4 papers
When is a System Discoverable from Data? Discovery Requires Chaos
Zakhar Shumaylov, Peter Zaika, Philipp Scholl +3
The deep learning revolution has spurred a rise in advances of using AI in sciences. Within physical sciences the main focus has been on discovery of dynamical systems from observa…
Muon is Not That Special: Random or Inverted Spectra Work Just as Well
Zakhar Shumaylov, Nathaël Da Costa, Peter Zaika +6
The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear min…
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…
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…