9 citations · 13 across the 13 of their papers we have counts for
15 papers
Stable neural networks and connections to continuous dynamical systems
Matthias J. Ehrhardt, Davide Murari, Ferdia Sherry
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhanci…
Enhanced Denoising and Convergent Regularisation Using Tweedie Scaling
Naïl Khelifa, Ferdia Sherry, Carola-Bibiane Schönlieb
The inherent ill-posed nature of image reconstruction problems, due to limitations in the physical acquisition process, is typically addressed by introducing a regularisation term…
Generalized Lie Symmetries in Physics-Informed Neural Operators
Amy Xiang Wang, Zakhar Shumaylov, Peter Zaika +2
Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated…
Benchmarking learned algorithms for computed tomography image reconstruction tasks
Maximilian B. Kiss, Ander Biguri, Zakhar Shumaylov +4
Computed tomography (CT) is a widely used non-invasive diagnostic method in various fields, and recent advances in deep learning have led to significant progress in CT image recons…
Symplectic Neural Flows for Modeling and Discovery
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulation…
Hamiltonian Matching for Symplectic Neural Integrators
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical…
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…
Resilient Graph Neural Networks: A Coupled Dynamical Systems Approach
Moshe Eliasof, Davide Murari, Ferdia Sherry +1
Graph Neural Networks (GNNs) have established themselves as a key component in addressing diverse graph-based tasks. Despite their notable successes, GNNs remain susceptible to inp…
Convergent regularization in inverse problems and linear plug-and-play denoisers
Andreas Hauptmann, Subhadip Mukherjee, Carola-Bibiane Schönlieb +1
Plug-and-play (PnP) denoising is a popular iterative framework for solving imaging inverse problems using off-the-shelf image denoisers. Their empirical success has motivated a lin…
Designing Stable Neural Networks using Convex Analysis and ODEs
Ferdia Sherry, Elena Celledoni, Matthias J. Ehrhardt +3
Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lip…
Dynamical systems' based neural networks
Elena Celledoni, Davide Murari, Brynjulf Owren +2
Neural networks have gained much interest because of their effectiveness in many applications. However, their mathematical properties are generally not well understood. If there is…
Imaging with Equivariant Deep Learning
Dongdong Chen, Mike Davies, Matthias J. Ehrhardt +3
From early image processing to modern computational imaging, successful models and algorithms have relied on a fundamental property of natural signals: symmetry. Here symmetry refe…
Equivariant neural networks for inverse problems
Elena Celledoni, Matthias J. Ehrhardt, Christian Etmann +3
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of…
Structure preserving deep learning
Elena Celledoni, Matthias J. Ehrhardt, Christian Etmann +4
Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing…
Learning the Sampling Pattern for MRI
Ferdia Sherry, Martin Benning, Juan Carlos De los Reyes +5
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly int…