6 papers
A Plug-in Interpretation of Conditioning in Score-Based Diffusion Models
Libo Chen, Souvik Ghosh, Teo Deveney +2
We propose a conditioning mechanism for diffusion models based on multi-speed joint diffusion of the target and the condition. The mechanism learns an unconditional joint score net…
Adaptive Correction for Ensuring Conservation Laws in Neural Operators
Chaoyu Liu, Yangming Li, Zhongying Deng +2
Physical laws, such as the conversation of mass and momentum, are fundamental principles in many physical systems. Neural operators have achieved promising performance in learning…
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…
Enhancing Fourier Neural Operators with Local Spatial Features
Chaoyu Liu, Davide Murari, Lihao Liu +3
Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions…
Inverse Evolution Data Augmentation for Neural PDE Solvers
Chaoyu Liu, Chris Budd, Carola-Bibiane Schönlieb
Neural networks have emerged as promising tools for solving partial differential equations (PDEs), particularly through the application of neural operators. Training neural operato…
Equidistribution-based training of Free Knot Splines and ReLU Neural Networks
Simone Appella, Simon Arridge, Chris Budd +2
We consider the problem of univariate nonlinear function approximation using shallow neural networks (NN) with a rectified linear unit (ReLU) activation function. We show that the…