4 papers
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…
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…