1 citations · 2 across the 6 of their papers we have counts for
7 papers
Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions
James Rowbottom, Nick Huang, Carola-Bibiane Schönlieb +1
State estimation is a critical task in scientific, engineering and control applications. Since the reliability of reconstructions depends on the number and position of sensors, opt…
GRIFDIR: Graph Resolution-Invariant Diffusion Models over Irregular Domains
James Rowbottom, Elizabeth L. Baker, Nick Huang +3
Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such…
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…
Graph Neural Regularizers for PDE Inverse Problems
William Lauga, James Rowbottom, Alexander Denker +3
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward opera…
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…
Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups
Zakhar Shumaylov, Peter Zaika, James Rowbottom +3
The quest for robust and generalizable machine learning models has driven recent interest in exploiting symmetries through equivariant neural networks. In the context of PDE solver…
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…