A Non-Intrusive Reduced Basis EKI for Time Fractional Diffusion Inverse Problems

Adaptive multi-fidelity polynomial chaos approach to Bayesian inference in inverse problems

(2019) Liang Yan et al.   JOURNAL OF COMPUTATIONAL PHYSICS

An adaptive Gaussian process-based iterative ensemble smoother for data assimilation

(2018) Lei Ju et al.   ADVANCES IN WATER RESOURCES

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

(2018) Mengwu Guo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Doubly stochastic radial basis function methods

(2018) Fenglian Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Non-intrusive reduced order modeling of nonlinear problems using neural networks

(2018) J.S. Hesthaven et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Bayesian approach to a nonlinear inverse problem for time-space fractional diffusion equation

(2018) Yuan-Xiang Zhang et al.   INVERSE PROBLEMS

Data-driven reduced order modeling for time-dependent problems

(2018) Mengwu Guo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Convergence analysis of surrogate-based methods for Bayesian inverse problems

(2017) Liang Yan et al.   INVERSE PROBLEMS

The Bayesian formulation and well-posedness of fractional elliptic inverse problems

(2017) Nicolás García Trillos et al.   INVERSE PROBLEMS

Analysis of the Ensemble Kalman Filter for Inverse Problems

(2017) Claudia Schillings et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Sparse Approximation using $\ell_1-\ell_2$ Minimization and Its Application to Stochastic Collocation

(2017) Liang Yan et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems

(2016) Marco A Iglesias   INVERSE PROBLEMS

On the uniqueness and reconstruction for an inverse problem of the fractional diffusion process

(2015) J.J. Liu et al.   APPLIED NUMERICAL MATHEMATICS

The method of approximate particular solutions for the time-fractional diffusion equation with a non-local boundary condition

(2015) Liang Yan et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

On the reconstruction of unknown time-dependent boundary sources for time fractional diffusion process by distributing measurement

(2015) J J Liu et al.   INVERSE PROBLEMS

A tutorial on inverse problems for anomalous diffusion processes

(2015) Bangti Jin et al.   INVERSE PROBLEMS

Stochastic Collocation Algorithms Using $l_1$-Minimization for Bayesian Solution of Inverse Problems

(2015) Liang Yan et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

(2015) Peter Benner et al.   SIAM REVIEW

A review of surrogate models and their application to groundwater modeling

(2015) M. J. Asher et al.   WATER RESOURCES RESEARCH

Efficient Kansa-type MFS algorithm for time-fractional inverse diffusion problems

(2014) Liang Yan et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

Data-driven model reduction for the Bayesian solution of inverse problems

(2014) Tiangang Cui et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation

(2013) Gongsheng Li et al.   INVERSE PROBLEMS

Ensemble Kalman methods for inverse problems

(2013) Marco A Iglesias et al.   INVERSE PROBLEMS

An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling

(2013) Weixuan Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Nonintrusive reduced-order modeling of parametrized time-dependent partial differential equations

(2013) Christophe Audouze et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Boundary particle method for Laplace transformed time fractional diffusion equations

(2012) Zhuo-Jia Fu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Inverse source problem for a fractional diffusion equation

(2011) Ying Zhang et al.   INVERSE PROBLEMS

Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems

(2011) Kenichi Sakamoto et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Two regularization methods for solving a Riesz–Feller space-fractional backward diffusion problem

(2010) G H Zheng et al.   INVERSE PROBLEMS

Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation

(2009) Jin Cheng et al.   INVERSE PROBLEMS