12 citations · 64 across the 21 of their papers we have counts for
22 papers
Non-centered parametric variational Bayes' approach for hierarchical inverse problems of partial differential equations
Jiaming Sui, Junxiong Jia
This paper proposes a non-centered parameterization based infinite-dimensional mean-field variational inference (NCP-iMFVI) approach for solving the hierarchical Bayesian inverse p…
Variational Inverting Network for Statistical Inverse Problems of Partial Differential Equations
Junxiong Jia, Yanni Wu, Peijun Li +1
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-j…
Stein variational gradient descent on infinite-dimensional space and applications to statistical inverse problems
Junxiong Jia, Peijun Li, Deyu Meng
In this paper, we propose an infinite-dimensional version of the Stein variational gradient descent (iSVGD) method for solving Bayesian inverse problems. The method can generate ap…
Posterior contraction for empirical Bayesian approach to inverse problems under non-diagonal assumption
Junxiong Jia, Jigen Peng, Jinghuai Gao
We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior pro…
An adaptive augmented regularization method and its applications
Junxiong Jia, Qihang Sun, Bangyu Wu +1
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging.…
Iterative thresholding algorithm based on non-convex method for modified lp-norm regularization minimization
Angang Cui, Jigen Peng, Haiyang Li +2
Recently, the -norm regularization minimization problem has attracted great attention in compressed sensing. However, the -norm in problem…
A New Nonconvex Strategy to Affine Matrix Rank Minimization Problem
Angang Cui, Jigen Peng, Haiyang Li +2
The affine matrix rank minimization (AMRM) problem is to find a matrix of minimum rank that satisfies a given linear system constraint. It has many applications in some important a…
Recursive linearization method for inverse medium scattering problems with complex mixture Gaussian error learning
Junxiong Jia, Bangyu Wu, Jigen Peng +1
This paper is concerned with the modeling errors appeared in the numerical methods of inverse medium scattering problems (IMSP). Optimization based iterative methods are wildly emp…
Generalized singular value thresholding operator to affine matrix rank minimization problem
Angang Cui, Haiyang Li, Jigen Peng +1
It is well known that the affine matrix rank minimization problem is NP-hard and all known algorithms for exactly solving it are doubly exponential in theory and in practice due to…
A Carleman type estimate of variable order space-fractional diffusion equations and applications to some inverse problems
Junxiong Jia, Jigen Peng
Variable order space-fractional diffusion equation derived as an important model to describe complex anomalous diffusion phenomenon. In this article, well-posedness theory has been…
Studies on an inverse source problem for a space-time fractional diffusion equation by constructing a strong maximum principle
Junxiong Jia, Jigen Peng, Jiaqing Yang
In this paper, we focus on a space-time fractional diffusion equation with the generalized Caputo's fractional derivative operator and a general space nonlocal operator (with the f…
Maximum principles for a time-space fractional diffusion equation
Junxiong Jia, Kexue Li
In this paper, we focus on maximum principles of a time-space fractional diffusion equation. Maximum principles for classical solution and weak solution are all obtained by using p…
Explosive solutions of parabolic stochastic partial differential equations with Lvy noise
Kexue Li, Jigen Peng, Junxiong Jia
In this paper, we study the explosive solutions to a class of parbolic stochastic semilinear differential equations driven by a L$\acute{\mbox{e}}$vy type noise. The sufficient con…
Infinite-dimensional Bayesian approach for inverse scattering problems of a fractional Helmholtz equation
Junxiong Jia, Shigang Yu, Jigen Peng +1
In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave…
Variable Total Variation Regularization for Backward Time-Space Fractional Diffusion Problem
Junxiong Jia, Jigen Peng, Jinghuai Gao +1
In this paper, we consider a backward problem for a time-space fractional diffusion process. For this problem, we propose to construct the initial data by minimizing data residual…
Bayesian approach to inverse problems for functions with variable index Besov prior
Junxiong Jia, Jigen Peng, Jinghuai Gao
We adopt Bayesian approach to consider the inverse problem of estimate a function from noisy observations. One important component of this approach is the prior measure. Total vari…
Well-posedness for compressible MHD system with highly oscillating initial data
Junxiong Jia, Jigen Peng, Jinghuai Gao
In this paper, we transform compressible MHD system written in Euler coordinate to Lagrange coordinate in critical Besov space. Then we construct unique local solutions for compres…
Optimal Time Decay Rate for the Compressible Viscoelastic Equations in Critical Spaces
Junxiong Jia, Jigen Peng
In this paper, we are concerned with the convergence rates of the global strong solution to constant equilibrium state for the compressible viscoelastic fluids in the whole space.…
Optimal Time Decay of Navier-Stokes Equations With Low Regularity Initial Data
Junxiong Jia, Jigen Peng
In this paper, we study the optimal time decay rate of isentropic Navier-Stokes equations under the low regularity assumptions about initial data. In the previous works about optim…
On the global well-posedness of a generalized 2D Boussinesq equations
Junxiong Jia, Jigen Peng, Kexue Li
In this paper, we consider the global solutions to a generalized 2D Boussinesq equation \begin{align*} \left \{\begin{aligned} & \partial_{t} ω+ u\cdot \nabla ω+ νΛ^α ω= θ_{x_{1}}…
On the Decay and Stability of Global Solutions to the 3D Inhomogeneous MHD system
Junxiong Jia, Jigen Peng, Kexue Li
In this paper, we investigative the large time decay and stability to any given global smooth solutions of the D incompressible inhomogeneous MHD systems. We proved that given a…
Well-Posedness and Optimal Time-Decay for Compressible MHD System in Besov Space
Junxiong Jia, Jigen Peng, Kexue Li
In this paper, firstly, we prove the global well-posedness of three dimensional compressible magnetohydrodynamics equations for some classes of large initial data, which may have l…