Zobrazeno 1 - 10
of 434
pro vyhledávání: '"65M99"'
Autor:
Xie, Zhengrong
The flux vector splitting (FVS) method has firstly been incorporated into the discontinuous Galerkin (DG) framework for reconstructing the numerical fluxes required for the spatial semi-discrete formulation, setting it apart from the conventional DG
Externí odkaz:
http://arxiv.org/abs/2411.16367
Autor:
Frame, Peter, Towne, Aaron
Most model reduction methods are space-only in that they reduce the spatial dimension of the solution but not the temporal one. These methods integrate an encoding of the state of the nonlinear dynamical system forward in time. We propose a space-tim
Externí odkaz:
http://arxiv.org/abs/2411.13531
We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face challenges in this
Externí odkaz:
http://arxiv.org/abs/2411.08750
This paper explores alternative formulations of the Kolmogorov Superposition Theorem (KST) as a foundation for neural network design. The original KST formulation, while mathematically elegant, presents practical challenges due to its limited insight
Externí odkaz:
http://arxiv.org/abs/2410.01990
We consider the subcritical nonlinear Schr\"odinger (NLS) in dimension one posed on the unbounded real line. Several previous works have considered the deep neural network approximation of NLS solutions from the numerical and theoretical point of vie
Externí odkaz:
http://arxiv.org/abs/2409.17938
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the solutions
Externí odkaz:
http://arxiv.org/abs/2409.08941
We introduce estimatable variation neural networks (EVNNs), a class of neural networks that allow a computationally cheap estimate on the $BV$ norm motivated by the space $BMV$ of functions with bounded M-variation. We prove a universal approximation
Externí odkaz:
http://arxiv.org/abs/2409.08909
We introduce a hybrid filter that incorporates a mathematically accurate moment-based filter with a data driven filter for discontinuous Galerkin approximations to PDE solutions that contain discontinuities. Numerical solutions of PDEs suffer from an
Externí odkaz:
http://arxiv.org/abs/2408.05193
We consider reflectionless wave propagation in networks modeled in terms of the nonlocal nonlinear Schr\"odinger (NNLS) equation on metric graphs, for which transparent boundary conditions are imposed at the vertices. By employing the ``potential app
Externí odkaz:
http://arxiv.org/abs/2408.03709
Autoencoders have found widespread application, in both their original deterministic form and in their variational formulation (VAEs). In scientific applications it is often of interest to consider data that are comprised of functions; the same persp
Externí odkaz:
http://arxiv.org/abs/2408.01362