9 citations · 13 across the 13 of their papers we have counts for
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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…
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…
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…
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…