[HTML][HTML] De Rham compatible deep neural network FEM
On general regular simplicial partitions T of bounded polytopal domains Ω⊂ R d, d∈{2, 3},
we construct exact neural network (NN) emulations of all lowest order finite element spaces …
we construct exact neural network (NN) emulations of all lowest order finite element spaces …
[PDF][PDF] De rham compatible deep neural networks
M Longo, JAA Opschoor, N Disch, CH Schwab… - dimension, 2022 - sam.math.ethz.ch
We construct several classes of neural networks with ReLU and BiSU (Binary Step Unit)
activations, which exactly emulate the lowest order Finite Element (FE) spaces on regular …
activations, which exactly emulate the lowest order Finite Element (FE) spaces on regular …
Deep ReLU Neural Network Emulation in High-Frequency Acoustic Scattering
F Henríquez, C Schwab - arXiv preprint arXiv:2405.12624, 2024 - arxiv.org
We obtain wavenumber-robust error bounds for the deep neural network (DNN) emulation of
the solution to the time-harmonic, sound-soft acoustic scattering problem in the exterior of a …
the solution to the time-harmonic, sound-soft acoustic scattering problem in the exterior of a …
First Order System Least Squares Neural Networks
We introduce a conceptual framework for numerically solving linear elliptic, parabolic, and
hyperbolic PDEs on bounded, polytopal domains in euclidean spaces by deep neural …
hyperbolic PDEs on bounded, polytopal domains in euclidean spaces by deep neural …
Numerical multiscale methods: from homogenization to milestoning
Z Chen - 2024 - repositories.lib.utexas.edu
The dissertation focuses on addressing the challenges posed by multiscale problems in
applied mathematics, which stem from the intricate interplay between microscales and the …
applied mathematics, which stem from the intricate interplay between microscales and the …