7 papers
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…
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…
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…
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…
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…
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…