Zobrazeno 1 - 10
of 89
pro vyhledávání: '"CYR, ERIC C."'
A machine-learnable variational scheme using Gaussian radial basis functions (GRBFs) is presented and used to approximate linear problems on bounded and unbounded domains. In contrast to standard mesh-free methods, which use GRBFs to discretize stron
Externí odkaz:
http://arxiv.org/abs/2410.06219
The segmentation of ultra-high resolution images poses challenges such as loss of spatial information or computational inefficiency. In this work, a novel approach that combines encoder-decoder architectures with domain decomposition strategies to ad
Externí odkaz:
http://arxiv.org/abs/2407.21266
We develop multigrid-in-time preconditioners for Karush-Kuhn-Tucker (KKT) systems that arise in the solution of time-dependent optimization problems. We focus on a specific instance of KKT systems, known as augmented systems, which underpin the compo
Externí odkaz:
http://arxiv.org/abs/2405.04808
Sparse matrix computations are ubiquitous in scientific computing. With the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NN). Unfortunately, multi-layer perceptron (
Externí odkaz:
http://arxiv.org/abs/2310.14084
Autor:
Cyr, Eric C.
Solving optimization problems with transient PDE-constraints is computationally costly due to the number of nonlinear iterations and the cost of solving large-scale KKT matrices. These matrices scale with the size of the spatial discretization times
Externí odkaz:
http://arxiv.org/abs/2305.04421
Autor:
Glines, Forrest W., Beckwith, Kristian R. C., Braun, Joshua R., Cyr, Eric C., Ober, Curtis C., Bettencourt, Matthew, Cartwright, Keith L., Conde, Sidafa, Miller, Sean T., Roberds, Nicholas, Roberts, Nathan V., Swan, Matthew S., Pawlowski, Roger
In this work, we present a discontinuous-Galerkin method for evolving relativistic hydrodynamics. We include an exploration of analytical and iterative methods to recover the primitive variables from the conserved variables for the ideal equation of
Externí odkaz:
http://arxiv.org/abs/2205.00095
Autor:
Moon, Gordon Euhyun, Cyr, Eric C.
Parallelizing Gated Recurrent Unit (GRU) networks is a challenging task, as the training procedure of GRU is inherently sequential. Prior efforts to parallelize GRU have largely focused on conventional parallelization strategies such as data-parallel
Externí odkaz:
http://arxiv.org/abs/2203.04738
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear problems, proj
Externí odkaz:
http://arxiv.org/abs/2110.10775
Autor:
Ohm, Peter, Wiesner, Tobias, Cyr, Eric C., Hu, Jonathan J., Shadid, John N., Tuminaro, Raymond S.
A multigrid framework is described for multiphysics applications. The framework allows one to construct, adapt, and tailor a monolithic multigrid methodology to different linear systems coming from discretized partial differential equations. The main
Externí odkaz:
http://arxiv.org/abs/2103.07537
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity and monomials. Motivated by this, we propose partition of unity networ
Externí odkaz:
http://arxiv.org/abs/2101.11256