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James Rowbottom

5 accepted papers

2025

G-Adaptivity: optimised graph-based mesh relocation for finite element methods

James Rowbottom, Georg Maierhofer, Teo Deveney, Eike Hermann Müller, Alberto Paganini, Katharina Schratz +3
ICML 2025spotlight

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 of mesh points. Mesh relocation (r-adaptivity) seeks to optimise the mesh geometry to obtain the best solution accuracy…

Cited by 2Source ↗PDF ↗code ↗Scholar ↗
2025

Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups

Zakhar Shumaylov, Peter Zaika, James Rowbottom, Ferdia Sherry, Melanie Weber, Carola-Bibiane Schönlieb
ICLR 2025poster

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 solvers, recent works have shown that Lie point symmetries can be a useful inductive bias for Physics-Informed Neural Networks…

Cited by 1Source ↗PDF ↗Scholar ↗
2022

Graph-Coupled Oscillator Networks

T. Konstantin Rusch, Ben Chamberlain, James Rowbottom, Siddhartha Mishra, Michael Bronstein
ICML 2022spotlight

We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear controlled and damped oscillators, coupled via the adjacency s…

Cited by 160Source ↗PDF ↗code ↗Scholar ↗
2021

Beltrami Flow and Neural Diffusion on Graphs

Benjamin Paul Chamberlain, James Rowbottom, Davide Eynard, Francesco Di Giovanni, Xiaowen Dong, Michael M. Bronstein
NeurIPS 2021poster

We propose a novel class of graph neural networks based on the discretized Beltrami flow, a non-Euclidean diffusion PDE. In our model, node features are supplemented with positional encodings derived from the graph topology and jointly evolved by the Beltrami flow, producing simultaneously contin…

Cited by 95Source ↗PDF ↗code ↗Scholar ↗
2021

GRAND: Graph Neural Diffusion

Ben Chamberlain, James Rowbottom, Maria I Gorinova, Michael Bronstein, Stefan Webb, Emanuele Rossi
ICML 2021spotlight

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and…

Cited by 352Source ↗PDF ↗code ↗Scholar ↗