18 papers
Hankel--Christoffel--Nevai Screening for Bayesian Inverse Problems
Zhiliang Deng, Xiaomei Yang
Likelihood evaluation in Bayesian inverse problems often requires a forward-model solve. We study candidate screening using a likelihood-weighted prior moment matrix and two associ…
Posterior Convergence without Force Convergence: Resolution-Stable Sampling for Rough Bayesian Inverse Problems
Zhiliang Deng, Xiaomei Yang
Bayesian targets may converge under model refinement even when the exact sensitivities used by gradient-based samplers do not. We study this probability--sensitivity mismatch and i…
Dilation-Covariant Hankel Pencils for Multiscale Recovery of Sparse Mellin Spectra
Zhiliang Deng, Xiaomei Yang
We study sparse Mellin spectral recovery from geometric samples. Dilation covariance is shown to generate the Hankel structure directly, rather than only after reduction to a class…
Coded Hankel Polynomial Chaos: Spectral Identification of Dominant Polynomial-Chaos Modes
Zhiliang Deng, Xiaomei Yang
Identification of dominant polynomial-chaos modes is usually formulated as a sparse-regression problem on a sampled multivariate polynomial dictionary. We develop coded Hankel poly…
Contour Hankel dynamics and indicator fields for the Riemann -function
Zhiliang Deng, Xiaomei Yang, Huazhong Lü
We develop a moving-contour Hankel framework for encoding local zero configurations of the Riemann -function. Weighted contour integrals of the logarithmic derivative , ex…
Representation--Symbol Correspondence for -Hamiltonian Mechanics on the Quantum Plane
Xiaomei Yang, Zhiliang Deng
We develop a representation--symbol correspondence for -Hamiltonian mechanics on the quantum plane. The coordinate algebra and its covariant differential calculus are realized s…
Contour-count indicator fields for visible pole clusters in meromorphic continuation
Zhiliang Deng, Xiaomei Yang
We develop a contour-count indicator method for visible pole clusters in outward meromorphic continuation from circular boundary data. The method starts from determinant characteri…
Determinant Characteristics and Argument-Principle Certification for Visible Poles in Meromorphic Continuation
Xiaomei Yang, Zhiliang Deng
We study outward meromorphic continuation from circular boundary data in the unit disk. The unknown function is holomorphic in the unit disk and admits a meromorphic continuation t…
A persistent-homology-Gaussian prior for solving infinite-dimensional Bayesian inverse scattering problems
Zhiyuan Wang, Hang Qi, Xiaofei Guan +2
Bayesian inference methods have been developed to address inverse problems in function spaces where the unknown parameters are of infinite dimension. However, conventional Gaussian…
A Moment--Hankel Rank Method for Identifying the Number of Point Sources in the Heat Equation
Zhiliang Deng, Xiaomei Yang, Ailin Qian
We develop a low-frequency moment--Hankel rank method for identifying the number of time-independent point sources in the heat equation from boundary flux data. The method is formu…
A Hankel determinant zero-order principle for source counting in an inverse heat point-source problem
Zhiliang Deng, Ailin Qian, Xiaomei Yang
This paper studies the identification of an unknown number of stationary point sources in a two-dimensional heat equation from boundary flux measurements. Unlike many reconstructio…
Fourier--Hankel Moment Recovery in Acoustic Scattering: Multichannel Stabilization and Radial Interface Resolution
Zhiliang Deng, Xiaofei Guan, Xiaomei Yang
We study direct recovery of visible phase centers and concentric radial interfaces from full-aperture acoustic far-field data under the Born approximation. Two complementary moment…
Dual-Filtration Topology Recovery from Qualitative Acoustic Scattering Indicators
Xiaomei Yang, Jiaying Jia, Zhiliang Deng
Qualitative inverse scattering methods produce gray-scale indicator fields, from which the topology of the scatterer must be inferred without a prescribed threshold. We propose a d…
A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem
Xiaomei Yang, Jiaying Jia, Zhiliang Deng
The reconstruction of time-dependent Robin coefficients is a challenging inverse heat transfer problem due to its inherent ill-posedness. This paper introduces a hierarchical Bayes…
Hamiltonian Monte Carlo from -deformed phase-space mechanics
Xiaomei Yang, Zhiliang Deng
Hamiltonian Monte Carlo (HMC) generates efficient Markov transitions by combining Hamiltonian dynamics with a Metropolis correction. This paper develops a geometric \(q\)-analogue…
A novel viewpoint for Bayesian inversion based on the Poisson point process
Zhiliang Deng, Zhiyuan Wang, Xiaomei Yang +1
We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The poster…
A Bayesian thinning algorithm for the point source identification of heat equation
Zhiliang Deng, Chen Li, Xiaomei Yang
In this work, we propose a Bayesian thinning algorithm for recovering weighted point source functions in the heat equation from boundary flux observations. The major challenge in t…
A persistent-homology-based Bayesian prior for potential coefficient reconstruction in an elliptic PDE
Zhiliang Deng, Haiyang Liu, Xiaofei Guan +2
We address the reconstruction of a potential coefficient in an elliptic partial differential equation from distributed observations within the Bayesian framework. The choice of pri…