7 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…
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 FEM Diffusion Models in Function Spaces 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…
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…
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…
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…