82 citations · 181 across the 28 of their papers we have counts for
28 papers
A Multifidelity Monte Carlo Method for Realistic Computational Budgets
Anthony Gruber, Max Gunzburger, Lili Ju +1
A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of…
Energetically Consistent Model Reduction for Metriplectic Systems
Anthony Gruber, Max Gunzburger, Lili Ju +1
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimin…
A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations
Yanlai Chen, Lijie Ji, Zhu Wang
The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method…
Nonlinear Reduced DNN Models for State Estimation
Wolfgang Dahmen, Min Wang, Zhu Wang
We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, repre…
A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling
Anthony Gruber, Max Gunzburger, Lili Ju +1
The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite t…
Verifiability of the Data-Driven Variational Multiscale Reduced Order Model
Birgul Koc, Changhong Mou, Honghu Liu +3
In this paper, we focus on the mathematical foundations of reduced order model (ROM) closures. First, we extend the verifiability concept from large eddy simulation to the ROM sett…
Bilinear Control of Convection-Cooling: From Open-Loop to Closed-Loop
Weiwei Hu, Jun Liu, Zhu Wang
This paper is concerned with a bilinear control problem for enhancing convection-cooling via an incompressible velocity field. Both optimal open-loop control and closed-loop feedba…
Parallel Exponential Time Differencing Methods for Geophysical Flow Simulations
Rihui Lan, Wei Leng, Zhu Wang +2
Two ocean models are considered for geophysical flow simulations: the multi-layer shallow water equations and the multi-layer primitive equations. For the former, we investigate th…
High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations
Rihui Lan, Lili Ju, Zhu Wang +2
In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive eq…
An efficient iterative method for solving parameter-dependent and random convention-diffusion problems
Xiaobing Feng, Yan Luo, Liet Vo +1
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of…
Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver
Yuankai Teng, Xiaoping Zhang, Zhu Wang +1
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image p…
Nonlinear Level Set Learning for Function Approximation on Sparse Data with Applications to Parametric Differential Equations
Anthony Gruber, Max Gunzburger, Lili Ju +2
A dimension reduction method based on the "Nonlinear Level set Learning" (NLL) approach is presented for the pointwise prediction of functions which have been sparsely sampled. Lev…
A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations
Lihong Feng, Guosheng Fu, Zhu Wang
The basis generation in reduced order modeling usually requires multiple high-fidelity large-scale simulations that could take a huge computational cost. In order to accelerate the…
Structure-Preserving Galerkin POD-DEIM Reduced-Order Modeling of Hamiltonian Systems
Zhu Wang
A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditiona…
A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems from evolutionary PDEs
Jun Liu, Zhu Wang
In this paper we propose to use model reduction techniques for speeding up the diagonalization-based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once…
Reduced Order Models for the Quasi-Geostrophic Equations: A Brief Survey
Changhong Mou, Zhu Wang, David R. Wells +2
Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, f…
POD-(H)DG Method for Incompressible Flow Simulations
Guosheng Fu, Zhu Wang
We present a reduced order method (ROM) based on proper orthogonal decomposition (POD) for the viscous Burgers' equation and the incompressible Navier-Stokes equations discretized…
High Order Explicit Local Time-Stepping Methods For Hyperbolic Conservation Laws
Thi-Thao-Phuong Hoang, Lili Ju, Wei Leng +1
In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we…
Overlapping Localized Exponential Time Differencing Methods for Diffusion Problems
Thi-Thao-Phuong Hoang, Lili Ju, Zhu Wang
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences.…
An ensemble algorithm for numerical solutions to deterministic and random parabolic PDEs
Yan Luo, Zhu Wang
In this paper, we develop an ensemble-based time-stepping algorithm to efficiently find numerical solutions to a group of linear, second-order parabolic partial differential equati…
Non-commutative Discretize-then-Optimize Algorithms for Elliptic PDE-Constrained Optimal Control Problems
Jun Liu, Zhu Wang
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for sol…
Numerical Analysis of the Leray Reduced Order Model
Xuping Xie, David Wells, Zhu Wang +1
Standard ROMs generally yield spurious numerical oscillations in the simulation of convection-dominated flows. Regularized ROMs use explicit ROM spatial filtering to decrease these…
Efficient Time Domain Decomposition Algorithms for Parabolic PDE-Constrained Optimization Problems
Jun Liu, Zhu Wang
Optimization with time-dependent partial differential equations (PDEs) as constraints {appears} in many science and engineering applications. The associated first-order necessary o…
POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification
Hongfei Fu, Hong Wang, Zhu Wang
In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-…