72 citations · 118 across the 10 of their papers we have counts for
11 papers
A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling
QiZhi He, Mauro Perego, Amanda A. Howard +2
One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise. A large part of the uncertainty of sea level p…
Hierarchical off-diagonal low-rank approximation of Hessians in inverse problems, with application to ice sheet model initializaiton
Tucker Hartland, Georg Stadler, Mauro Perego +2
Obtaining lightweight and accurate approximations of Hessian applies in inverse problems governed by partial differential equations (PDEs) is an essential task to make both determi…
Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems
William Reese, Joseph Hart, Bart van Bloemen Waanders +3
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain…
Performance portable ice-sheet modeling with MALI
Jerry Watkins, Max Carlson, Kyle Shan +6
High resolution simulations of polar ice-sheets play a crucial role in the ongoing effort to develop more accurate and reliable Earth-system models for probabilistic sea-level proj…
Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems
Amanda A. Howard, Mauro Perego, George E. Karniadakis +1
Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires…
An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions
Marta D'Elia, David Littlewood, Jeremy Trageser +2
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupli…
Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint
Eric C. Cyr, Mamikon A. Gulian, Ravi G. Patel +2
Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs.…
A conservative, consistent, and scalable meshfree mimetic method
Nathaniel Trask, Pavel Bochev, Mauro Perego
Mimetic methods discretize divergence by restricting the Gauss theorem to mesh cells. Because point clouds lack such geometric entities, construction of a compatible meshfree diver…
A Coupling Approach for Linear Elasticity Problems with Spatially Noncoincident Interfaces
Pavel Bochev, James Cheung, Max Gunzburger +1
We present a new formulation based on the classical Dirichlet-Neumann formulation for interface coupling problems in linearized elasticity. By using Taylor series expansions, we de…
Optimally accurate higher-order finite element methods on polytopial approximations of domains with smooth boundaries
James Cheung, Mauro Perego, Pavel Bochev +1
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the dom…
A high-order staggered meshless method for elliptic problems
Nathaniel Trask, Mauro Perego, Pavel Bochev
We present a new meshless method for scalar diffusion equations which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach…