of characteristic functions and singular functions.

math.NA↗

arXiv2025

Omnidirectional Depth-Aided Occupancy Prediction based on Cylindrical Voxel for Autonomous Driving

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.

cs.CV↗

arXiv2024

Effective Medium Theory for Time-modulated Subwavelength Resonators

This paper provides a general framework for deriving effective material properties of one-dimensional, time-modulated systems of subwavelength resonators. It applies to subwavelength resonator systems with a general form of time-dependent parameters. We show that the resonators can be accurately described by a point-scattering formulation when the width of the resonators is small. In contrast to the static setting, where this point interaction approximation yields a Lippmann-Schwinger equation for the effective material properties, the mode coupling in the time-modulated case instead yields an infinite linear system of Lippmann-Schwinger-type equations. The effective equations can equivalently be written as a system of differential equations. Moreover, we introduce a numerical scheme to approximately solve the system of coupled equations and illustrate the validity of the effective equation.

physics.optics↗

arXiv2024

Robust and Flexible Omnidirectional Depth Estimation with Multiple 360-degree Cameras

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.

cs.CV↗

arXiv2024

Scattering from time-modulated subwavelength resonators

We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We consider the one-dimensional setting. In order to understand the energy of the system, we prove a novel higher-order discrete, capacitance matrix approximation of the subwavelength resonant quasifrequencies. Further, we perform numerical experiments to support and illustrate our analytical results and show how periodically time-dependent material parameters affect the scattered wave field.

math-ph↗

arXiv2023

The Non-Hermitian Skin Effect With Three-Dimensional Long-Range Coupling

We study the non-Hermitian skin effect in a three-dimensional system of finitely many subwavelength resonators with an imaginary gauge potential. We introduce a discrete approximation of the eigenmodes and eigenfrequencies of the system in terms of the eigenvectors and eigenvalues of the so-called gauge capacitance matrix $\mathcal{C}_N^γ$, which is a dense matrix due to long-range interactions in the system. Based on translational invariance of this matrix and the decay of its off-diagonal entries, we prove the condensation of the eigenmodes at one edge of the structure by showing the exponential decay of its pseudo-eigenvectors. In particular, we consider a range-k approximation to keep the long-range interaction to a certain extent, thus obtaining a k-banded gauge capacitance matrix $\mathcal{C}_{N,k}^γ$ . Using techniques for Toeplitz matrices and operators, we establish the exponential decay of the pseudo-eigenvectors of $\mathcal{C}_{N,k}^γ$ and demonstrate that they approximate those of the gauge capacitance matrix $\mathcal{C}_N^γ$ well. Our results are numerically verified. In particular, we show that long-range interactions affect only the first eigenmodes in the system. As a result, a tridiagonal approximation of the gauge capacitance matrix, similar to the nearest-neighbour approximation in quantum mechanics, provides a good approximation for the higher modes. Moreover, we also illustrate numerically the behaviour of the eigenmodes and the stability of the non-Hermitian skin effect with respect to disorder in a variety of three-dimensional structures.

math.AP↗

arXiv2023

Mathematical foundations of the non-Hermitian skin effect

We study the skin effect in a one-dimensional system of finitely many subwavelength resonators with a non-Hermitian imaginary gauge potential. Using Toeplitz matrix theory, we prove the condensation of bulk eigenmodes at one of the edges of the system. By introducing a generalised (complex) Brillouin zone, we can compute spectral bands of the associated infinitely periodic structure and prove that this is the limit of the spectra of the finite structures with arbitrarily large size. Finally, we contrast the non-Hermitian systems with imaginary gauge potentials considered here with systems where the non-Hermiticity arises due to complex material parameters, showing that the two systems are fundamentally distinct.

math.AP↗

arXiv2023

Transmission properties of time-dependent one-dimensional metamaterials

We solve the wave equation with periodically time-modulated material parameters in a one-dimensional high-contrast resonator structure in the subwavelength regime exactly, for which we compute the subwavelength quasifrequencies numerically using Muller's method. We prove a formula in the form of an ODE using a capacitance matrix approximation. Comparison of the exact results with the approximations reveals that the method of capacitance matrix approximation is accurate and significantly more efficient. We prove various transmission properties in the aforementioned structure and illustrate them with numerical simulations. In particular, we investigate the effect of time-modulated material parameters on the formation of degenerate points, band gaps and k-gaps.

math.AP↗

arXiv2023

Edge modes in subwavelength resonators in one dimension

We present the mathematical theory of one-dimensional infinitely periodic chains of subwavelength resonators. We analyse both Hermitian and non-Hermitian systems. Subwavelength resonances and associated modes can be accurately predicted by a finite dimensional eigenvalue problem involving a capacitance matrix. We are able to compute the Hermitian and non-Hermitian Zak phases, showing that the former is quantised and the latter is not. Furthermore, we show the existence of localised edge modes arising from defects in the periodicity in both the Hermitian and non-Hermitian cases. In the non-Hermitian case, we provide a complete characterisation of the edge modes.

math.AP↗

arXiv2022

Transmission properties of space-time modulated metamaterials

We prove the possibility of achieving exponentially growing wave propagation in space-time modulated media and give an asymptotic analysis of the quasifrequencies in terms of the amplitude of the time modulation at the degenerate points of the folded band structure. Our analysis provides the first proof of existence of k-gaps in the band structures of space-time modulated systems of subwavelength resonators.

math.AP↗

arXiv2022

Unidirectional edge modes in time-modulated metamaterials

We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces. When the trimers are time-modulated with two opposite orientations, the degenerate eigenspace splits into two one-dimensional eigenspaces described by an analytical formula, each corresponds to a mode which is localized at one edge of the structure. Our results on the localization and stability of these edge modes with respect to fluctuations in the time-modulation amplitude are illustrated by several numerical simulations.

math.AP↗

arXiv2021

Non-reciprocal wave propagation in space-time modulated media

We prove the possibility of achieving non-reciprocal wave propagation in space-time modulated media and give an asymptotic analysis of the non-reciprocity property in terms of the amplitude of the time-modulation. Such modulation causes a folding of the band structure of the material, which may induce degenerate points. By breaking time-reversal symmetry, we show that these degeneracies may open into non-symmetric, unidirectional band gaps. Finally we illustrate our results by several numerical simulations.

math.AP↗