25 citations · 30 across the 4 of their papers we have counts for
4 papers
A Unified Framework for U-Net Design and Analysis
Christopher Williams, Fabian Falck, George Deligiannidis +3
U-Nets are a go-to, state-of-the-art neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however t…
A Multi-Resolution Framework for U-Nets with Applications to Hierarchical VAEs
Fabian Falck, Christopher Williams, Dominic Danks +5
U-Net architectures are ubiquitous in state-of-the-art deep learning, however their regularisation properties and relationship to wavelets are understudied. In this paper, we formu…
Accurate simulations of nonlinear dynamic shear ruptures on pre-existing faults in 3D elastic solids with dual-pairing SBP methods
Kenneth Duru, Christopher Williams, Frederick Fung
In this paper we derive and analyse efficient and stable numerical methods for accurate numerical simulations of nonlinear dynamic shear ruptures on non-planar faults embedded in 3…
Provably Stable Full-Spectrum Dispersion Relation Preserving Schemes
Christopher Williams, Kenneth Duru
The dispersion error is often the dominant error for computed solutions of wave propagation problems with high-frequency components. In this paper, we define and give explicit exam…