Max Gunzburger
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View article: Nonlocal modeling of spatial fractional diffusion with truncated interaction domains and truncated kernel function singularity
Nonlocal modeling of spatial fractional diffusion with truncated interaction domains and truncated kernel function singularity Open
Parabolic partial differential equations (PDEs) are in ubiquitous, very effective use to model diffusion processes. However, there are many applications (e.g., such as in hydrology, animal foraging, biology, and light diffusion just do nam…
View article: Splitting Method for Stochastic Navier-Stokes Equations
Splitting Method for Stochastic Navier-Stokes Equations Open
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS com…
View article: An end-to-end deep learning method for solving nonlocal Allen–Cahn and Cahn–Hilliard phase-field models
An end-to-end deep learning method for solving nonlocal Allen–Cahn and Cahn–Hilliard phase-field models Open
View article: Multifidelity uncertainty quantification for ice sheet simulations
Multifidelity uncertainty quantification for ice sheet simulations Open
View article: AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems
AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems Open
View article: Multifidelity Uncertainty Quantification for Ice Sheet Simulations
Multifidelity Uncertainty Quantification for Ice Sheet Simulations Open
Ice sheet simulations suffer from vast parametric uncertainties, such as the basal sliding boundary condition or geothermal heat flux. Quantifying the resulting uncertainties in predictions is of utmost importance to support judicious deci…
View article: An End-to-End Deep Learning Method for Solving Nonlocal Allen-Cahn and Cahn-Hilliard Phase-Field Models
An End-to-End Deep Learning Method for Solving Nonlocal Allen-Cahn and Cahn-Hilliard Phase-Field Models Open
We propose an efficient end-to-end deep learning method for solving nonlocal Allen-Cahn (AC) and Cahn-Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential equation-ba…
View article: Multifidelity methods for uncertainty quantification of a nonlocal model for phase changes in materials
Multifidelity methods for uncertainty quantification of a nonlocal model for phase changes in materials Open
View article: Optimal control of stochastic cylinder flow using data-driven compressive sensing method
Optimal control of stochastic cylinder flow using data-driven compressive sensing method Open
A stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder is used as a prototype optimal control problem for the stochastic Navier-Stokes equations. The inlet flow and the rotation speed of the…
View article: Realistic Subglacial Hydrology For Improved Ice Sheet-Climate Coupling and Sea Level Prediction
Realistic Subglacial Hydrology For Improved Ice Sheet-Climate Coupling and Sea Level Prediction Open
View article: A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type Open
View article: Multifidelity Methods for Uncertainty Quantification of a Nonlocal Model for Phase Changes in Materials
Multifidelity Methods for Uncertainty Quantification of a Nonlocal Model for Phase Changes in Materials Open
This study is devoted to the construction of a multifidelity Monte Carlo (MFMC) method for the uncertainty quantification of a nonlocal, non-mass-conserving Cahn-Hilliard model for phase transitions with an obstacle potential. We are inter…
View article: An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps
An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps Open
Here, we introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-…
View article: A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type Open
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world eng…
View article: Canonical and noncanonical Hamiltonian operator inference through benchmark examples
Canonical and noncanonical Hamiltonian operator inference through benchmark examples Open
View article: Efficient and Scalable Time-Stepping Algorithms and Reduced-Order Modeling for Ocean System Simulations (Scientific/Technical Report)
Efficient and Scalable Time-Stepping Algorithms and Reduced-Order Modeling for Ocean System Simulations (Scientific/Technical Report) Open
This report provides a description of major accomplishments and results obtained by the University of South Carolina/Florida State University/Los Alamos National Laboratory team participating in the project "Efficient and Scalable Time-Ste…
View article: Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling
Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling Open
Uncertainties in an output of interest that depends on the solution of a complex system (e.g., of partial differential equations with random inputs) are often, if not nearly ubiquitously, determined in practice using Monte Carlo (MC) estim…
View article: A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces
A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces Open
View article: Energetically consistent model reduction for metriplectic systems
Energetically consistent model reduction for metriplectic systems Open
View article: Comment on egusphere-2022-797
Comment on egusphere-2022-797 Open
Abstract. Uncertainties in an output of interest that depends on the solution of a complex system (e.g., of partial differential equations with random inputs) are often, if not nearly ubiquitously, determined in practice u…
View article: Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report)
Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report) Open
Nonlocal models provide a much-needed predictive capability for important Sandia mission applications, ranging from fracture mechanics for nuclear components to subsurface flow for nuclear waste disposal, where traditional partial differen…
View article: Multifidelity Monte Carlo Estimation for Efficient Uncertainty Quantification in Climate-Related Modeling
Multifidelity Monte Carlo Estimation for Efficient Uncertainty Quantification in Climate-Related Modeling Open
Uncertainties in an output of interest that depends on the solution of a complex system (e.g., of partial differential equations with random inputs) are often, if not nearly ubiquitously, determined in practice using Monte Carlo (MC) estim…
View article: Convolutional neural networks for data compression and reduced-order modeling.
Convolutional neural networks for data compression and reduced-order modeling. Open
View article: A Multifidelity Monte Carlo Method for Realistic Computational Budgets
A Multifidelity Monte Carlo Method for Realistic Computational Budgets Open
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 optimization problems each with a globally minimizing close…
View article: Energetically Consistent Model Reduction for Metriplectic Systems
Energetically Consistent Model Reduction for Metriplectic Systems Open
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not pres…
View article: An asymptotically compatible coupling formulation for nonlocal interface problems with jumps
An asymptotically compatible coupling formulation for nonlocal interface problems with jumps Open
We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedn…
View article: A comparison of neural network architectures for data-driven reduced-order modeling
A comparison of neural network architectures for data-driven reduced-order modeling Open
View article: A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere
A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere Open
View article: High-order multirate explicit time-stepping schemes for the baroclinic-barotropic split dynamics in primitive equations
High-order multirate explicit time-stepping schemes for the baroclinic-barotropic split dynamics in primitive equations Open
View article: Parallel exponential time differencing methods for geophysical flow simulations
Parallel exponential time differencing methods for geophysical flow simulations Open