63 citations · 308 across the 48 of their papers we have counts for
24 papers · 1 filter
Second-order consistency for learning chaotic dynamics via randomized Jacobian matching
Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh
Short-horizon accuracy does not ensure that a learned chaotic system has correct long-time dynamics. Trajectory (zeroth-order) matching constrains vector-field values, and Jacobian…
From an Elementary Proof of Error Representation for Hermite Quadrature to a Rediscovery of Legendre Polynomials and Rodrigues Formula
Tan Bui-Thanh, Giancarlo Villatoro, C. G. Krishnanunni
We generalize two-point interpolatory Hermite quadrature to functions with available values and the first (n-1) derivatives at both end points. Armed with integration by parts in t…
A New Look at the Ensemble Kalman Filter for Inverse Problems: Duality, Non-Asymptotic Analysis and Convergence Acceleration
C G Krishnanunni, Jonathan Wittmer, Tan Bui-Thanh +1
This work presents new results and understanding of the Ensemble Kalman filter (EnKF) for inverse problems. In particular, using a Lagrangian dual perspective we show that EnKF can…
Improvements on uncertainty quantification with variational autoencoders
Andrea Tonini, Tan Bui-Thanh, Francesco Regazzoni +2
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. I…
A Divergence-Free and -Conforming Embedded-Hybridized DG Method for the Incompressible Resistive MHD equations
Jau-Uei Chen, Tamás L. Horváth, Tan Bui-Thanh
We present a divergence-free and -conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving…
An autoencoder compression approach for accelerating large-scale inverse problems
Jonathan Wittmer, Jacob Badger, Hari Sundar +1
PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately…
Unified -HDG Frameworks for Friedrichs' PDE systems
Jau-Uei Chen, Shinhoo Kang, Tan Bui-Thanh +1
This work proposes a unified -adaptivity framework for hybridized discontinuous Galerkin (HDG) method for a large class of partial differential equations (PDEs) of Friedrichs'…
On Unifying Randomized Methods For Inverse Problems
Jonathan Wittmer, C. G. Krishnanunni, Hai V. Nguyen +1
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing…
Bridging and Improving Theoretical and Computational Electric Impedance Tomography via Data Completion
Tan Bui-Thanh, Qin Li, Leonardo Zepeda-Núñez
In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to obtain accurate inferences, the collected data…
A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD
Sriramkrishnan Muralikrishnan, Stephen Shannon, Tan Bui-Thanh +1
We present a scalable block preconditioning strategy for the trace system coming from the high-order hybridized discontinuous Galerkin (HDG) discretization of incompressible resist…
A scalable exponential-DG approach for nonlinear conservation laws: with application to Burger and Euler equations
Shinhoo Kang, Tan Bui-Thanh
We propose an Exponential DG approach for numerically solving partial differential equations (PDEs). The idea is to decompose the governing PDE operators into linear (fast dynamics…
Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs
Ilona Ambartsumyan, Wajih Boukaram, Tan Bui-Thanh +5
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for…
A Multilevel Approach for Trace System in HDG Discretizations
Sriramkrishnan Muralikrishnan, Tan Bui-Thanh, John N. Shadid
We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decompos…
Unified geometric multigrid algorithm for hybridized high-order finite element methods
Tim Wildey, Sriramkrishnan Muralikrishnan, Tan Bui-Thanh
We consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite…
Scalable matrix-free adaptive product-convolution approximation for locally translation-invariant operators
Nick Alger, Vishwas Rao, Aaron Myers +2
We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operat…
An Improved Iterative HDG Approach for Partial Differential Equations
Sriramkrishnan Muralikrishnan, Minh-Binh Tran, Tan Bui-Thanh
We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM…
Analysis of an HDG Method for Linearized Incompressible Resistive MHD Equations
Jeonghun J. Lee, Stephen Shannon, Tan Bui-Thanh +1
We present a hybridized discontinuous Galerkin (HDG) method for stationary linearized incompressible magnetohydrodynamics (MHD) equations. At the heart of the paper is the introduc…
A data scalable augmented Lagrangian KKT preconditioner for large scale inverse problems
Nick Alger, Umberto Villa, Tan Bui-Thanh +1
Current state of the art preconditioners for the reduced Hessian and the Karush-Kuhn-Tucker (KKT) operator for large scale inverse problems are typically based on approximating the…
iHDG: An Iterative HDG Framework for Partial Differential Equations
Sriramkrishnan Muralikrishnan, Minh-Binh Tran, Tan Bui-Thanh
We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between d…
A Data-Scalable Randomized Misfit Approach for Solving Large-Scale PDE-Constrained Inverse Problems
Ellen B. Le, Aaron Myers, Tan Bui-Thanh +1
A randomized misfit approach is presented for the efficient solution of large-scale PDE-constrained inverse problems with high-dimensional data. The purpose of this paper is to off…
eHDG:An Exponentially Convergent Iterative Solver for HDG Discretizations of Hyperbolic Partial Differential Equations
Sriramkrishnan Muralikrishnan, Minh-Binh Tran, Tan Bui-Thanh
We present a scalable and efficient iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of hyperbolic partial differential equations. It is an i…
Accelerating MCMC with active subspaces
Paul G. Constantine, Carson Kent, Tan Bui-Thanh
The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its ite…
Discretely exact derivatives for hyperbolic PDE-constrained optimization problems discretized by the discontinuous Galerkin method
Lucas C. Wilcox, Georg Stadler, Tan Bui-Thanh +1
This paper discusses the computation of derivatives for optimization problems governed by linear hyperbolic systems of partial differential equations (PDEs) that are discretized by…
A computational framework for infinite-dimensional Bayesian inverse problems. Part I: The linearized case, with application to global seismic inversion
Tan Bui-Thanh, Omar Ghattas, James Martin +1
We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian…