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math.NA2026
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…
math.NA2025
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…
math.NA2025
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…