4 papers
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…
Information decomposition for disentangled and interpretable manifold learning of fluid flows via variational autoencoders
Zhiyuan Wang, Iacopo Tirelli, Stefano Discetti +1
We introduce an information-theoretic framework that uses variational autoencoders (VAEs) to extract compact, physically interpretable manifolds from high-dimensional flow-field da…
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 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…