3 citations · 14 across the 13 of their papers we have counts for
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Hybrid Projection Methods for Solution Decomposition in Large-scale Bayesian Inverse Problems
Julianne Chung, Jiahua Jiang, Scot M. Miller +1
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios…
Learn an index operator by CNN for solving diffusive optical tomography: a deep direct sampling method
Jiahua Jiang, Yi Li, Ruchi Guo
In this work, we investigate the diffusive optical tomography (DOT) problem in the case that limited boundary measurements are available. Motivated by the direct sampling method (D…
Low-CP-rank Tensor Completion via Practical Regularization
Jiahua Jiang, Fatoumata Sanogo, Carmeliza Navasca
Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARA…
Construct Deep Neural Networks Based on Direct Sampling Methods for Solving Electrical Impedance Tomography
Ruchi Guo, Jiahua Jiang
This work investigates the electrical impedance tomography (EIT) problem when only limited boundary measurements are available, which is known to be challenging due to the extreme…
Hybrid Projection Methods with Recycling for Inverse Problems
Julianne Chung, Eric de Sturler, Jiahua Jiang
Iterative hybrid projection methods have proven to be very effective for solving large linear inverse problems due to their inherent regularizing properties as well as the added fl…
Hybrid Projection Methods for Large-scale Inverse Problems with Mixed Gaussian Priors
Taewon Cho, Julianne Chung, Jiahua Jiang
When solving ill-posed inverse problems, a good choice of the prior is critical for the computation of a reasonable solution. A common approach is to include a Gaussian prior, whic…
Adaptive greedy algorithms based on parameter-domain decomposition and reconstruction for the reduced basis method
Jiahua Jiang, Yanlai Chen
The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-exec…
Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations
Bo Dong, Jiahua Jiang, Yanlai Chen
We develop and analyze the first hybridizable discontinuous Galerkin (HDG) method for solving fifth-order Korteweg-de Vries (KdV) type equations. We show that the semi-discrete sch…
A robust error estimator and a residual-free error indicator for reduced basis methods
Yanlai Chen, Jiahua Jiang, Akil Narayan
The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approxim…
Offline-Enhanced Reduced Basis Method through adaptive construction of the Surrogate Parameter Domain
Jiahua Jiang, Yanlai Chen, Akil Narayan
The Reduced Basis Method (RBM) is a popular certified model reduction approach for solving parametrized partial differential equations. One critical stage of the \textit{offline} p…
A goal-oriented RBM-Accelerated generalized polynomial chaos algorithm
Jiahua Jiang, Yanlai Chen, Akil Narayan
The non-intrusive generalized Polynomial Chaos (gPC) method is a popular computational approach for solving partial differential equations (PDEs) with random inputs. The main hurdl…