4 papers
HypeR Adaptivity: Joint -Adaptive Meshing via Hypergraph Multi-Agent Deep Reinforcement Learning
Niccolò Grillo, James Rowbottom, Pietro Liò +2
Adaptive mesh refinement is central to the efficient solution of partial differential equations (PDEs) via the finite element method (FEM). Classical -adaptivity optimizes verte…
Multi-Level Monte Carlo Training of Neural Operators
James Rowbottom, Stefania Fresca, Pietro Lio +2
Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on dis…
Deep Spectral Prior
Yanqi Cheng, Xuxiang Zhao, Tieyong Zeng +3
We introduce the Deep Spectral Prior (DSP), a new framework for unsupervised image reconstruction that operates entirely in the complex frequency domain. Unlike the Deep Image Prio…
G-Adaptivity: optimised graph-based mesh relocation for finite element methods
James Rowbottom, Georg Maierhofer, Teo Deveney +6
We present a novel, and effective, approach to achieve optimal mesh relocation in finite element methods (FEMs). The cost and accuracy of FEMs is critically dependent on the choice…